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a cube is painted such that one pair of surfaces is painted brown and the other pair of surfaces is painted orange . the cube is cut in to 64 small cubes of equal size . find how many cubes have both the color brown and orange ? | [
"10']",
"12'",
"11'",
"16'"
] | D | there are 6 surfaces to the cube . in which opposite surfaces are painted brown and other 2 opposite surfaces are painted orange . then 4 edges of the cube have both the colors . since the big cube cut in to 64 smaller cubes , the 4 edges of the cube have both the colors . since the big cube cut into 64 smaller cubes , the 4 edges of the big cube has 4 × 4 = 16 smaller cubes have both brown and orange colors . answer = 16 answer : b | 5 |
The change in fur color of the Arctic hare from brown in the summer to white in the winter is an example of | [
"mimicry.",
"heredity.",
"diversity.",
"camouflage."
] | D | 1 |
|
What parts of comets make them easy to see? | [
"craters and tails",
"arcs and tails",
"comas and tails",
"novas and tails"
] | C | Gases in the coma and tail of a comet reflect light from the Sun. Comets are very hard to see except when they have comas and tails. That is why they appear only when they are near the Sun. They disappear again as they move back to the outer solar system. | 7 |
Hans reserved a table at a fine dining restaurant for twelve people. He has to pay a deposit for the reservation, and the deposit is a flat $20 plus an extra $3 per adult but only $1 per child. Two of the people in Hans’s party are his kid cousins, and the rest are adults. How many dollars does Hans have to pay as a deposit for the restaurant reservation? | [
"12.0",
"52.0",
"22.0",
"20.0"
] | B | Hans’s party includes 12 - 2 = <<12-2=10>>10 adults and 2 children.
The adults will cost 3 * 10 = $<<3*10=30>>30 for the deposit.
The children will cost 2 * 1 = $<<2*1=2>>2 for the deposit.
Thus, Hans has to pay 30 + 2 + 20 = $<<30+2+20=52>>52 as a deposit for the restaurant reservation.
#### 52 | 3 |
Which is competition? | [
"a giraffe eats the highest leaves",
"a bear takes a salmon from the stream",
"a shark eats a tuna that an orca was hunting",
"a slug eats a blade of grass"
] | C | if an animal takes a resource from another animal then that animal competes for resources successfully | 6 |
Lisa walks 10 meters each minute. Every day, she walks for an hour. How many meters will Lisa walk in two days? | [
"10.0",
"12.0",
"5.0",
"1200.0"
] | D | Since there are 60 minutes in 1 hour, then Lisa walks for 1 x 60 = <<60=60>>60 minutes every day.
For 60 minutes, Lisa walks 60 x 10 = <<60*10=600>>600 meters.
Thus, she walks for 600 x 2 = <<600*2=1200>>1200 meters in two days.
#### 1200 | 3 |
A company is hosting a seminar. So far, 30 attendees from company A have been registered; company B has twice the number of attendees of company A; company C has 10 more attendees than company A; company D has 5 fewer attendees than company C. If a total of 185 attendees have registered, how many attendees who registered are not from either company A, B, C or D? | [
"85.0",
"50.0",
"20.0",
"100.0"
] | C | There are 30 x 2 = <<30*2=60>>60 attendees from company B.
Company C has 30 + 10 = <<30+10=40>>40 attendees.
Company D has 40 - 5 = <<40-5=35>>35 registered attendees.
So, the total attendees from company A, B, C, and D is 30 + 60 + 40 + 35 = <<30+60+40+35=165>>165.
Therefore there are 185 - 165 = <<185-165=20>>20 attendees that are not from companies A, B, C, or D.
#### 20 | 3 |
Vinegar is a solution of which acid? | [
"crystalline",
"acetic",
"magnesium",
"boric"
] | B | Figure 14.11 Vinegar is a solution of acetic acid, a weak acid. (credit: modification of work by “HomeSpot HQ”/Flickr). | 7 |
a bag contains 6 black and 8 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ? | [
"4 / 3",
"1 / 8",
"3 / 4",
"4 / 7"
] | D | "let number of balls = ( 6 + 8 ) = 14 . number of white balls = 8 . p ( drawing a white ball ) = 8 / 14 = 4 / 7 . option b ." | 5 |
Cooper is building a brick fence around all four sides of his property. Each of the four walls of his fence is 20 bricks long, 5 bricks high, and 2 bricks deep. How many bricks does Cooper need to complete his fence? | [
"12200.0",
"100.0",
"800.0",
"25.0"
] | C | A single layer of each wall requires 5 rows * 20 bricks per row = <<5*20=100>>100 bricks.
As each wall has a thickness of 2 bricks, he will need 100 bricks * 2 = <<100*2=200>>200 bricks per wall.
If the complete fence contains four walls, he will require a total of 200*4=<<200*4=800>>800 bricks.
#### 800 | 3 |
What do the ears have to be protected from in order to avoid hearing loss? | [
"Storms",
"Cold weather",
"loud sounds",
"Water"
] | C | Hearing loss caused by loud sounds is permanent. However, this type of hearing loss can be prevented by protecting the ears from loud sounds. | 7 |
The dog toys Samantha buys for her dog are "buy one get one half off" and all cost $12.00 each. She buys 4 toys. How much does she spend on dog toys? | [
"18.0",
"40.0",
"36.0",
"56.0"
] | C | If she buys 1 toy at $12.00 she gets the 2nd toy 1/2 off, the 2nd toy is 12*.5 = $<<12*.5=6.00>>6.00
1 full-priced toy is $12.00 and 1/2 priced toy is $6.00 so these 2 toys come to 12+6 = $<<12+6=18.00>>18.00
She buys 2 more toys that are "buy one get one 1/2 off" so all total she spends 2*18 = $<<2*18=36.00>>36.00
#### 36 | 3 |
Let $h(4x-1) = 2x + 7$. For what value of $x$ is $h(x) = x$? | [
"x=3.5",
"4",
"3",
"15"
] | D | First, we find an expression for $h(x)$. From our definition of $h$, we have $h(4y-1) = 2y+7$. So, if we let $x=4y-1$, so that $y = (x+1)/4$, we have \[h(x) = 2\cdot\frac{x+1}{4} + 7 = \frac{x+1}{2} + 7.\] Setting this equal to $x$ gives \[x =\frac{x+1}{2} + 7.\] Multiplying both sides by 2 gives $2x = x+1 + 14$, so $x = \boxed{15}$. | 4 |
for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 90 units raises the average to 54 units per day , what is the value of n ? | [
"30",
"9",
"10",
"18"
] | B | "( average production for n days ) * n = ( total production for n days ) - - > 50 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 50 n + 90 = 54 * ( n + 1 ) - - > n = 9 . or as 40 extra units increased the average for n + 1 days by 4 units per day then 40 / ( n + 1 ) = 4 - - > n = 9 . answer d ." | 5 |
by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 25 % ? | [
"rs . 487",
"rs . 480",
"rs . 488",
"rs . 482"
] | B | "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 25 % = 25 % of 640 = rs . 160 sp = cp - loss = 640 - 160 = rs . 480 answer : b" | 5 |
What membrane is populated by two types of photosystems that cooperate in the light reactions of photosynthesis? | [
"subcutaneous",
"choroid",
"thylakoid",
"chloroplasts"
] | C | 7 |
|
$ABCD$, a rectangle with $AB = 12$ and $BC = 16$, is the base of pyramid $P$, which has a height of $24$. A plane parallel to $ABCD$ is passed through $P$, dividing $P$ into a frustum $F$ and a smaller pyramid $P'$. Let $X$ denote the center of the circumsphere of $F$, and let $T$ denote the apex of $P$. If the volume of $P$ is eight times that of $P'$, then the value of $XT$ can be expressed as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Compute the value of $m + n$.
| [
"335",
"nd 1$\n\\",
"$.\\",
"177"
] | D | As we are dealing with volumes, the ratio of the volume of $P'$ to $P$ is the cube of the ratio of the height of $P'$ to $P$.
Thus, the height of $P$ is $\sqrt [3]{8} = 2$ times the height of $P'$, and thus the height of each is $12$.
Thus, the top of the frustum is a rectangle $A'B'C'D'$ with $A'B' = 6$ and $B'C' = 8$.
Now, consider the plane that contains diagonal $AC$ as well as the altitude of $P$. Taking the cross section of the frustum along this plane gives the trapezoid $ACC'A'$, inscribed in an equatorial circular section of the sphere. It suffices to consider this circle.
First, we want the length of $AC$. This is given by the Pythagorean Theorem over triangle $ABC$ to be $20$. Thus, $A'C' = 10$. Since the height of this trapezoid is $12$, and $AC$ extends a distance of $5$ on either direction of $A'C'$, we can use a 5-12-13 triangle to determine that $AA' = CC' = 13$.
Now, we wish to find a point equidistant from $A$, $A'$, and $C$. By symmetry, this point, namely $X$, must lie on the perpendicular bisector of $AC$. Let $X$ be $h$ units from $A'C'$ in $ACC'A'$. By the Pythagorean Theorem twice,\begin{align*} 5^2 + h^2 & = r^2 \\ 10^2 + (12 - h)^2 & = r^2 \end{align*}Subtracting gives $75 + 144 - 24h = 0 \Longrightarrow h = \frac {73}{8}$. Thus $XT = h + 12 = \frac {169}{8}$ and $m + n = \boxed{177}$. | 4 |
What is $\frac{3}{4}$ divided by $\frac{7}{8}$? | [
"\\frac{3}{4}",
"\\frac{6}{7}",
"\\frac{24}{49}",
" \\frac{3}{7}"
] | B | Recall that division is the same as multiplication by a reciprocal. In other words, if $b$ is nonzero, then $a \div b = a\cdot \frac{1}{b}$. In this case, \[
\frac{3}{4}\div \frac{7}{8} = \frac{3}{4}\cdot \frac{8}{7} = \frac{3\cdot 8}{4\cdot 7}=\frac{8}{4} \cdot \frac{3}{7} = 2 \cdot \frac{3}{7} = \boxed{\frac{6}{7}}.
\] | 4 |
the sum of the first 40 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ? | [
"10",
"7",
"19",
"6"
] | D | "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 40 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 40 positive even integers = 2550 sum of 1 st 100 odd numbers = 5050 - 2550 = 2500 so 101 + 103 + . . . . . . . 199 = 40 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 4000 + 2500 = 6500 a is the answer ." | 5 |
What organ is made up of over one million nephrons that dot the renal cortex? | [
"kidney",
"lungs",
"stomach",
"gall bladder"
] | A | Which of the following statements about the kidney is false? a. The renal pelvis drains into the ureter. The renal pyramids are in the medulla. The cortex covers the capsule. Nephrons are in the renal cortex. Because the kidney filters blood, its network of blood vessels is an important component of its structure and function. The arteries, veins, and nerves that supply the kidney enter and exit at the renal hilum. Renal blood supply starts with the branching of the aorta into the renal arteries (which are each named based on the region of the kidney they pass through) and ends with the exiting of the renal veins to join the inferior vena cava. The renal arteries split into several segmental arteries upon entering the kidneys. Each segmental artery splits further into several interlobar arteries and enters the renal columns, which supply the renal lobes. The interlobar arteries split at the junction of the renal cortex and medulla to form the arcuate arteries. The arcuate “bow shaped” arteries form arcs along the base of the medullary pyramids. Cortical radiate arteries, as the name suggests, radiate out from the arcuate arteries. The cortical radiate arteries branch into numerous afferent arterioles, and then enter the capillaries supplying the nephrons. Veins trace the path of the arteries and have similar names, except there are no segmental veins. As mentioned previously, the functional unit of the kidney is the nephron, illustrated in Figure 41.6. Each kidney is made up of over one million nephrons that dot the renal cortex, giving it a granular appearance when sectioned sagittally. There are two types of nephrons— cortical nephrons (85 percent), which are deep in the renal cortex, and juxtamedullary nephrons (15 percent), which lie in the renal cortex close to the renal medulla. A nephron consists of three parts—a renal corpuscle, a renal tubule, and the associated capillary network, which originates from the cortical radiate arteries. | 7 |
Asthma, pneumonia, and emphysema are diseases of what system? | [
"respiratory",
"pulmonary",
"reproductive",
"digestive"
] | A | Diseases of the respiratory system include asthma, pneumonia, and emphysema. | 7 |
the age of father 10 years ago was thirce the age of his son . 10 years hence , father ’ s age will be twice that of his son . the ration of their present ages is : | [
"13 : 4",
"7 : 3",
"5 : 2",
"9 : 2"
] | B | solution let the ages of father and son 10 year ago be 3 x and x years respectively . then , ( 3 x + 10 ) + 10 = 2 [ ( x + 10 ) + 10 ⇔ 3 x + 20 = 2 x + 40 ⇔ x = 20 . ∴ required ratio = ( 3 x + 10 ) : ( x + 10 ) = 70 : 30 : 7 : 3 . answer b | 5 |
if ( x + 3 ) ^ 2 / ( 3 x + 65 ) = 2 , then the difference between the two possible values of x is : | [
"24",
"18",
"20",
"22"
] | D | "( x + 3 ) ^ 2 / ( 3 x + 65 ) = 2 ( x + 3 ) ^ 2 = 2 ( 3 x + 65 ) x ^ 2 + 6 x + 9 = 6 x + 130 x ^ 2 - 121 = 0 ( x - 11 ) ( x + 11 ) = 0 x = 11 or x = - 11 the answer is d ." | 5 |
the ratio of the ages of mini and minakshi is 4 : 3 . the sum of their ages is 14 years . the ratio of their ages after 8 years will be | [
"5 : 3",
"8 : 11",
"8 : 7",
"6 : 5"
] | C | "let mini ’ s age = 4 x and minakshi ’ s age = 3 x then 4 x + 3 x = 14 x = 2 mini ’ s age = 8 years and minakshi ’ s age = 6 years ratio of their ages after 8 years = ( 8 + 8 ) : ( 6 + 8 ) = 16 : 14 = 8 : 7 answer : c" | 5 |
praveen starts business with rs . 3360 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ? | [
"s . 9000",
"s . 6000",
"s . 8500",
"s . 8640"
] | D | let hari ’ s capital be rs . x . then , 3360 * 12 / 7 x = 2 / 3 = > 14 x = 120960 = > x = 8640 . answer : b | 5 |
Cally and Danny washed their clothes. Cally has 10 white shirts, 5 colored shirts, 7 pairs of shorts, and 6 pairs of pants, while Danny has 6 white shirts, 8 colored shirts, 10 shorts, and 6 pairs of pants. How many clothes did they wash? | [
"38.0",
"29.0",
"30.0",
"58.0"
] | D | They washed 10 + 6 = <<10+6=16>>16 white shirts.
They washede 5 + 8 = <<5+8=13>>13 colored shirts.
They washed 7 + 10 = <<7+10=17>>17 shorts.
They washed 6 + 6 = <<6+6=12>>12 pants.
Therefore, Cally and Danny washed a total of 16 + 13 + 17 + 12 = <<16+13+17+12=58>>58 clothes.
#### 58 | 3 |
How do most plants create food? | [
"electrolysis",
"photosynthesis",
"atherosclerosis",
"glycolysis"
] | B | Plants are multicellular eukaryotes. They have organelles called chloroplasts and cell walls made of cellulose. Plants also have specialized reproductive organs. Almost all plants make food by photosynthesis. Life as we know it would not be possible without plants. | 7 |
During April, the baker sold 453 cakes at $12 and 126 pies at $7. How much did the baker earn? | [
"10875.0",
"6318.0",
"5686.0",
"1566.36"
] | B | The baker sold cakes for 453 * 12 = $<<453*12=5436>>5436.
And pies for 126 * 7 = $<<126*7=882>>882.
In total the baker earned 5436 + 882 = $<<5436+882=6318>>6318.
#### 6318 | 3 |
a man invests some money partly in 4 % stock at 48 and partly in 10 % stock at 110 . to obtain equal dividends from both , he must invest the money in the ratio : | [
"3 : 4",
"none",
"6 : 5",
"4 : 5"
] | C | "solution for an income of rs . 1 in 9 % stock at 96 , investment = rs . ( 48 / 4 ) = rs . 12 . for an income of rs . 1 in 12 % stock at 120 , investment = rs . ( 110 / 10 ) = rs . 10 . ∴ ratio of investments = 12 : 10 = 6 : 5 answer d" | 5 |
find out the square of a number which when doubled exceeds its one nineth by 17 ? | [
"17",
"26",
"16",
"81"
] | D | "let the number be p , then the square will be p ^ 2 according to question : 2 p = ( p / 9 ) + 17 = > 18 p = p + 153 = > p = 9 p ^ 2 = 9 ^ 2 = 81 answer : c" | 5 |
1,000 ^ 2 + 1,001 ^ 2 = | [
"6",
"6",
"6",
"6"
] | D | "interesting problem . i think key is to notice that all the given answer choices differs in last two digits . therefore , our entire focus should be to figure out how the given terms contribute to last two digits of total . 1000 ^ 2 - > 00 1001 ^ 1 - > 01 total - > * 1 answer b ." | 5 |
What is the smallest positive integer that can be written in the form $2002m + 44444n$, where $m$ and $n$ are integers? | [
"",
"8047684",
"89999",
"2"
] | D | Notice that the question is essentially asking us for the greatest common divisor of $2002$ and $44444$: any number that can be written in the given form must be divisible by the greatest common divisor of $2002$ and $44444$. Conversely, we can find the values of $m$ and $n$ through repeated applications of the Euclidean algorithm. In particular, \begin{align*}
&\text{gcd}\,(2002, 44444) \\
&\qquad= \text{gcd}\,(2002, 44444 - 22 \cdot 2002)\\&\qquad = \text{gcd}\,(2002, 400) \\
&\qquad= \text{gcd}\,(2002 - 5 \cdot (44444 - 22 \cdot 2002), 400) \\&\qquad= \text{gcd}\,(2, 400) \\
&\qquad= \boxed{2}.
\end{align*}Notice that \begin{align*}
&2002 - 5 \cdot (44444 - 22 \cdot 2002)\\ &\qquad= 2002 - 5 \cdot 44444 + 110 \cdot 2002 \\ &\qquad= (111) \cdot 2002 + (-5) \cdot 44444 \\ &\qquad= 2,\end{align*}as desired. | 4 |
find the simple interest on rs . 450 for 8 months at 5 paisa per month ? | [
"266",
"121",
"180",
"277"
] | C | "i = ( 450 * 8 * 5 ) / 100 = 180 answer : c" | 5 |
a bag of potatoes weighs 16 kg divided by a quarter of its weight . how much does the bag weigh ? | [
"8 kg",
"3 kg",
"4 kg",
"7 kg"
] | A | b 8 kg 8 kg : 16 / 2 | 5 |
two numbers are in the ratio of 5 : 7 . if 20 is subtracted from each number , they are in the ratio of 5 : 9 . what are the two numbers ? | [
"45",
"35",
"50",
"40"
] | D | "( 5 x - 20 ) : ( 7 x - 20 ) = 5 y : 9 y 5 x - 20 = 5 y 7 x - 20 = 9 y 140 - 100 = 45 y - 35 y 40 = 10 y y = 4 5 x - 20 = 20 x = 8 the two numbers are 5 x and 7 x which are 40 and 56 . the answer is b ." | 5 |
a work which could be finished in 10 days was finished 3 days earlier after 10 more men joined . the number of men employed was ? | [
"20",
"71",
"11",
"15"
] | D | "x - - - - - - - 10 ( x + 10 ) - - - - 6 x * 10 = ( x + 10 ) 6 x = 15 \ answer : a" | 5 |
Toby has two rectangles of cloth. The first is 4 inches wide and 5 inches tall. The second is 3 inches wide and 6 inches tall. How many more square inches is the area of the first compared to the second? | [
"100.0",
"4.0",
"12.0",
"2.0"
] | D | The first has an area of 20 square inches because (4 x 5) = <<4*5=20>>20.
The second has an area of 18 square inches because (3 x 6) = <<(3*6)=18>>18.
The difference in area is 20-18=<<20-18=2>>2 square inches.
#### 2 | 3 |
Mrs. Lim milks her cows twice a day. Yesterday morning, she got 68 gallons of milk and in the evening, she got 82 gallons. This morning, she got 18 gallons fewer than she had yesterday morning. After selling some gallons of milk in the afternoon, Mrs. Lim has only 24 gallons left. How much was her revenue for the milk if each gallon costs $3.50? | [
"84.0",
"616.0",
"16.0",
"584.0"
] | B | Mrs. Lim got 68 gallons - 18 gallons = <<68-18=50>>50 gallons this morning.
So she was able to get a total of 68 gallons + 82 gallons + 50 gallons = <<68+82+50=200>>200 gallons.
She was able to sell 200 gallons - 24 gallons = <<200-24=176>>176 gallons.
Thus, her total revenue for the milk is $3.50/gallon x 176 gallons = $<<3.50*176=616>>616.
#### 616 | 3 |
what is the remainder when 43 ^ 89 is divided by 5 ? | [
"3",
"4",
"0",
"2"
] | A | "the units digit of the exponents of 3 cycle in a group of 4 : { 3 , 9 , 7 , 1 } 89 has the form 4 k + 1 so the units digit of 43 ^ 89 is 3 . the remainder when dividing by 5 is 3 . the answer is d ." | 5 |
if $ 5,000 is invested in an account that earns 10 % interest compounded semi - annually , then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8 % simple yearly interest ? | [
"$ 16",
"$ 8",
"$ 4",
"$ 10"
] | D | solution amount ( ci ) = p + ( 1 + r / n ) ^ nt = 5000 + ( 1 + 0.10 / 2 ) ^ 2 = 5410 amount ( si ) = p + ptr / 100 = 5000 + ( 5000 * 1 * 10 / 100 ) = 5400 difference = 5410 - 5400 = 10 $ e | 5 |
A complete fossil has been found of a type of bird that cannot be identified. What can most likely be determined about the bird from the fossil? | [
"The bird lived for a very short time.",
"The bird lived in a dry environment.",
"The bird existed at one time but is now extinct.",
"The bird was not well preserved during the process of fossilization."
] | C | 1 |
|
rani bought more apples than oranges . she sells apples at ₹ 23 apiece and makes 15 % profit . she sells oranges at ₹ 10 apiece and makes 25 % profit . if she gets ₹ 653 after selling all the apples and oranges , find her profit percentage c . | [
"19.1 %",
"18.5 %",
"16.8 %",
"17.4 %"
] | D | "given : selling price of an apple = 23 - - > cost price = 23 / 1.15 = 20 selling price of an orange = 10 - - > cost price = 10 / 1.25 = 8 a > o 23 * ( a ) + 10 * ( o ) = 653 653 - 23 * ( a ) has to be divisible by 10 - - > units digit has to be 0 values of a can be 1 , 11 , 21 , 31 , . . . . - - > 1 can not be the value between 11 and 21 , if a = 11 , o = 30 - - > not possible if a = 21 , o = 17 - - > possible cost price = 20 * 21 + 8 * 17 = 420 + 136 = 556 profit = 653 - 556 = 97 profit % c = ( 97 / 556 ) * 100 = 17.4 % answer : b" | 5 |
for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.6 ? | [
"15.8 .",
"16.2 .",
"12.6 .",
"14.4 ."
] | A | [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.6 = 6 * 0 + 2 * 7.2 + 8 - 6.6 = 0 + 14.4 + 1.4 15.8 answer c | 5 |
An acquired characteristic is | [
"a jagged raised welt you've had since you fell down the stairs 6 years ago",
"freckles from your mom's genes",
"brown, curly hair that resembles your sister's",
"a large nose just like your dad's"
] | A | a scar is an acquired characteristic | 6 |
What is the disease where some alveoli of the lungs fill with fluid? | [
"leukemia",
"pneumonia",
"lyme disease",
"lung cancer"
] | B | Pneumonia is a disease in which some of the alveoli of the lungs fill with fluid so gas exchange cannot occur. Symptoms usually include coughing, chest pain, and difficulty breathing. Pneumonia may be caused by an infection or injury of the lungs. | 7 |
what is the sum of all remainders obtained when the first 110 natural numbers are divided by 9 ? | [
"403",
"405",
"397",
"399"
] | A | "a positive integer can give only the following 9 remainders when divided by 9 : 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 0 . 1 divided by 9 gives the remainder of 1 ; 2 divided by 9 gives the remainder of 2 ; . . . 8 divided by 9 gives the remainder of 8 ; 9 divided by 9 gives the remainder of 0 . we ' ll have 11 such blocks , since 99 / 9 = 11 . the last will be : 91 divided by 9 gives the remainder of 1 ; 92 divided by 9 gives the remainder of 2 ; . . . 98 divided by 9 gives the remainder of 8 ; 99 divided by 9 gives the remainder of 0 . the last number , 100 , gives the remainder of 1 when divided by 9 , thus the sum of all remainders will be : 11 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 0 ) + 1 = 403 . answer : c ." | 5 |
a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 30 % ? | [
"772",
"650",
"882",
"652"
] | B | "cost price = rs . 500 profit = 30 % of 500 = rs . 150 selling price = cost price + profit = 500 + 150 = 650 answer : a" | 5 |
in how many seconds will a train 150 meters long pass an oak tree , if the speed of the train is 54 km / hr ? | [
"10",
"8",
"14",
"6"
] | A | "speed = 54 * 5 / 18 = 15 m / s time = 150 / 15 = 10 seconds the answer is c ." | 5 |
a certain number when divided by 50 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ? | [
"9",
"5",
"8",
"4"
] | B | "explanation : 50 + 25 = 75 / 15 = 5 ( remainder ) b" | 5 |
Which is least likely to make a tasty meal for a predator? | [
"a rabbit",
"a deer",
"a skunk",
"a baby moose"
] | C | a skunk produces a bad odor | 6 |
Mara has 12 bags with 2 marbles in each bag. Markus has 2 bags with 13 marbles in each bag. How many more marbles does Markus have? | [
"70.0",
"2.0",
"-86.0",
"6.0"
] | B | Mara has 2 x 12 = <<2*12=24>>24 marbles.
Markus has 2 x 13 = <<2*13=26>>26 marbles.
Markus has 26 - 24 = <<26-24=2>>2 more marbles than Mara.
#### 2 | 3 |
For Halloween, Taquon, Mack and Jafari put their candy together and they had 418 pieces of candy. If Taquon and Mack each had 171 pieces of candy, how many pieces of candy did Jafari start with? | [
"76.0",
"7.0",
"185.0",
"5.0"
] | A | Taquon + Mack = 2 * 171 = 342 pieces
418 - 342 = <<418-342=76>>76 pieces
Jafari started with 76 pieces of candy.
#### 76 | 3 |
how many 3 digit positive integers exist that when divided by 7 leave a remainder of 5 ? | [
"129",
"142",
"128",
"143"
] | A | "explanatory answer step 1 : find the first and last term of the series the smallest 3 - digit positive integer that leaves a remainder of 5 when divided by 7 is 103 . the largest 3 - digit positive integer that leaves a remainder of 5 when divided by 7 is 999 . the series of numbers that satisfy the condition that the number should leave a remainder of 5 when divided by 7 is an a . p ( arithmetic progression ) with the first term being 103 and the last term being 999 . the common difference of the sequence is 7 . step 2 : compute the number of terms in an a . p , the last term l = a + ( n - 1 ) * d , where ' a ' is the first term , ' n ' is the number of terms of the series and ' d ' is the common difference . therefore , 999 = 103 + ( n - 1 ) * 7 or 999 - 103 = ( n - 1 ) * 7 or 896 = ( n - 1 ) * 7 so , n - 1 = 128 or n = 129 choice e is the correct answer ." | 5 |
a cycle is bought for rs . 600 and sold for rs . 1080 , find the gain percent ? | [
"20",
"11",
"22",
"80"
] | D | "600 - - - - 180 100 - - - - ? = > 80 % answer : d" | 5 |
What part of an atom is positive due to the presence of positively charged protons? | [
"Neutron",
"Electron",
"nucleus",
"Proton"
] | C | Charge Carried by Electrons and Protons Franklin wrote in his letters and books that he could see the effects of electric charge but did not understand what caused the phenomenon. Today we have the advantage of knowing that normal matter is made of atoms, and that atoms contain positive and negative charges, usually in equal amounts. Figure 18.5 shows a simple model of an atom with negative electrons orbiting its positive nucleus. The nucleus is positive due to the presence of positively charged protons. Nearly all charge in nature is due to electrons and protons, which are two of the. | 7 |
A shipping boat's crew consisted of 17 sailors, with five inexperienced sailors. Each experienced sailor was paid 1/5 times more than the inexperienced sailors. If the inexperienced sailors were paid $10 per hour for a 60-hour workweek, calculate the total combined monthly earnings of the experienced sailors. | [
"3400.0",
"1200.0",
"62.0",
"34560.0"
] | D | If the experienced sailors received 1/5 times more money than the inexperienced sailors, they were paid 1/5*10 = $<<1/5*10=2>>2 more.
The total hourly earnings for the experienced sailors each is $10+$2= $<<10+2=12>>12
In a 60-hour workweek, an experienced sailor is paid 60*$12 = $<<60*12=720>>720
In a month, an experienced sailor is paid 4*$720 = $<<4*720=2880>>2880
If there were five inexperienced sailors, the total number of experienced sailors was 17-5 = 12
If each experienced sailor was paid $2280 per month, the total combined monthly earnings for the experienced is 12*2880 = $<<12*2880=34560>>34560
#### 34560 | 3 |
if the average ( arithmetic mean ) of x , x + 2 , and x + 4 is 103 , what is the value of x ? | [
"97",
"101",
"95",
"87"
] | B | "am of x , x + 2 , and x + 4 = x + ( x + 2 ) + ( x + 4 ) / 3 = 3 x + 6 / 3 = x + 2 given that x + 2 = 103 x = 101 answer : c" | 5 |
The phase transition of a substance changing from a liquid state to a gaseous state is an example of what? | [
"entropoy",
"trichina",
"catostrophy",
"spirogyra"
] | A | There are many examples in the chemical world of changes in entropy. Phase transitions are one obvious example. When a substance makes a transition from the liquid state to the gaseous state, the particles have many more possible arrangements, because they are no longer confined to a specified volume in which they are close to each other; gas particles can move freely throughout their container. Vaporization represents an increase in entropy. In the opposite direction, a liquid loses entropy when it freezes to a solid. Because solids have very ordered structures, there are fewer possible arrangements of particles that would result in the properties associated with a solid. | 7 |
Two farmers agree that pigs are worth $\$300$ and that goats are worth $\$210$. When one farmer owes the other money, he pays the debt in pigs or goats, with ``change'' received in the form of goats or pigs as necessary. (For example, a $\$390$ debt could be paid with two pigs, with one goat received in change.) What is the amount of the smallest positive debt that can be resolved in this way? | [
"4",
"\\$30",
"244",
"000"
] | B | If a debt of $D$ dollars can be resolved in this way, then integers $p$ and $g$ must exist with \[
D = 300p + 210g = 30(10p + 7g).
\]As a consequence, $D$ must be a multiple of 30, and no positive debt less than $\$30$ can be resolved. A debt of $\boxed{\$30}$ can be resolved since \[
30 = 300(-2) + 210(3).
\]This is done by giving 3 goats and receiving 2 pigs. | 4 |
The oldest fossil of land plants date back how many millions of years? | [
"470 million years",
"520 million years",
"430 million years",
"350 million years"
] | A | Plants may have colonized the land as early as 700 million years ago. The oldest fossils of land plants date back about 470 million years. The first land plants probably resembled modern plants called liverworts , like the one shown in Figure below . | 7 |
Find the solutions to $z^3 = -8.$ Enter the solutions, separated by commas. | [
"2",
"-2, 1 + i \\sqrt{3}, 1 - i \\sqrt{3}",
"-\\frac{1}{2}",
"9"
] | B | From the equation $z^3 = -8,$ $z^3 + 8 = 0.$ We see that $z = -2$ is one solution, so we can take out a factor of $z + 2 = 0,$ which gives us
\[(z + 2)(z^2 - 2z + 4) = 0.\]By the quadratic formula, the roots of $z^2 - 2z + 4 = 0$ are
\[z = \frac{2 \pm \sqrt{2^2 - 4 \cdot 4}}{2} = \frac{2 \pm 2i \sqrt{3}}{2} = 1 \pm i \sqrt{3}.\]Thus, the solutions are $\boxed{-2, 1 + i \sqrt{3}, 1 - i \sqrt{3}}.$ | 4 |
If a kitten is unable to nurse from birth | [
"it will expire",
"sleep",
"decide to leave",
"it will laugh"
] | A | a mammal usually nurses its offspring | 6 |
deep sea animals live way down in the | [
"volcanoes",
"wet abyss",
"sky",
"mount everest"
] | B | deep sea animals live deep in the ocean | 6 |
a sum of money at simple interest amounts to rs . 825 in 3 years and to rs . 850 in 4 years . the sum is ? | [
"s . 738",
"s . 730",
"s . 650",
"s . 750"
] | D | "s . i . for 1 year = ( 850 - 825 ) = rs . 25 s . i . for 3 years = 25 * 3 = rs . 75 principal = ( 825 - 75 ) = rs . 750 . answer : b" | 5 |
Select the \emph{incorrect} statement. | [
"The order of an element is always multiple of the order of its group.",
"An ideal $I$ of commutative ring $R$ is a subgroup closed under multiplication by all elements of $R$.",
"Given a prime $p$, we have $a^{p} = a$ for every $a \\in \\mathbb{Z}_p$.",
"Any element of order $\\varphi(n)$ is a generator of $\\mathbb{Z}_n^*$."
] | A | 2 |
|
What is the rainy season in north america? | [
"fall",
"spring",
"winter",
"summer"
] | B | a new season occurs four times per year | 6 |
in a group of ducks and cows , the total number of legs are 36 more than twice the no . of heads . find the total no . of buffaloes . | [
"13",
"18",
"15",
"12"
] | B | "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 36 = > 2 x = 36 = > x = 18 e" | 5 |
If a bird has a larger beak than its friends, it likely had | [
"mother without a beak",
"father with a long trunk",
"parents with smaller beaks",
"ancestors with similar beaks"
] | D | the thickness of the parts of an organism is an inherited characteristic | 6 |
a boat goes 100 km downstream in 10 hours , and 60 m upstream in 15 hours . the speed of the stream is ? | [
"22 1 / 4",
"22 1 / 3",
"3",
"22 1 / 1"
] | C | "100 - - - 10 ds = 10 ? - - - - 1 60 - - - - 15 us = 4 ? - - - - - 1 s = ( 10 - 4 ) / 2 = 3 kmp answer : a" | 5 |
The cones of a jack pine tree require great amounts of heat to release their seeds. When are jack pine tree seeds most likely released? | [
"during a flood",
"after a fire",
"during a drought",
"after a disease"
] | B | 1 |
|
the volume of a cube is 343 cc . find its surface . | [
"294",
"864",
"556",
"287"
] | A | "a 3 = 343 = > a = 7 6 a 2 = 6 * 7 * 7 = 294 answer : c" | 5 |
Juan takes a number, adds $2$ to it, multiplies the answer by $2$, subtracts $2$ from the result, and finally divides that number by $2$. If his answer is $7$, what was the original number? | [
"6",
"3\\sqrt{11}",
"x=\\frac{61}{4}",
"J\\%6"
] | A | Let $n$ be the original number. Doing Juan's operations in order, we get $(2(n + 2) - 2)/2 = 7$. So $2(n + 2) - 2 = 14$, from which $2(n + 2) = 16$, from which $n + 2 = 8$, giving $n = \boxed{6}$. | 4 |
In 2 years, Maxwell will be twice his sister's age. If his sister is now 2, how old is Maxwell now? | [
"6.0",
"8.0",
"200.0",
"30.0"
] | A | In two years, Maxwell's sister will be 2 years + 2 years = <<2+2=4>>4 years old.
Therefore, Maxwell will be 4 years x 2 = <<4*2=8>>8 years old in two years.
Maxwell is now 8 years - 2 years = <<8-2=6>>6 years old.
#### 6 | 3 |
the market value of a certain machine decreased by 10 percent of its purchase price each year . if the machine was purchased in 1982 for its market value of $ 8,000 , what was its market value two years later ? | [
"$ 8",
"$ 800",
"$ 3",
"$ 6"
] | D | d market value in 1982 = $ 8000 market value in 1983 = $ 8000 - ( $ 8000 x 10 / 100 ) = 8000 - 800 = $ 7200 market value in 1984 = market value in 1983 - ( 10 % of $ 8000 ) = 7200 - 800 = $ 6400 | 5 |
30 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ? | [
"87",
"17",
"36",
"10"
] | C | binders books days 30 1400 21 x 1600 20 x / 30 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 36 answer : d | 5 |
Evaluate $(a^b)^a - (b^a)^b$ for $a = 2$ and $b = 3$. | [
"-665",
"-1",
"729",
"336"
] | A | We have \begin{align*}
(a^b)^a - (b^a)^b &= (2^3)^2 - (3^2)^3\\
&=8^2 - 9^3\\
&=64-729\\
&=\boxed{-665}.
\end{align*} | 4 |
Jim is a maintenance worker at a pool. Every time someone jumps in the pool, they cause 400 ml of water to splash out and evaporate. Jim has to get everyone out of the pool, clean, and refill it when it gets below 80% full. If the pool holds 2000 L of water, how many times can people jump in the pool before Jim has to clean it? | [
"1000.0",
"20000.0",
"4.0",
"3.0"
] | A | First figure out how many liters of water are left in the pool when it's 80% full: 2000L * .8 = <<2000*.8=1600>>1600 L
Now subtract that amount from the pool's total capacity to find how much water can splash out before Jim has to refill it: 2000 L - 1600 L = <<2000-1600=400>>400 L
Now multiply that amount by 1000 to convert it to milliliters: 400 L * 1000 ml/L = <<400*1000=400000>>400,000 ml
Finally, divide that amount by the amount that splashes out with each jump to find the number of jumps before pool cleaning: 400,000 ml / 400 ml/jump = <<400000/400=1000>>1000 jumps
#### 1000 | 3 |
on selling 11 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is : | [
"s . 55",
"s . 120",
"s . 50",
"s . 60"
] | B | "( c . p . of 11 balls ) - ( s . p . of 11 balls ) = ( c . p . of 5 balls ) c . p . of 6 balls = s . p . of 11 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 6 = rs . 120 . answer : option e" | 5 |
A company has 500 employees, each paid $12 per hour, working 10 hours a day, five days a week, 4 weeks a month. In August, the amount of work increased, and the company hired 200 more people. How much money does the company pay in total per month after the new hires? | [
"8.0",
"0.0",
"12.0",
"1680000.0"
] | D | The total pay per employee in a day is 12*10 = $<<12*10=120>>120
An employee works for 5*4 = <<5*4=20>>20 days in a month.
The total amount of money paid to each employee monthly is 20*120 = $<<20*120=2400>>2400
When the number of employees increased to 500+200 = <<500+200=700>>700 after the new hires in August.
The company pays a total of 700*2400 = $<<700*2400=1680000>>1680000 per month to its employees
#### 1680000 | 3 |
For the gala luncheon planning committee, Margaret wants to serve chicken salad sandwiches using mini croissants. She wants there to be enough food that each person on the committee can have 2 sandwiches each. Her bakery offers 12 minis croissants for $8.00. There are 24 people on the committee. How much will she spend on croissants? | [
"32.0",
"384.0",
"8000.0",
"280.0"
] | A | There are 24 people on the committee and she wants 2 sandwiches per person so that's 24*2 = <<24*2=48>>48 sandwiches
She can buy the croissants by the dozen and she needs 48 croissants so she needs 48/12 = <<48/12=4>>4 dozen croissants
A dozen croissants cost $8.00 and she needs 4 dozens so that will costs 8*4 = $<<8*4=32.00>>32.00
#### 32 | 3 |
John eats 3 meals a day. Breakfast is 500 calories. His lunch contains 25% more calories than that. His dinner is twice as many calories as lunch. He also has 3 shakes that are each 300 calories. How many calories does he get in a day? | [
"1800.0",
"3275.0",
"3125.0",
"300.0"
] | B | Lunch is 500 * .25 = <<500*.25=125>>125 more calories than breakfast
That means it is 500 + 125 = <<500+125=625>>625 calories
So dinner is 625 * 2 = <<625*2=1250>>1250 calories
The shakes are 3 * 300 = <<3*300=900>>900 calories
So in total he eats 500 + 625 + 1250 + 900 = <<500+625+1250+900=3275>>3275 calories
#### 3275 | 3 |
The tensor fascia latae acts as what, in relation to the gluteus medius and iliopsoas, for the purpose of flexing and abducting the thigh? | [
"synergist",
"spicule",
"symbiotic",
"antagonist"
] | A | The tensor fascia latae is a thick, squarish muscle in the superior aspect of the lateral thigh. It acts as a synergist of the gluteus medius and iliopsoas in flexing and abducting the thigh. It also helps stabilize the lateral aspect of the knee by pulling on the iliotibial tract (band), making it taut. Deep to the gluteus maximus, the piriformis, obturator internus, obturator externus, superior gemellus, inferior gemellus, and quadratus femoris laterally rotate the femur at the hip. The adductor longus, adductor brevis, and adductor magnus can both medially and laterally rotate the thigh depending on the placement of the foot. The adductor longus flexes the thigh, whereas the adductor magnus extends it. The pectineus adducts and flexes the femur at the hip as well. The pectineus is located in the femoral triangle, which is formed at the junction between the hip and the leg and also includes the femoral nerve, the femoral artery, the femoral vein, and the deep inguinal lymph nodes. | 7 |
Reducing bacteria in food prevents what? | [
"electricity",
"maladies",
"observation",
"signals"
] | B | reducing bacteria in food prevents illness in people | 6 |
Given that the diagonals of a rhombus are always perpendicular bisectors of each other, what is the area of a rhombus with side length $\sqrt{89}$ units and diagonals that differ by 6 units? | [
"80",
"11\\sqrt{2}",
"41",
"\\sqrt{89}"
] | A | Because the diagonals of a rhombus are perpendicular bisectors of each other, they divide the rhombus into four congruent right triangles. Let $x$ be half of the length of the shorter diagonal of the rhombus. Then $x+3$ is half of the length of the longer diagonal. Also, $x$ and $x+3$ are the lengths of the legs of each of the right triangles. By the Pythagorean theorem, \[
x^2+(x+3)^2=\left(\sqrt{89}\right)^2.
\] Expanding $(x+3)^2$ as $x^2+6x+9$ and moving every term to the left-hand side, the equation simplifies to $2x^2+6x-80=0$. The expression $2x^2+6x-80$ factors as $2(x-5)(x+8)$, so we find $x=5$ and $x=-8$. Discarding the negative solution, we calculate the area of the rhombus by multiplying the area of one of the right triangles by 4. The area of the rhombus is $4\cdot\left(\frac{1}{2}\cdot 5(5+3)\right)=\boxed{80}$ square units.
[asy]
unitsize(3mm);
defaultpen(linewidth(0.7pt)+fontsize(11pt));
dotfactor=3;
pair A=(8,0), B=(0,5), C=(-8,0), D=(0,-5), Ep = (0,0);
draw(A--B--C--D--cycle);
draw(A--C);
draw(B--D);
label("$x$",midpoint(Ep--B),W);
label("$x+3$",midpoint(Ep--A),S);
label("$\sqrt{89}$",midpoint(A--B),NE);[/asy] | 4 |
What is the branch of science that studies the physical world? | [
"social science",
"Ecology",
"botany",
"physics"
] | D | What is physics ? Physics is the branch of science that studies the physical world, including objects as small as subatomic particles and as large as galaxies. It studies the nature of matter and energy and how they interact. Physicists are inquisitive people who want to know the causes of what they see. How does the moon move? Why does the moon move? Why do the stars shine? Why do your hands get warm when you rub them together? Physicists, like all scientists, hope to find explanations that describe more than one phenomenon and offer a better understanding of how the universe works. | 7 |
What two planets is the asteroid belt found between? | [
"mars and jupiter",
"Mars and Earth",
"Jupiter and Saturn",
"Jupiter and Earth"
] | A | Asteroids are irregularly-shaped, rocky bodies that orbit the Sun. Most of them are found in the asteroid belt, between the orbits of Mars and Jupiter. | 7 |
Which of these events occurs about every three months? | [
"high tide",
"new moon",
"new season",
"solar eclipse"
] | C | 0 |
|
a factory producing tennis balls stores them in either big boxes , 25 balls per box , or small boxes , 20 balls per box . if 146 freshly manufactured balls are to be stored , what is the least number of balls that can be left unboxed ? | [
"5",
"4",
"2",
"1"
] | D | "we have to work with multiples of 20 and 25 . first , we must know the limits of this multiples , so : 146 / 25 = 5 . . . . so the max is 5 146 / 20 = 7 . . . so the max is 7 146 - 145 = 1 ( 6 small box + 1 big box ) answer : d" | 5 |
a certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint . if 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans , what is the least amount of paint r , in gallons , that must be purchased in order to measure out the portions needed for the mixture ? | [
"2",
"2 1 / 2",
"4",
"3 1 / 2"
] | B | given w : b = 3 : 5 that means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture . but we want least amount of whiteblack paints for minimum of 2 gallons of mixture , so lets reduce keeping same ratio , 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture , but we want only 2 gallons , lets further reduce 0.75 : 1.25 gives 1 + 1.5 = 2.5 gallons of mixture . this looks ok , but lets reduce further just to be sure 0.375 : 0.625 gives 0.5 + 1 = 1.5 gallons of mixture , thats less than 2 gallons of mixture , so not acceptable . so correct ans is 2.5 gallons . b | 5 |
What are the two main types of diabetes? | [
"type 3, 4",
"type a, b",
"type 1, type 2",
"type 0, 1"
] | C | There are two main types of diabetes: type 1 diabetes and type 2 diabetes. The two types of diabetes have different causes. | 7 |
an athlete runs 200 metres race in 24 seconds . what is his speed ? | [
"25 km / hr",
"30 km / hr",
"20 km / hr",
"40 km / hr"
] | B | speed = dist / time = 200 / 24 200 / 24 * 18 / 5 = 40 * 3 / 4 = 30 km / hr answer b | 5 |
I have a picture with dimensions $x$ and $y$ (in inches), such that $x$ and $y$ are both integers greater than one. I would like to place this picture in an elongated frame of dimensions $(2x + 3)$ and $(y+2)$. If I measured the area of the frame to be $34$ square inches, what is the area of the picture in square inches? (Note that by "the area of the frame," we mean the shaded region shown below). [asy]
size(5cm);
defaultpen(linewidth(0.7));
real eps=0.2;
filldraw((0,0)--(2,0)--(2,1)--(0,1)--cycle,gray);
filldraw((0,0)+(eps,eps)--(2,0)+(-eps,eps)--(2,1)+(-eps,-eps)--(0,1)+(eps,-eps)--cycle,white);
label("picture",(1,0.5));
label("frame",(1,1-eps/2));
[/asy] | [
"68",
"8",
" x+y = \\frac{(4 + \\sqrt{38})\\cdot 8}{4} ",
"\\frac{4}{3}"
] | B | The area of the frame is equal to \begin{align*}
(2x + 3) \cdot (y+2) - x \cdot y &= 2xy + 4x + 3y + 6 - xy \\
&= xy + 4x + 3y + 6 \\
&= 34.
\end{align*}To apply Simon's Favorite Factoring Trick, we add $6$ to both sides of the equation: $$xy + 4x + 3y + 12 = 40,$$so $$(x + 3)(y+4) = 40.$$Considering the factor pairs of 40, we see that the ordered pair $(x+3, y+4)$ must be among $$(1,40),(2,20),(4,10),(5,8),(8,5),(10,4),(20,2),(40,1).$$Solving for $x$ and $y$ for each pair of factors, we find that $(x,y)$ must be among the pairs $$(-2,36), (-1,16), (1,6), (2,4), (5,1), (7,0), (17,-2), (37,-3).$$Of these, only $(x,y) = (2,4)$ satisfy the condition that both $x$ and $y$ are greater than $1$. The area of the picture is thus $x \times y = \boxed{8}$ square inches. | 4 |
Darwin has 600$. He spent 1/3 of it on gas for his car, and 1/4 of what was left on food. How much money did he have left? | [
"300.0",
"900.0",
"16.0",
"180.0"
] | A | 600/3=<<600/3=200>>200$ for gas
After buying gas, Darwin has 600-200=<<600-200=400>>400$ left
400/4=<<400/4=100>>100$ on food
Darwin has 400-100=<<400-100=300>>300$ left
#### 300 | 3 |
the average salary / head of allthe workers in a workshop is rs . 850 , if the average salary / head of 7 technician is rs . 1000 and the average salary / head of the rest is rs . 780 , the total no . of workers in the work - shop is ? | [
"18",
"22",
"24",
"26"
] | B | "let the total number of workers be y . so sum of salary for all workers = sum of salary of 7 technician + sum of salary for other y - 7 workers . 7 x 1000 + 780 ( y - 7 ) = 850 y ⇒ 7000 + 780 y - 5460 = 850 y ⇒ 70 y = 1540 ∴ y = 22 so total number of workers = 22 c" | 5 |
What is the vector sum of all the torques acting on the object called? | [
"critical torque",
"total torque",
"net torque",
"gross torque"
] | C | The net torque is the vector sum of all the torques acting on the object. When adding torques it is necessary to subtract CW from CCW torques. | 7 |
what is the remainder when 8 ^ 381 is divided by 5 ? | [
"1",
"3",
"2",
"4"
] | B | i also agree that the remainder is ' 3 ' ( using the last digit of the powers of 7 ) . could we have the official answer please ? d | 5 |
We define two sequences of vectors $(\mathbf{v}_n)$ and $(\mathbf{w}_n)$ as follows: First, $\mathbf{v}_0 = \begin{pmatrix} 1 \\ 3 \end{pmatrix},$ $\mathbf{w}_0 = \begin{pmatrix} 4 \\ 0 \end{pmatrix}.$ Then for all $n \ge 1,$ $\mathbf{v}_n$ is the projection of $\mathbf{w}_{n - 1}$ onto $\mathbf{v}_0,$ and $\mathbf{w}_n$ is the projection of $\mathbf{v}_n$ onto $\mathbf{w}_0.$ Find
\[\mathbf{v}_1 + \mathbf{v}_2 + \mathbf{v}_3 + \dotsb.\] | [
"\\begin{pmatrix} 1 \\\\ 1 \\end{pmatrix}",
"\\begin{pmatrix} 0 \\\\ 0 \\end{pmatrix}",
"\\begin{pmatrix} 4/9 \\\\ 4/3 \\end{pmatrix}",
"\\begin{pmatrix} 26/29 \\\\ 65/29 \\end{pmatrix}"
] | C | Since $\mathbf{v}_n$ is always a projection onto $\mathbf{v}_0,$
\[\mathbf{v}_n = a_n \mathbf{v}_0\]for some constant $a_n.$ Similarly,
\[\mathbf{w}_n = b_n \mathbf{w}_0\]for some constant $b_n.$
[asy]
unitsize(1.5 cm);
pair[] V, W;
V[0] = (1,3);
W[0] = (4,0);
V[1] = (W[0] + reflect((0,0),V[0])*(W[0]))/2;
W[1] = (V[1] + reflect((0,0),W[0])*(V[1]))/2;
V[2] = (W[1] + reflect((0,0),V[0])*(W[1]))/2;
W[2] = (V[2] + reflect((0,0),W[0])*(V[2]))/2;
V[3] = (W[2] + reflect((0,0),V[0])*(W[2]))/2;
W[3] = (V[3] + reflect((0,0),W[0])*(V[3]))/2;
draw((-1,0)--(5,0));
draw((0,-1)--(0,4));
draw((0,0)--V[0],red,Arrow(6));
draw((0,0)--W[0],red,Arrow(6));
draw((0,0)--V[1],red,Arrow(6));
draw((0,0)--W[1],red,Arrow(6));
draw((0,0)--V[2],red,Arrow(6));
draw((0,0)--W[2],red,Arrow(6));
draw(W[0]--V[1]--W[1]--V[2]--W[2],dashed);
label("$\mathbf{v}_0$", V[0], NE);
label("$\mathbf{v}_1$", V[1], NW);
label("$\mathbf{v}_2$", V[2], NW);
label("$\mathbf{w}_0$", W[0], S);
label("$\mathbf{w}_1$", W[1], S);
label("$\mathbf{w}_2$", W[2], S);
[/asy]
Then
\begin{align*}
\mathbf{v}_n &= \operatorname{proj}_{\mathbf{v}_0} \mathbf{w}_{n - 1} \\
&= \frac{\mathbf{w}_{n - 1} \cdot \mathbf{v}_0}{\|\mathbf{v}_0\|^2} \mathbf{v}_0 \\
&= \frac{b_{n - 1} \cdot \mathbf{w}_0 \cdot \mathbf{v}_0}{\|\mathbf{v}_0\|^2} \mathbf{v}_0 \\
&= \frac{b_{n - 1} \begin{pmatrix} 4 \\ 0 \end{pmatrix} \cdot \begin{pmatrix} 1 \\ 3 \end{pmatrix}}{\left\| \begin{pmatrix} 1 \\ 3 \end{pmatrix} \right\|^2} \mathbf{v}_0 \\
&= \frac{2}{5} b_{n - 1} \mathbf{v}_0.
\end{align*}Thus, $a_n = \frac{2}{5} b_{n - 1}.$
Similarly,
\begin{align*}
\mathbf{w}_n &= \operatorname{proj}_{\mathbf{w}_0} \mathbf{v}_n \\
&= \frac{\mathbf{v}_n \cdot \mathbf{w}_0}{\|\mathbf{w}_0\|^2} \mathbf{w}_0 \\
&= \frac{a_n \cdot \mathbf{v}_0 \cdot \mathbf{w}_0}{\|\mathbf{v}_0\|^2} \mathbf{w}_0 \\
&= \frac{a_n \begin{pmatrix} 1 \\ 3 \end{pmatrix} \cdot \begin{pmatrix} 4 \\ 0 \end{pmatrix}}{\left\| \begin{pmatrix} 4 \\ 0 \end{pmatrix} \right\|^2} \mathbf{w}_0 \\
&= \frac{1}{4} a_n \mathbf{w}_0.
\end{align*}Thus, $b_n = \frac{1}{4} a_n.$
Since $b_0 = 1,$ $a_1 = \frac{2}{5}.$ Also, for $n \ge 2,$
\[a_n = \frac{2}{5} b_{n - 1} = \frac{2}{5} \cdot \frac{1}{4} a_{n - 1} = \frac{1}{10} a_{n - 1}.\]Thus, $(a_n)$ is a geometric sequence with first term $\frac{2}{5}$ and common ratio $\frac{1}{10},$ so
\begin{align*}
\mathbf{v}_1 + \mathbf{v}_2 + \mathbf{v}_3 + \dotsb &= \frac{2}{5} \mathbf{v_0} + \frac{2}{5} \cdot \frac{1}{10} \cdot \mathbf{v}_0 + \frac{2}{5} \cdot \left( \frac{1}{10} \right)^2 \cdot \mathbf{v}_0 + \dotsb \\
&= \frac{2/5}{1 - 1/10} \mathbf{v}_0 = \frac{4}{9} \mathbf{v}_0 = \boxed{\begin{pmatrix} 4/9 \\ 4/3 \end{pmatrix}}.
\end{align*} | 4 |
A chemical reaction can be caused by | [
"pouring soda into milk",
"putting vinegar in a bowl",
"bleach vinegar combo solution",
"pouring baking soda out of a box"
] | C | baking soda can react chemically with vinegar | 6 |
a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 180,000 . the 75 associates have an average salary of $ 30,000 . what is the average salary for the company ? | [
"$ 55",
"$ 65",
"$ 45",
"$ 75"
] | A | "another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 6 a * 1 + a * 5 ) / 6 = 11 a / 6 = 55000 answer is c . $ 55,000" | 5 |
Jenny brought in 40 peanut butter cookies and 50 chocolate chip cookies for the bake sale. Marcus brought in 30 peanut butter cookies and and 20 lemon cookies. If Renee, who's allergic to peanuts, picks a cookie at random, what is the chance she'll have an allergic reaction expressed as a percentage? | [
"50.0",
"25.0",
"55.6",
"84.0"
] | A | First find the total number of peanut butter cookies: 40 peanut butter cookies + 30 peanut butter cookies = <<40+30=70>>70 peanut butter cookies
Then find the total number of cookies by adding the number of peanut butter cookies to the number of the other two types: 70 peanut butter cookies + 50 chocolate chip cookies + 20 lemon cookies = <<70+50+20=140>>140 cookies
Then divide the number of peanut butter cookies by the total number of cookies and multiply by 100% to find the percentage chance of Renee getting a peanut butter cookie: 70 peanut butter cookies / 140 cookies * 100% = 50%
#### 50 | 3 |
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