question
stringlengths 1
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|---|---|---|---|---|
Lee can make 18 cookies with two cups of flour. How many cookies can he make with three cups of flour? | [
"1412",
"11",
"12",
"27"
] | D | Let $x$ be the number of cookies that Lee can make with three cups of flour. We can set up the proportion $\frac{18}{2} = \frac{x}{3}$. Solving for $x$, we find that $x = \boxed{27}$. | 4 |
the area of a circle is added to its diameter , and the circumference is then subtracted from this total , the result is 10 . what is the radius of the circle ? | [
"pi'",
"2'",
"4']",
"2 * pi'"
] | C | the equation is ; diameter + area - circumference = d + a - c = d + pi * r ^ 2 - 2 * pi * r = 2 r + pi * r ( r - 2 ) . by plugging in the answers we can test the answers quickly ; then , 4 is the only possible answer . answer : e | 5 |
A person protecting the environment they have control over will most likely | [
"block in their yard",
"salt their whole yard",
"burn trash in their yard",
"flood their whole yard"
] | A | An example of protecting the environment is creating protected areas | 6 |
In the city park, there are various attractions for kids and their parents. The entrance ticket to the park is $5, but for each attraction, you have to pay separately - such ticket costs $2 for kids and $4 for parents. How much would a family with 4 children, their parents, and her grandmother pay for visiting the park, and one attraction inside? | [
"60.0",
"21.0",
"67.0",
"55.0"
] | D | The whole family consists of 4 + 2 + 1 = <<4+2+1=7>>7 persons.
The entrance ticket to the park costs the same for every person, so the family would need to pay 7 * 5 = $<<7*5=35>>35 to enter.
For visiting the attraction the tickets would cost 4 * 2 = $<<4*2=8>>8 for the kids.
Their parents and grandmother would need to pay 3 * 4 = $<<3*4=12>>12.
That means a total cost for the family standing at 35 + 8 + 12 = $<<35+8+12=55>>55.
#### 55 | 3 |
A ball rolling over carpet will go ______ than a ball rolling over concrete. | [
"slower",
"speedier",
"greater",
"faster"
] | A | as the roughness of something increases , the friction of that something will increase when its surface moves against another surface | 6 |
A decomposer is an organism that | [
"hunts and eats animals",
"migrates for the winter",
"breaks down dead plants and animals",
"uses water and sunlight to make food"
] | C | 1 |
|
16 men can complete a piece of work in 25 days . in how many days can 20 men complete that piece of work ? | [
"20",
"27",
"27",
"23"
] | A | "16 * 25 = 20 * x = > x = 20 days answer : c" | 5 |
the sum of two numbers is 73 and their difference is 28 . find the difference between their squares . | [
"2044",
"101",
"2048",
"45"
] | A | "explanation : let x and y be the two given numbers ( x + y ) = 73 ; ( x – y ) = 28 ( x 2 – y 2 ) = ( x + y ) ( x – y ) = 73 * 28 = 2044 answer : c" | 5 |
two pipes a and b can separately fill a cistern in 24 minutes and 48 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 12 minutes . in how much time , the third pipe alone can empty the cistern ? | [
"130 min",
"54 min",
"90 min",
"48 min"
] | D | "1 / 12 - ( 1 / 24 + 1 / 48 ) = - 1 / 48 third pipe can empty in 48 minutes answer : b" | 5 |
the sides of a rectangular field are in the ratio 3 : 4 . if the area of the field is 7500 sq . m , the cost of fencing the field @ 25 paise per metre is | [
"rs . 86.50",
"rs . 55.50",
"rs . 87.50",
"none of these"
] | C | "solution let length = ( 3 x ) metres and breadth = ( 4 x ) metres . then , 3 x × 4 x = 7500 ⇔ 12 x 2 = 7500 ⇔ x 2 = 625 ⇔ x = 25 . so , length = 75 m and breadth = 100 m . perimeter = [ 2 ( 75 + 100 ) ] m = 350 m . ∴ cost of fencing = rs . ( 0.25 × 350 ) = rs . 87.50 . answer d" | 5 |
Excretion of ions occurs mainly through what organ? | [
"Heart",
"tissues",
"lungs",
"kidneys"
] | D | down to supply the blood and other tissues with these minerals. Phosphate is a normal constituent of nucleic acids; hence, blood levels of phosphate will increase whenever nucleic acids are broken down. Excretion of ions occurs mainly through the kidneys, with lesser amounts lost in sweat and in feces. Excessive sweating may cause a significant loss, especially of sodium and chloride. Severe vomiting or diarrhea will cause a loss of chloride and bicarbonate ions. Adjustments in respiratory and renal functions allow the body to regulate the levels of these ions in the ECF. Table 26.1 lists the reference values for blood plasma, cerebrospinal fluid (CSF), and urine for the six ions addressed in this section. In a clinical setting, sodium, potassium, and chloride are typically analyzed in a routine urine sample. In contrast, calcium and phosphate analysis requires a collection of urine across a 24-hour period, because the output of these ions can vary considerably over the course of a day. Urine values reflect the rates of excretion of these ions. Bicarbonate is the one ion that is not normally excreted in urine; instead, it is conserved by the kidneys for use in the body’s buffering systems. | 7 |
niki covers a distance in 45 min , if she drives at a speed of 60 km / h on an average . find the speed at which she must drive at to reduce the time of the journey by 50 % . | [
"121.62 kmph",
"111.00 kmph",
"101.02 kmph",
"121.00 kmph"
] | A | given speed = 60 kmph . it means niki covered 60 km in 60 min ( 1 hour ) . so , in 45 min he will cover 45 km . 50 % time reduced = 45 - 50 % of 45 = 22.5 min . thus , niki needs to cover 45 km in 22.5 min ( 0.37 hour ) . speed * time = distance . speed * 0.37 = 45 speed = 121.62 kmph . answer : option b | 5 |
a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 210 sq . feet , how many feet of fencing will be required ? | [
"41",
"88",
"68",
"none"
] | A | "explanation we have : l = 20 ft and lb = 210 sq . ft . so , b = 10.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 21 ) ft = 41 ft . answer b" | 5 |
a train crosses a platform of 200 m in 20 sec , same train crosses another platform of length 350 m in 25 sec . then find the length of the train ? | [
"180 m",
"150 m",
"400 m",
"250 m"
] | C | "length of the train be ‘ x ’ x + 200 / 20 = x + 350 / 25 5 x + 1000 = 4 x + 1400 x = 400 m answer : c" | 5 |
what is the total cost of 2 sandwiches at $ 2.44 each and 4 sodas at $ 0.87 each ? | [
"$ 3.36",
"$ 8.36",
"$ 10.08",
"$ 6.85"
] | B | "answer = c 2 * 2.44 + 4 * 0.87 = 2 ( 2.50 - 0.06 ) + 4 ( 1.00 - 0.13 ) = 5 + 4 - 0.12 - 0.52 = 9 - 0.64 = 8.36" | 5 |
There are 24 toys in the box and ¼ of them are action figures. The remaining toys are all dolls. How many dolls are there? | [
"6.0",
"18.0",
"5.0",
"48.0"
] | B | Since there are 24 toys in the box, there are ¼ * 24 = 6 action figures.
Because the rest of the toys are dolls, there are 24 - 6 = <<24-6=18>>18 dolls in the box.
#### 18 | 3 |
a survey of n people in the town of eros found that 50 % of them preferred brand a . another survey of 120 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ? | [
"240",
"150",
"50",
"100"
] | A | "it is simply a weighted average question . since the given average of 50 % and 60 % is 55 % ( right in the middle ) , it means the number of people surveyed in eros ( n ) is same as the number of people surveyed in angie . so n = 120 total = 120 + 120 = 240 answer ( e )" | 5 |
when a merchant imported a certain item , he paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 101.50 , what was the total value of the item ? | [
"$ 2",
"$ 2",
"$ 3",
"$ 1"
] | A | "let x be the value in excess of $ 1,000 . 0.07 x = 101.5 x = $ 1,450 the total value was $ 1,450 + $ 1,000 = $ 2,450 . the answer is b ." | 5 |
Let $\mathbf{p}$ and $\mathbf{q}$ be two three-dimensional unit vectors such that the angle between them is $30^\circ.$ Find the area of the parallelogram whose diagonals correspond to $\mathbf{p} + 2 \mathbf{q}$ and $2 \mathbf{p} + \mathbf{q}.$ | [
"9 \\sqrt{3}",
"3",
"\\frac{3}{4}",
"2"
] | C | Suppose that vectors $\mathbf{a}$ and $\mathbf{b}$ generate the parallelogram. Then the vectors corresponding to the diagonals are $\mathbf{a} + \mathbf{b}$ and $\mathbf{b} - \mathbf{a}.$
[asy]
unitsize(0.4 cm);
pair A, B, C, D, trans;
A = (0,0);
B = (7,2);
C = (1,3);
D = B + C;
trans = (10,0);
draw(B--D--C);
draw(A--B,Arrow(6));
draw(A--C,Arrow(6));
draw(A--D,Arrow(6));
label("$\mathbf{a}$", (A + B)/2, SE);
label("$\mathbf{b}$", (A + C)/2, W);
label("$\mathbf{a} + \mathbf{b}$", interp(A,D,0.7), NW, UnFill);
draw(shift(trans)*(B--D--C));
draw(shift(trans)*(A--B),Arrow(6));
draw(shift(trans)*(A--C),Arrow(6));
draw(shift(trans)*(B--C),Arrow(6));
label("$\mathbf{a}$", (A + B)/2 + trans, SE);
label("$\mathbf{b}$", (A + C)/2 + trans, W);
label("$\mathbf{b} - \mathbf{a}$", (B + C)/2 + trans, N);
[/asy]
Thus,
\begin{align*}
\mathbf{a} + \mathbf{b} &= \mathbf{p} + 2 \mathbf{q}, \\
\mathbf{b} - \mathbf{a} &= 2 \mathbf{p} + \mathbf{q}.
\end{align*}Solving for $\mathbf{a}$ and $\mathbf{b},$ we find
\begin{align*}
\mathbf{a} &= \frac{\mathbf{q} - \mathbf{p}}{2}, \\
\mathbf{b} &= \frac{3 \mathbf{p} + 3 \mathbf{q}}{2}.
\end{align*}The area of the parallelogram is then given by
\begin{align*}
\|\mathbf{a} \times \mathbf{b}\| &= \left\| \frac{\mathbf{q} - \mathbf{p}}{2} \times \frac{3 \mathbf{p} + 3 \mathbf{q}}{2} \right\| \\
&= \frac{3}{4} \| (\mathbf{q} - \mathbf{p}) \times (\mathbf{p} + \mathbf{q}) \| \\
&= \frac{3}{4} \|\mathbf{q} \times \mathbf{p} + \mathbf{q} \times \mathbf{q} - \mathbf{p} \times \mathbf{p} - \mathbf{p} \times \mathbf{q} \| \\
&= \frac{3}{4} \|-\mathbf{p} \times \mathbf{q} + \mathbf{0} - \mathbf{0} - \mathbf{p} \times \mathbf{q} \| \\
&= \frac{3}{4} \|-2 \mathbf{p} \times \mathbf{q}\| \\
&= \frac{3}{2} \|\mathbf{p} \times \mathbf{q}\|
\end{align*}Since $\mathbf{p}$ and $\mathbf{q}$ are unit vectors, and the angle between them is $30^\circ,$
\[\|\mathbf{p} \times \mathbf{q}\| = \|\mathbf{p}\| \|\mathbf{q}\| \sin 30^\circ = \frac{1}{2}.\]Therefore, the area of the parallelogram is $\frac{3}{2} \cdot \frac{1}{2} = \boxed{\frac{3}{4}}.$ | 4 |
walking with 4 / 5 of my usual speed , i arrive at the bus stop 7 minutes later than normal . how many minutes does it take to walk to the bus stop at my usual speed ? | [
"12",
"16",
"28",
"24"
] | C | let t = usual time = distance / usual speed t + 7 = distance / ( 4 * usual speed / 5 ) = ( 5 * distance ) / ( 4 * usual speed ) = 5 t / 4 t = 28 the answer is e . | 5 |
Which is likeliest to be torn by human hands? | [
"wood",
"steel",
"taffy",
"diamond"
] | C | tearing means changing a whole into pieces | 6 |
if circles x and y have the same area and circle x has a circumference of 20 π , half of the radius of circle y is : | [
"4",
"2",
"5",
"1"
] | C | "x b é radius of circle x ý b é radius of circle y given : pi * x ^ 2 = pi * ý ^ 2 also , 2 * pi * x = 20 * pi x = 10 thus ý = 10 y / 2 = 5 ans : b" | 5 |
How does the epidermis renew its layer? | [
"scabbing",
"shedding dead cells",
"loofah",
"exfoliating scrub"
] | B | 7 |
|
Many states require vehicles to be examined and to meet safety and pollution standards. What impact might vehicle inspections have on the environment? | [
"The environment will not be polluted.",
"The environment will become more polluted.",
"Fewer pollutants will be released by vehicles.",
"Fewer pollutants will be produced by older vehicles."
] | C | 0 |
|
What is the relationship of multiple action potentials from a single cell resulting in a significant change in the membrane potential? | [
"temporal summation",
"distinct summation",
"nature summation",
"bipolar summation"
] | A | membrane is a positive 15 mV, meaning that the membrane depolarizes from -70 mV to -55 mV, then the graded potentials will result in the membrane reaching threshold. For receptor potentials, threshold is not a factor because the change in membrane potential for receptor cells directly causes neurotransmitter release. However, generator potentials can initiate action potentials in the sensory neuron axon, and postsynaptic potentials can initiate an action potential in the axon of other neurons. Graded potentials summate at a specific location at the beginning of the axon to initiate the action potential, namely the initial segment. For sensory neurons, which do not have a cell body between the dendrites and the axon, the initial segment is directly adjacent to the dendritic endings. For all other neurons, the axon hillock is essentially the initial segment of the axon, and it is where summation takes place. These locations have a high density of voltage-gated Na+ channels that initiate the depolarizing phase of the action potential. Summation can be spatial or temporal, meaning it can be the result of multiple graded potentials at different locations on the neuron, or all at the same place but separated in time. Spatial summation is related to associating the activity of multiple inputs to a neuron with each other. Temporal summation is the relationship of multiple action potentials from a single cell resulting in a significant change in the membrane potential. Spatial and temporal summation can act together, as well. | 7 |
An integer greater than 9 and less than 100 is randomly chosen. What is the probability that its digits are different? | [
"\\frac{9}{99}",
"\\frac{1}{10}",
"\\frac{9}{10}",
"7.20"
] | C | We calculate the probability that the digits are the same, and subtract from 1. From the 90 integers to be chosen from, only 9 have the same digits: 11, 22, 33, ..., 99. Therefore, the probability that the digits are the same is $\frac{9}{90} = \frac{1}{10}$, so the probability that the digits are different is $1-\frac{1}{10}= \boxed{\frac{9}{10}}$. | 4 |
When performing an experiment for a science fair, what should be done if the data do not support the hypothesis? | [
"Check for errors and run the experiment again.",
"Change the hypothesis to match the conclusion.",
"Change the variable so the data will match the hypothesis.",
"Ignore the data and prepare the science fair display anyway."
] | A | 0 |
|
What kind of electricity can you generate with the energy found in flowing water? | [
"transient power",
"hydroelectric power",
"electrical power",
"wind energy"
] | B | The mechanical energy of rapidly flowing water can turn a turbine and generate electricity. Electricity produced in this way is called hydroelectric power. The water may flow over a waterfall or through a dam. You can see a picture of a dam in the Figure below . A drawback of dams is that they flood land upstream from the dam and reduce water flow downstream from the dam, and this can destroy ecosystems. At the following URL, you can learn more about hydroelectric power and see an animation of a hydroelectric power plant. | 7 |
When high winds knocked down pine trees in a wooded region, it created a gap in the crowded canopy and allowed sunlight to fall on the ground. The increased sunlight allowed a dense growth of raspberry plants which protected young pine seedlings from being eaten by herbivores. Over time, the pine seedlings grew and blocked sunlight from falling on the woodland floor, thereby preventing growth of more raspberry plants. Which of these terms best describes the process of change observed in this woodlands community? | [
"adaptation",
"cooperation",
"natural selection",
"ecological succession"
] | D | 0 |
|
Recrystallization is a process that can remove what, which result when compounds are synthesized? | [
"minerals",
"contaminants",
"chemicals",
"substances"
] | B | When compounds are synthesized, they often have contaminating materials mixed in with them. The process of recrystallization can be used to remove these impurities. The crystals are dissolved in a hot solvent, forming a solution. When the solvent is cooled the compound is no longer as soluble and will precipitate out of solution, leaving other materials still dissolved. | 7 |
the mass of 1 cubic meter of a substance is 300 kilograms under certain conditions . what is the volume , in cubic centimeters , of 1 gram of this substance under these conditions ? ( 1 kilogram = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters ) | [
"80.0']",
"1.25'",
"8.0'",
"1.33'"
] | D | density is mass divided by volume . so density of the given substance will be mass / volume = 800 kg / 1 m ^ 3 = 300 kg / m ^ 3 or 1 g / 1.33 cm ^ 3 = 0.3 g / cm ^ 3 . next , ask yourself if 300,000 g is equivalent to 1 , 000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters ? - - > 1 g - 1 , 000,000 / 300,000 = 10 / 3 = 1.33 cubic centimeters . answer is a | 5 |
a bucket contains 2 mixtures a and b in the ratio 3 : 2 . if 5 liters of the mixture is replaced by 5 liters of liquid b , then the ratio of the two liquids becomes 3 : 5 . how much of the liquid a was there in the bucket ? | [
"8 liters",
"12 liters",
"18 liters",
"10 liters"
] | A | "1 st ratio = 3 : 2 2 nd ratio = 3 : 5 difference of cross products ratio = 3 * 5 - 3 * 2 = 9 common factor of the 1 st ratio = ( quantity replaced / sum of terms in 1 st ratio ) + ( quantity replaced * term a in 2 nd ratio / difference ) = ( 5 / 5 ) + ( 5 * 3 / 9 ) = 1 + 5 / 3 = 2.67 quantity of a = 3 * 2.67 = 8 liters approximately answer is a" | 5 |
in two alloys , copper and tin are related in the ratios of 4 : 1 and 1 : 3 . 10 kg of ist alloy , 16 kg of 2 nd alloy and some pure copper melted together . an alloy obtained in which the ratio of copper and tin was 3 : 2 . find the weight of the new alloy . | [
"30 kg",
"35 kg",
"36 kg",
"34 kg"
] | B | suppose x kg of pure copper is melted with 10 kg of ist alloy and 16 kg of 2 nd alloy , then pure cooper in new alloy = 10 * 4 / 5 + 16 * 1 / 4 + x = 12 + x kg pure tin in new alloy = 10 * 1 / 5 + 16 * 3 / 4 = 14 kg as per given condition ( 12 + x ) / 14 = 3 / 2 24 + 2 x = 42 x = 9 kg total weight of new alloy = 10 + 16 + 9 = 35 kg answer : b | 5 |
a and b started a business in partnership investing rs . 20000 and rs . 15000 respectively . after 6 months , c joined them with rs . 20000 . what will be b ' s share in the total profit of rs . 25000 earned at the end of 2 years from the starting of the business ? | [
"rs . 9000",
"rs . 9500",
"none",
"rs . 7500"
] | D | solution a : b : c = ( 20000 × 24 ) : ( 15000 × 24 ) : ( 20000 × 18 ) = 4 : 3 : 3 b ' s share = rs . ( 25000 × 3 / 10 ) = rs . 7500 . answer a | 5 |
What do you call an animal in which the embryo, often termed a joey, is born immature and must complete its development outside the mother's body? | [
"placental mammal",
"eukaryotic",
"marsupial",
"monotreme"
] | C | All other mammals give birth to live young and belong to one of two different categories, the marsupials and the placental mammals. A marsupial is an animal in which the embryo, which is often called a joey, is born at an immature stage. Development must be completed outside the mother's body. Most female marsupials have an abdominal pouch or skin fold where there are mammary glands. The pouch is a place for completing the development of the baby. Although blind, without fur, and with only partially formed hind legs, the tiny newborns have well developed forelimbs with claws that enable them to climb their way into their mother's pouch where they drink their mother's milk and continue their development. Marsupials include kangaroos, koalas, and opossums. Other marsupials are the wallaby and the Tasmanian Devil. Most marsupials live in Australia and nearby areas. ( Figure below ). | 7 |
during a special promotion , a certain filling station is offering a 8 percent discount on gas purchased after the first 10 gallons . if kim purchased 20 gallons of gas , and isabella purchased 25 gallons of gas , then isabella ‟ s total per - gallon discount is what percent of kim ‟ s total per - gallon discount ? | [
"115 %",
"120 %",
"105 %",
"80 %"
] | C | "kim purchased 20 gallons of gas . she paid for 4 + 0.9 * 16 = 18.4 gallons , so the overall discount she got was 1.6 / 20 = 8 % . isabella purchased 25 gallons of gas . she paid for 4 + 0.9 * 21 = 22.9 gallons , so the overall discount she got was 2.1 / 25 = 8.4 % . 8.4 / 8 * 100 = 105 % . answer : b ." | 5 |
if 5 cats can kill 5 rats in 5 minutes , how long will it take 100 cats to kill 100 rats ? | [
"3 minutes",
"5 minutes",
"1 minutes",
"4 minutes"
] | B | "it will take 5 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 5 minutes , so 100 cats can kill 100 rats in 5 minutes answer e" | 5 |
Which two letters are most associated with painful, red flesh? | [
"O and A",
"Q and P",
"U and V",
"F and J"
] | C | sunlight contains ultraviolet light | 6 |
in a school 10 % of the boys are same in number as 1 / 2 th of the girls . what is the ratio of boys to the girls in the school ? | [
"2 : 5",
"2 : 3",
"3 : 7",
"5 : 1"
] | D | "10 % of b = 1 / 2 g 10 b / 100 = g / 2 b = 5 g / 1 b / g = 5 / 1 b : g = 5 : 1 answer is a" | 5 |
Suppose the function $f$ has all real numbers in its domain and range and is invertible. Some values of $f$ are given by the following table: $$\begin{array}{c || c | c | c | c | c}
x & 1 & 2 & 3 & 4 & 5 \\
\hline
f(x) & 2 & 3 & 5 & 7 & 8
\end{array}$$What is the value of $f(f(3)) + f(f^{-1}(4)) + f^{-1}(f^{-1}(5))?$ If there is not enough information to answer this question, enter "NEI". | [
"7",
"14",
"x = 3",
"-4"
] | B | Reading the table, we see that $f(f(3)) = f(5) = 8.$
Although we can't look up $f^{-1}(4)$ in the table, we know that $f(f^{-1}(4)) = 4,$ since $f(f^{-1}(x))=x$ for all $x$ (by the definition of an inverse function).
Since $f(3) = 5,$ we have $f^{-1}(5) = 3,$ and so $$f^{-1}(f^{-1}(5)) = f^{-1}(3).$$Then, since $f(2) = 3,$ we have $$f^{-1}(f^{-1}(5)) = f^{-1}(3) = 2.$$Combining the information above, we get $$f(f(3)) + f(f^{-1}(4)) + f^{-1}(f^{-1}(5)) = 8+4+2 = \boxed{14}.$$ | 4 |
A biofilm is a colony of prokaryotes that is stuck to what? | [
"surface",
"the middle",
"the bottom",
"skin"
] | A | Some prokaryotes form structures consisting of many individual cells, like the cells in Figure below . This is called a biofilm. A biofilm is a colony of prokaryotes that is stuck to a surface. The surface might be a rock or a host's tissues. The sticky plaque that collects on your teeth between brushings is a biofilm. It consists of millions of prokaryotic cells. | 7 |
when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 1.30 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ? | [
"$ 663",
"$ 275",
"$ 510",
"$ 255"
] | A | "total no . of boxes = 3060000 / ( 20 × 20 × 15 ) = 510 total cost = 510 × $ 1.30 = $ 663 answer e" | 5 |
When a car's brakes are applied, it travels 7 feet less in each second than the previous second until it comes to a complete stop. A car goes 28 feet in the first second after the brakes are applied. How many feet does the car travel from the time the brakes are applied to the time the car stops? | [
"70",
"0",
"21",
"41"
] | A | The number of feet the car travels in each second is an arithmetic sequence with first term 28 and common difference $-7$. We are summing all the positive terms in this sequence (these terms represent the number of feet the car travels in each second). Thus, we want to find the sum $28+21+14+7 = \boxed{70}$. | 4 |
carol spends 1 / 4 of her savings on a stereo and 1 / 6 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ? | [
"2 / 7",
"11 / 24",
"1 / 2",
"1 / 4"
] | B | "total savings = s amount spent on stereo = ( 1 / 4 ) s amount spent on television = ( 1 - 1 / 6 ) ( 1 / 4 ) s = ( 5 / 6 ) * ( 1 / 4 ) * s = ( 5 / 24 ) s ( stereo + tv ) / total savings = s ( 1 / 4 + 5 / 24 ) / s = 11 / 24 answer : e" | 5 |
Cassidy is grounded for 14 days for lying about her report card, plus 3 extra days for each grade below a B. If Cassidy got four grades below a B, how long is she grounded for? | [
"26.0",
"38.0",
"3.14",
"48.0"
] | A | First find how many days Cassidy is grounded for the low grades: 4 grades * 3 days/grade = <<4*3=12>>12 days
Then add that time to the 14 days she's grounded for lying to find the total grounding length: 12 days + 14 days = <<12+14=26>>26 days
#### 26 | 3 |
An ant moves on the following lattice, beginning at the dot labeled $A$. Each minute he moves to one of the dots neighboring the dot he was at, choosing from among its neighbors at random. What is the probability that after 5 minutes he is at the dot labeled $B$? [asy]
draw((-2,0)--(2,0));
draw((0,-2)--(0,2));
draw((1,1)--(1,-1)--(-1,-1)--(-1,1)--cycle);
dot((0,0)); dot((1,0)); dot((2,0)); dot((-1,0)); dot((-2,0)); dot((0,1)); dot((0,2)); dot((0,-1)); dot((0,-2)); dot((1,1)); dot((1,-1)); dot((-1,-1)); dot((-1,1));
label("$A$",(0,0),SW);
label("$B$",(0,1),NE);
[/asy] | [
"\\frac{9}{4}",
"5",
"\\frac{3}{5}",
"\\frac{1}{4}"
] | D | Color the dots red and blue as shown below. Notice that whenever the ant moves, it moves from a red dot to a blue dot or a blue dot to a red dot. So since $A$ is a red dot, it must move to a blue dot, then a red dot, then a blue dot, then a red dot, and end up on a blue dot. There are only four blue dots, and the ant is equally likely to end up on any one of these four, since the diagram is symmetric to a $90^\circ$ rotation. The probability that the ant ends on $B$ after five minutes is therefore $\boxed{\frac{1}{4}}$. [asy]
draw((-2,0)--(2,0));
draw((0,-2)--(0,2));
draw((1,1)--(1,-1)--(-1,-1)--(-1,1)--cycle);
dot((0,0),red); dot((1,0),blue); dot((2,0),red); dot((-1,0),blue); dot((-2,0),red); dot((0,1),blue); dot((0,2),red); dot((0,-1),blue); dot((0,-2),red); dot((1,1),red); dot((1,-1),red); dot((-1,-1),red); dot((-1,1),red);
label("$A$",(0,0),SW);
label("$B$",(0,1),NE);
[/asy] | 4 |
Habitat loss, introduced species, overharvesting, and global change are major threats to what? | [
"transportation",
"the sun",
"the earth's gravity",
"biodiversity"
] | D | 7 |
|
What do you call the system of glands that release chemical messenger molecules into the bloodstream? | [
"limbic system",
"homeostasis system",
"nervous system",
"endocrine system"
] | D | The nervous system isn’t the only message-relaying system of the human body. The endocrine system also carries messages. The endocrine system is a system of glands that release chemical messenger molecules into the bloodstream. The messenger molecules are hormones. Hormones act slowly compared with the rapid transmission of electrical messages by the nervous system. They must travel through the bloodstream to the cells they affect, and this takes time. On the other hand, because endocrine hormones are released into the bloodstream, they travel throughout the body. As a result, endocrine hormones can affect many cells and have body-wide effects. | 7 |
two airplanes fly the same exact route from atlanta to chicago . plane a flies 200 mph while plane b flies 300 mph ( assume that simple model versus actual acceleration / deceleration near the airports ) . if plane a took off exactly 40 minutes before plane b , after how many minutes will plane b overtake plane a ? | [
"115",
"120",
"65",
"80"
] | D | we can use some form of the equation d = rt [ distance = rate * time ] rate of plane a : 200 mph rate of plane b : 300 mph plane a will be in the sky 40 minutes longer than plane b ( 2 / 3 of an hour ) time of plane a when b overtakes it : t + ( 2 / 3 ) use 2 / 3 of an hour since the rate is in hours time of plane b when b overtakes a : t at the time that b overtakes a , they will have travelled the same distance so rt is equal for each plane : 200 * ( t + 2 / 3 ) = 300 * t 200 t + 400 / 3 = 300 t 400 / 3 = 100 t 4 / 3 = t this is 1 and a third hour , so 60 minutes + 20 minutes = 80 minutes b | 5 |
a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 11 brown mice in the experiment , how many mice in total are in the experiment ? | [
"33",
"26",
"39",
"21"
] | A | "let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 11 = > m = 33 answer b" | 5 |
the perimeter of a square is 48 m . find the area of the square . | [
"144 m â ² .'",
"273 m â ² .']",
"161 m â ² .'",
"166 m â ² .'"
] | A | perimeter of square = 48 m but perimeter of square = 4 ã — side therefore , 4 ã — side = 48 m therefore , side = 48 / 4 m = 12 m now , the area of the square = ( side ã — side ) therefore , area of the square = 12 ã — 12 m â ² = 144 m â ² . answer : option b | 5 |
A chef has served 58 adults, 35 fewer children than the number of adults, and twice as many seniors as children. What is the total number of guests served? | [
"127.0",
"5.0",
"369.0",
"75.0"
] | A | The chef has served 58 - 35 = <<58-35=23>>23 children.
The chef has served 23 x 2 = <<23*2=46>>46 seniors.
Therefore, the total number of guests that the chef has served is 58 + 23 + 46 = <<58+23+46=127>>127.
#### 127 | 3 |
The creation and destruction of oceanic crust is the reason what moves? | [
"oceans",
"planets",
"continents",
"animals"
] | C | In some places, the oceanic crust comes up to a continent. The moving crust pushes that continent away from the ridge axis as well. If the moving oceanic crust reaches a deep sea trench, the crust sinks into the mantle. The creation and destruction of oceanic crust is the reason that continents move. | 7 |
the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 45 . what is a possible value for the mean of the distribution ? | [
"47",
"50",
"52",
"49"
] | C | "the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 45 : { mean } - 3 * { sd } > 45 ; { mean } - 6 > 45 ; { mean } > 51 . answer : a ." | 5 |
Peggy has 6 dolls. Her grandmother gives Peggy her own collection of 30 dolls. Over the year, Peggy receives half that amount of dolls between her birthday and Christmas. How many dolls does Peggy now have? | [
"26.0",
"51.0",
"21.0",
"2.0"
] | B | Peggy has 6 dolls and her grandmother gave her 30 so that’s 6+30 = <<6+30=36>>36 dolls
Over the holidays, Peggy is gifted half the number of dolls her grandmother gave her, so she receives 30/2 = <<30/2=15>>15 more dolls
Peggy had 36 dolls and received another 15 for a total of 36+15 = <<36+15=51>>51 dolls
#### 51 | 3 |
What kind of map can show the features of the bottom of a body of water? | [
"topographic",
"bathymetric",
"basic",
"country"
] | B | Oceanographers use bathymetric maps to show the features of the bottom of a body of water. | 7 |
The digits of a two-digit number $AB$ are reversed to form a second two-digit number, and the lesser of the two-digit numbers is subtracted from the greater. What prime number must be a factor of the difference if $A\neq B$? | [
"114",
"4",
"22",
"3"
] | D | $AB -BA= 10\cdot A+B - (10\cdot B+A)= 9\cdot A-9\cdot B=3(3\cdot A-3\cdot B)$. If $A\neq B$, then the difference is a (non-zero) multiple of 3. Thus, $\boxed{3}$ must be a factor of $AB -BA$. | 4 |
A desert environment is | [
"frigid",
"parched",
"rainy",
"tropical"
] | B | a desert environment is dry | 6 |
The most magnetic material in nature is what? | [
"magnetite",
"gold",
"molecules",
"crystals"
] | A | Some materials are natural permanent magnets. The most magnetic material in nature is the mineral magnetite. | 7 |
A company which causes long lasting products will likely? | [
"Sell less",
"Produce more",
"Produce Less",
"Sell more"
] | A | as the time a tool lasts increases , the number of tools discarded will decrease | 6 |
The body is made up of how many types of tissue? | [
"four",
"six",
"seven",
"five"
] | A | As for all animals, your body is made of four types of tissue: epidermal, muscle, nerve, and connective tissues. Plants, too, are built of tissues, but not surprisingly, their very different lifestyles derive from different kinds of tissues. All three types of plant cells are found in most plant tissues. Three major types of plant tissues are dermal, ground, and vascular tissues. | 7 |
a student finds the average of 9 positive integers . each integer contains two digits . by mistake , the boy interchanges the digits of one number say pq for qp . due to this , the average becomes 1 less than the previous one . what was the difference of the two digits p and q ? | [
"1",
"2",
"8",
"4"
] | A | explanation : let the original number be pq i . e . , ( 10 p + q ) . after interchanging the digits , the new number becomes qp i . e . , ( 10 q + p ) . the question states that the average of 9 numbers has become 1 less than the original average . therefore , the sum of the original 9 numbers will be 9 * 1 more than the sum of the 9 numbers with the digits interchanged . i . e . , 10 p + q = 10 q + p + 9 = > 9 a - 9 b = 9 = > a - b = 1 . answer : c | 5 |
what is the probability of getting sum 10 with the help of three dice ? | [
"1 / 24",
"1 / 16",
"1 / 4",
"1 / 8"
] | D | "( 1 , 3,6 ) 3 ! = 6 ( 2 , 2,6 ) = 3 ! / 2 = 3 ( 1 , 4,5 ) 3 ! = 6 ( 2 , 4,4 ) = 3 ( 2 , 3,5 ) 3 ! = 6 ( 3 , 3,4 ) = 3 prob . of getting sum 10 = ( 6 + 6 + 6 + 3 + 3 + 3 ) / 216 = 1 / 8 ans answer : b" | 5 |
Deceleration is the opposite of what? | [
"vibration",
"stopping",
"stimulation",
"acceleration"
] | D | Discussion The minus sign indicates that acceleration is to the left. This sign is reasonable because the train initially has a positive velocity in this problem, and a negative acceleration would oppose the motion. Again, acceleration is in the same direction as the change in velocity, which is negative here. This acceleration can be called a deceleration because it has a direction opposite to the velocity. | 7 |
a circle graph shows how the budget of a certain company was spent : 15 percent for transportation , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for salaries . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent salaries ? | [
"234 °",
"222 °",
"240 °",
"216 °"
] | A | "the percent of the budget for salaries is 100 - ( 15 + 9 + 5 + 4 + 2 ) = 65 % 100 % of the circle is 360 degrees . then ( 65 % / 100 % ) * 360 = 234 degrees the answer is d ." | 5 |
The Sahara Desert in Africa has high daytime temperatures but low nighttime temperatures. Which factor is mainly responsible for low nighttime temperatures in the Sahara Desert? | [
"coarse soil",
"low latitude",
"lack of clouds",
"high altitude"
] | C | 0 |
|
2 tablespoons of popcorn kernels will make 4 cups of popcorn. For movie night, Joanie wants 3 cups of popcorn, Mitchell wants 4 cups of popcorn, Miles and Davis said they would split 6 cups of popcorn and Cliff said he would only eat 3 cups. How many tablespoons of popcorn kernels will they need? | [
"0.075",
"1.0",
"8.0",
"150.0"
] | C | If Joanie wants 3 cups, Mitchell wants 4 cups, Miles & Davis want 6 cups and Cliff wants 3 cups then they want 3+4+6+3 = <<3+4+6+3=16>>16 cups of popcorn
Every 2 tablespoons makes 4 cups and they want 16 cups so 16/4 = <<16/4=4>>4 groups of 2 tablespoons are needed.
Thus they need 4 * 2 = <<4*2=8>>8 tablespoons in total.
#### 8 | 3 |
a number when divided by a certain divisor left remainder 255 , when twice the number was divided by the same divisor , the remainder was 112 . find the divisor ? | [
"365",
"460",
"370",
"398"
] | D | easy solution : n = dq 1 + 255 2 n = 2 dq 1 + 51 0 - ( 1 ) 2 n = dq 2 + 112 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 398 d * some integer = 398 checking all options only ( c ) syncs with it . answer c | 5 |
In a food chain, what group of organisms breaks down animal remains and wastes to get energy? | [
"producers",
"detritivores",
"primary consumers",
"decomposers"
] | D | Decomposers break down animal remains and wastes to get energy. | 7 |
Which is the most accurate statement? | [
"a phone's brain controls its body",
"a rock's brain controls its body",
"a sloth's brain controls its body",
"a bacteria's brain controls its body"
] | C | an animal 's brain controls that animal | 6 |
in a group of 27 junior high school students , 7 take french , 10 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ? | [
"6",
"4",
"9",
"6"
] | A | "a 7 add 7 + 10 + 4 to get 21 . then subtract 21 from the total students ⇒ 27 – 21 = 6 . answer is e" | 5 |
What do atoms make by rearranging their chemical bonds in a reactant? | [
"minerals",
"solutions",
"products",
"compounds"
] | C | When a chemical reaction occurs, the atoms in the reactants rearrange their chemical bonds to make products. The new arrangement of bonds does not have the same total energy as the bonds in the reactants. Therefore, when chemical reactions occur, there will always be an accompanying energy change. In some reactions, the energy of the products is lower than the energy of the reactants. Thus, in the course of the reaction, the substances lose energy to the surrounding environment. Such reactions are exothermic and can be represented by an energylevel diagram like the one in http://catalog. flatworldknowledge. com/bookhub/reader/2547 gob-ch07_s04_f01. In most cases, the energy is given off as heat (although a few reactions give off energy as light). Figure 7.3 Exothermic Reactions. | 7 |
bob invested $ 2000 in fund a and $ 1000 in fund b . over the next two years , the money in fund a earned a total interest of 12 percent for the two years combined and the money in fund b earned 30 percent annual interest compounded annually . two years after bob made these investments . bob ' s investment in fund a was worth how much more than his investment in fund b ? | [
"$ 500",
"$ 650",
"$ 600",
"$ 550"
] | D | bob earned 2000 * ( 1 + 0.12 ) in total by fund a and earned 1000 * ( 1 + 0.3 ) ^ 2 in total by fund b . so 2000 * ( 1.12 ) - 1000 * ( 1.69 ) = 550 . the answer is , therefore , ( b ) . | 5 |
What term describes a property of a liquid based on the strength of its intermolecular forces? | [
"tissue pressure",
"vapor pressure",
"analogous pressure",
"cellular pressure"
] | B | Because they cannot escape the container, the vapor molecules above the surface of the liquid exert a pressure on the walls of the container. The vapor pressure is a measure of the presure (force per unit area) exerted by a gas above a liquid in a sealed container. Vapor pressure is a property of a liquid based on the strength of its intermolecular forces. A liquid with weak intermolecular forces evaporates more easily and has a high vapor pressure. A liquid with stronger intermolecular forces does not evaporate easily and thus has a lower vapor pressure. For example, diethyl ether is a nonpolar liquid with weak dispersion forces. Its vapor pressure at 20°C is 58.96 kPa. Water is a polar liquid whose molecules are attracted to one another by relatively strong hydrogen bonding. The vapor pressure of water at 20°C is only 2.33 kPa, far less than that of diethyl ether. | 7 |
two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively . when they meet , it is found that one train has travelled 60 km more than the other one . the distance between the two stations is ? | [
"444 km",
"333 km",
"555 km",
"666 km"
] | A | d 444 km 1 h - - - - - 5 ? - - - - - - 60 12 h rs = 16 + 21 = 37 t = 12 d = 37 * 12 = 444 | 5 |
In solving the system of equations $y = 7$ and $x^2+ y^2= 100,$ what is the sum of the solutions for $x?$ | [
"0",
"= \\pm 7\\sqrt{4}",
"2",
"4y"
] | A | $y = 7$ represents a horizontal line that intersects a circle of radius $10$ around the origin. The symmetry of the circle guarantees that the points of intersection have a sum which add up to $0.$
Alternatively, we can simply substitute $7$ into the second equation for $y,$ to get that $x^2 = 51.$ Then, the two possible values for $x$ are $\sqrt{51},-\sqrt{51}.$ It's clear that they add up to $\boxed{0}.$ | 4 |
in an election a candidate who gets 60 % of the votes is elected by a majority of 1380 votes . what is the total number of votes polled ? | [
"c ) 6900",
"d ) 7520",
"e ) 6000",
"a ) 4500"
] | A | "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1380 20 x / 100 = 1380 x = 1380 * 100 / 20 = 6900 answer is c" | 5 |
Natalie's sister had 8 small diaries in her locker. Last summer she bought double the number of diaries she had and then lost 1/4 of what she had. How many diaries does Natalie's sister have now? | [
"40.0",
"20.0",
"18.0",
"13.435"
] | C | Natalie's sister bought 2 * 8 = <<2*8=16>>16 diaries.
So she then had 16 + 8 = <<16+8=24>>24 diaries.
Afterwards, she loses 1/4 * 24 = <<24*1/4=6>>6 diaries.
So, Natalie's sister now has 24 - 6 = <<24-6=18>>18 diaries.
#### 18 | 3 |
Solve the inequality
\[\frac{x^2 - 25}{x + 5} < 0.\] | [
"(-5,5)",
"-5",
"(D)",
"(-\\infty,-5) \\cup (-5,5)"
] | D | We can factor the numerator, to get
\[\frac{(x - 5)(x + 5)}{x + 5} < 0.\]If $x \neq -5,$ then this simplifies to $x - 5 < 0.$ Since the expression is not defined for $x = -5,$ the solution is
\[x \in \boxed{(-\infty,-5) \cup (-5,5)}.\] | 4 |
in kaya ' s teacher ' s desk there are 3 pink highlighters , 7 yellow highlighters , and 5 blue highlighters . how many highlighters are there in all ? | [
"33",
"77",
"15",
"88"
] | C | "add the numbers of highlighters . 3 + 7 + 5 = 15 . answer is b ." | 5 |
The mars rover collected round clumps of crystals that, on earth, usually form in what? | [
"water",
"rocks",
"volcanoes",
"air"
] | A | The ice ages were very recent as Earth history goes. The animals are familiar, but they're still very different from modern ones. For one thing, most of them were huge. A small surface area-to-volume ratio is better for keeping warm (less surface to lose heat from). Although the dominant animals were mammals, the Pleistocene Earth still does not look quite modern. | 7 |
Being exposed to sunlight will produce what vitamin in the skin? | [
"Vitamin E",
"vitamin d",
"B-complex",
"vitamin A"
] | B | Some vitamins are produced in the body. For example, vitamin D is made in the skin when it is exposed to sunlight. Vitamins B 12 and K are produced by bacteria that normally live inside the body. Most other vitamins must come from foods. Foods that are good sources of vitamins include whole grains, vegetables, fruits, and milk ( Table above ). | 7 |
In a generator, work done to turn the coil is converted to what type of energy? | [
"power",
"voltage",
"electric",
"solar"
] | C | Figure 23.5 Rotation of a coil in a magnetic field produces an emf. This is the basic construction of a generator, where work done to turn the coil is converted to electric energy. Note the generator is very similar in construction to a motor. | 7 |
how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 18 kmph ? | [
"80 sec",
"60 sec",
"50 sec",
"40 sec"
] | C | "d = 100 + 150 = 250 s = 18 * 5 / 18 = 5 mps t = 250 / 5 = 50 sec d ) 50 sec" | 5 |
the simple interest on rs . 26 for 6 months at the rate of 7 paise per rupeeper month is | [
"none",
"10.92",
"12.38",
"12.98"
] | B | "sol . s . i . = rs . [ 26 * 7 / 100 * 6 ] = rs . 10.92 answer b" | 5 |
Force times distance is the equation for what? | [
"work",
"gravity",
"speed",
"power"
] | A | Work is directly related to both the force applied to an object and the distance the object moves. It can be represented by the equation: Work = Force × Distance. | 7 |
x ^ y + y ^ x = 2408 find the values of x ? | [
"2405",
"2408",
"2407",
"2409"
] | C | 2407 ^ 1 + 1 ^ 2407 = 2408 answer : a | 5 |
Will's breakfast supplied him 900 calories of energy. Then he decided to jog for half an hour, which used up 10 calories of energy per minute. What is Will's net calorie intake after jogging? | [
"600.0",
"4490.0",
"0.0",
"-40.0"
] | A | Will jogged for 60/2 = <<60/2=30>>30 minutes.
He was able to use up 10 x 30 = <<10*30=300>>300 calories for jogging.
The net calorie intake of Will after jogging is 900 - 300 = <<900-300=600>>600.
#### 600 | 3 |
What are mid-wavelength electromagnetic waves commonly referred to as? | [
"electricity",
"x-rays",
"light",
"gamma rays"
] | C | Mid-wavelength electromagnetic waves are commonly called light. This range of electromagnetic waves has shorter wavelengths and higher frequencies than radio waves, but not as short and high as X rays and gamma rays. Light includes visible light, infrared light, and ultraviolet light. If you look back at Figure above , you can see where these different types of light waves fall in the electromagnetic spectrum. | 7 |
What do light emitters do to what you see? | [
"block frequencies",
"add frequencies",
"divide frequencies",
"subtract frequencies"
] | B | Discussions of colors can sometimes become confusing because of the difference between light emitters and light absorbers. Light absorbers, such as dyes and pigments, absorb frequencies from those that you see, while light emitters add frequencies to what you see. If I were to shine red light, green light, and blue light into your eye all at the same time, you would likely see some variation of white. If I were to mix red paint, green paint, and blue paint together, you would likely see black or some very dark color. | 7 |
Bart makes a mixtape. The first side has 6 songs. The second side has 4 songs. Each song is 4 minutes. How long is the total tape? | [
"61618.0",
"56.0",
"40.0",
"28.0"
] | C | There are 6+4=<<6+4=10>>10 songs on the tape.
In total, the time is 10*4=<<10*4=40>>40 minutes.
#### 40 | 3 |
a mixture contains alcohol and water in the ratio 4 : 3 . if 7 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture | [
"8 litres",
"15 litres",
"14 litres",
"22 litres"
] | C | "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 7 ) = 4 / 5 20 x = 4 ( 3 x + 7 ) 8 x = 28 x = 3.5 quantity of alcohol = ( 4 x 3.5 ) litres = 14 litres . answer is b ." | 5 |
in a certain circle there are 10 points . what is the number of the triangles connecting 4 points of the 10 points ? | [
"210",
"108",
"80",
"96"
] | A | "imo : e here we have to select 4 points out of 10 points . order is not important so the answer will be 10 c 4 = 210" | 5 |
What is $\frac{1}{4}\%$ of 120? Express your answer as a decimal. | [
"\\frac{3}{100}",
"0.17",
"0.003",
".3"
] | D | We have $$\frac14\%\times120=\frac{\frac14}{100}\times120=\frac{1}{400}\times120=\frac{12}{40}=\frac{3}{10}=\boxed{.3}.$$ | 4 |
60 % of the employees of a company are men . 60 % of the men in the company speak french and 50 % of the employees of the company speak french . what is % of the women in the company who do not speak french ? | [
"90 %",
"96 %",
"65 %",
"10 %"
] | C | "no of employees = 100 ( say ) men = 60 women = 40 men speaking french = 0.6 * 60 = 36 employees speaking french = 0.5 * 100 = 50 therefore women speaking french = 50 - 36 = 14 and women not speaking french = 40 - 14 = 26 % of women not speaking french = 26 / 40 * 100 = 65 % answer e" | 5 |
if x is an integer that has exactly 3 positive divisors ( these include 1 and x ) , how many positive divisors does x ^ 3 have ? | [
"8",
"7",
"5",
"6"
] | B | since factors of ' 4 ' are { 1 , 2,4 } 4 ^ 3 = 64 number of factors / divisors of 64 = 2 ^ 6 we know that when a number is expressed as a product of the prime factors as below : n = a ^ x * b ^ y * c ^ z then no . of divisors = ( x + 1 ) * ( y + 1 ) * ( z + 1 ) then here ( 6 + 1 ) = 7 answer : d | 5 |
What produces almost one-half of the earth's oxygen through photosynthesis? | [
"protists",
"algae",
"arthropods",
"prokaryotes"
] | A | Humans could not live on Earth if it were not for protists. Why? Plant-like protists produce almost one-half of the oxygen on the planet through photosynthesis. Other protists decompose and recycle nutrients that humans need to live. All protists make up a huge part of the food chain. | 7 |
Ninety-four bricks, each measuring $4''\times10''\times19'',$ are to be stacked one on top of another to form a tower 94 bricks tall. Each brick can be oriented so it contributes $4''\,$ or $10''\,$ or $19''\,$ to the total height of the tower. How many different tower heights can be achieved using all ninety-four of the bricks?
| [
"3^{94}",
"1",
"2",
"465"
] | D | We have the smallest stack, which has a height of $94 \times 4$ inches. Now when we change the height of one of the bricks, we either add $0$ inches, $6$ inches, or $15$ inches to the height. Now all we need to do is to find the different change values we can get from $94$ $0$'s, $6$'s, and $15$'s. Because $0$, $6$, and $15$ are all multiples of $3$, the change will always be a multiple of $3$, so we just need to find the number of changes we can get from $0$'s, $2$'s, and $5$'s.
From here, we count what we can get:
\[0, 2 = 2, 4 = 2+2, 5 = 5, 6 = 2+2+2, 7 = 5+2, 8 = 2+2+2+2, 9 = 5+2+2, \ldots\]
It seems we can get every integer greater or equal to four; we can easily deduce this by considering parity or using the Chicken McNugget Theorem, which says that the greatest number that cannot be expressed in the form of $2m + 5n$ for $m,n$ being positive integers is $5 \times 2 - 5 - 2=3$.
But we also have a maximum change ($94 \times 5$), so that will have to stop somewhere. To find the gaps, we can work backwards as well. From the maximum change, we can subtract either $0$'s, $3$'s, or $5$'s. The maximum we can't get is $5 \times 3-5-3=7$, so the numbers $94 \times 5-8$ and below, except $3$ and $1$, work. Now there might be ones that we haven't counted yet, so we check all numbers between $94 \times 5-8$ and $94 \times 5$. $94 \times 5-7$ obviously doesn't work, $94 \times 5-6$ does since 6 is a multiple of 3, $94 \times 5-5$ does because it is a multiple of $5$ (and $3$), $94 \times 5-4$ doesn't since $4$ is not divisible by $5$ or $3$, $94 \times 5-3$ does since $3=3$, and $94 \times 5-2$ and $94 \times 5-1$ don't, and $94 \times 5$ does.
Thus the numbers $0$, $2$, $4$ all the way to $94 \times 5-8$, $94 \times 5-6$, $94 \times 5-5$, $94 \times 5-3$, and $94\times 5$ work. That's $2+(94 \times 5 - 8 - 4 +1)+4=\boxed{465}$ numbers. | 4 |
March in the northern hemisphere is what in the southern hemisphere? | [
"Spring",
"Summer",
"Winter",
"Fall"
] | D | winter in the Northern Hemisphere is during the summer in the Southern Hemisphere | 6 |
Some flowers are unable to get enough sunlight because trees hover over them and do what to it | [
"sing to it",
"nothing",
"sell it",
"intercept it"
] | D | if a tree falls then sunlight becomes available to the surrounding plants | 6 |
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