q: A certain car uses 12 gallons of gasoline in traveling 180 miles. In order for the car to travel the same distance using 10 gallons of gasoline, by how many miles per gallon must the car’s gas mileage be increased?
Options:
(A) 2
(B) 3
(C) 6
(D) 8
(E) 10
a: Stream of consciousness: 180/10 = 18. The difference is 18 - 15 = 3. The answer is (B).


question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 2134
(B) 2245
(C) 3450
(D) 4500
(E) 5184
answer: Stream of consciousness: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62 The answer is (E).


q: You have a flashlight that takes 2 working batteries. You have 8 batteries but only 4 of them work.
What is the fewest number of pairs you need to test to guarantee you can get the flashlight on?
Options:
(A) 5
(B) 8
(C) 7
(D) 6
(E) 4
a: Stream of consciousness: If you break the batteries into 3 groups: Two groups of 3 and one group of 2. By doing this you guarantee that one of the groups has 2 working batteries. Both of the groups of 3 have 3 possible combinations of 2 batteries and the group of 2 only has 1 combination. So, 3 + 3 + 1 = 7 tries at most to find two working batteries. The answer is (C).


question: The ratio of men to women in the Snyder community choir is 4 to 5. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many women are in the Snyder choir?
Options:
(A) 20
(B) 24
(C) 30
(D) 32
(E) 34
answer: Stream of consciousness: Use simultaneous equations / By combination
4x = 5y + 4
5x = 6y + 6
Multiply (1) by 6
Multiply (2) by -5
Get rid of y, and x = 6
Then 5x = 30 The answer is (C).


q: The purchase price of an article is $48. In order to include 10% of cost for overhead and to provide $12 of net profit, the markup should be
Options:
(A) 15%
(B) 25%
(C) 35%
(D) 40%
(E) 45%
a: Stream of consciousness: Cost price of article = 48$
% of overhead cost = 10
Net profit = 12 $
We need to calculate % markup
Net profit as % of cost price = (12/48)*100 = 25%
Total markup should be = 25 + 10 = 35% The answer is (C).


q: What is the greatest positive integer x such that 5^x is a factor of 125^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
a:
Stream of consciousness: 125^10 = (5^3)^10 = 5^30 The answer is (E).
q: A certain car uses 12 gallons of gasoline in traveling 180 miles. In order for the car to travel the same distance using 10 gallons of gasoline, by how many miles per gallon must the car’s gas mileage be increased?
Options:
(A) 2
(B) 3
(C) 6
(D) 8
(E) 10
a: Stream of consciousness: 180/10 = 18. The difference is 18 - 15 = 3. The answer is (B).


question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 2134
(B) 2245
(C) 3450
(D) 4500
(E) 5184
answer: Stream of consciousness: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62 The answer is (E).


q: You have a flashlight that takes 2 working batteries. You have 8 batteries but only 4 of them work.
What is the fewest number of pairs you need to test to guarantee you can get the flashlight on?
Options:
(A) 5
(B) 8
(C) 7
(D) 6
(E) 4
a: Stream of consciousness: If you break the batteries into 3 groups: Two groups of 3 and one group of 2. By doing this you guarantee that one of the groups has 2 working batteries. Both of the groups of 3 have 3 possible combinations of 2 batteries and the group of 2 only has 1 combination. So, 3 + 3 + 1 = 7 tries at most to find two working batteries. The answer is (C).


question: The ratio of men to women in the Snyder community choir is 4 to 5. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many women are in the Snyder choir?
Options:
(A) 20
(B) 24
(C) 30
(D) 32
(E) 34
answer: Stream of consciousness: Use simultaneous equations / By combination
4x = 5y + 4
5x = 6y + 6
Multiply (1) by 6
Multiply (2) by -5
Get rid of y, and x = 6
Then 5x = 30 The answer is (C).


q: The purchase price of an article is $48. In order to include 10% of cost for overhead and to provide $12 of net profit, the markup should be
Options:
(A) 15%
(B) 25%
(C) 35%
(D) 40%
(E) 45%
a: Stream of consciousness: Cost price of article = 48$
% of overhead cost = 10
Net profit = 12 $
We need to calculate % markup
Net profit as % of cost price = (12/48)*100 = 25%
Total markup should be = 25 + 10 = 35% The answer is (C).


q: What is the greatest positive integer x such that 5^x is a factor of 125^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
a:
user
Stream of consciousness: 125^10 = (5^3)^10 = 5^30 The answer is (E).
assistant
q: A certain car uses 12 gallons of gasoline in traveling 180 miles. In order for the car to travel the same distance using 10 gallons of gasoline, by how many miles per gallon must the car’s gas mileage be increased?
Options:
(A) 2
(B) 3
(C) 6
(D) 8
(E) 10
a: Stream of consciousness: 180/10 = 18. The difference is 18 - 15 = 3. The answer is (B).


question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 2134
(B) 2245
(C) 3450
(D) 4500
(E) 5184
answer: Stream of consciousness: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62 The answer is (E).


q: You have a flashlight that takes 2 working batteries. You have 8 batteries but only 4 of them work.
What is the fewest number of pairs you need to test to guarantee you can get the flashlight on?
Options:
(A) 5
(B) 8
(C) 7
(D) 6
(E) 4
a: Stream of consciousness: If you break the batteries into 3 groups: Two groups of 3 and one group of 2. By doing this you guarantee that one of the groups has 2 working batteries. Both of the groups of 3 have 3 possible combinations of 2 batteries and the group of 2 only has 1 combination. So, 3 + 3 + 1 = 7 tries at most to find two working batteries. The answer is (C).


question: The ratio of men to women in the Snyder community choir is 4 to 5. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many women are in the Snyder choir?
Options:
(A) 20
(B) 24
(C) 30
(D) 32
(E) 34
answer: Stream of consciousness: Use simultaneous equations / By combination
4x = 5y + 4
5x = 6y + 6
Multiply (1) by 6
Multiply (2) by -5
Get rid of y, and x = 6
Then 5x = 30 The answer is (C).


q: The purchase price of an article is $48. In order to include 10% of cost for overhead and to provide $12 of net profit, the markup should be
Options:
(A) 15%
(B) 25%
(C) 35%
(D) 40%
(E) 45%
a: Stream of consciousness: Cost price of article = 48$
% of overhead cost = 10
Net profit = 12 $
We need to calculate % markup
Net profit as % of cost price = (12/48)*100 = 25%
Total markup should be = 25 + 10 = 35% The answer is (C).


q: What is the greatest positive integer x such that 5^x is a factor of 125^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
a:
Stream of consciousness: 125^10 = (5^3)^10 = 5^30 The answer is (E).