All The Quant

Question 1

The price of a cup of coffee increased from 80 cents to 84 cents. By what percent did the price change?

Answer 1

See: change

Do: percent change = change in value / original value

x/100 = 4/80
x/100 = 1/20
20x = 100
x = 5

Question 2

If the price of a $30 shirt is decreased by 20%, what is the final price of the shirt?

Answer 2

See: decreased by

Do: new percent (of the original) = new value / original value

80/100 = x/30
4/5 x 30 = x
24 = x

Question 3

What number is 50% greater than 60?

Answer 3

See: 50% greater than means 150%

Do: x = 150% x 60
x = 3/2 x 60
x = 90

Question 4

If a ticket increased in price by 20%, and then increased again by 5%, by what percent did the ticket price increase in total?

Answer 4

See: increase x2 (separate increases)

Do: Smart numbers

Ticket original price: 100
100 + 100 * 20% = 20 so new total = 120
120 + 120 * 5% = 126

Question 5

If 1,500 is increased by 20% and then reduced by y%, yielding 1,080, what is y?

Answer 5

See: increased by and reduced by…
(original number - {x%/100 * original number} = reduced number)

Do: 1500 * 120% = 1800 ..now to find y

1800 - (y/100 * 1800) = 1080
1800 - 1800y/100 = 1080
1800 - 1080 = 1800y/100
720 = 18y
40 = y

Question 6

What is 10/22 of 5/18 of 2000?

Answer 6

See: opportunity to estimate, close to nicer fractions

Do: 10/22 is a bit less than 1/2 , 5/18 is a bit more than 1/4

1/2 of 1/4 of 2000 = 250 therefore the answer is approx. 250
(think of rounding up or down to balance each other)

Question 7

Is c = d?

(1) cd = 1
(2) |c| = d

Answer 7

See: DS Y/N question
theory problem (|x|)
only variables

Think: Test numbers (negative and positive)

Question 8

Answer 8

See: Problem Solving
Contains variables with no real numbers
Profit
Answers in Terms of x

Think: Smart Numbers, avoid 0 and 1
Profit = Revenue - Cost

Do: Choose Smart Numbers, solve.
Plug x smart number into AC to find the answer I solved for

Question 9

Answer 9

See: “must”, variables, >0

Think: testing a must theory, testing cases, negative and positive

Do: Solve with one test both negative and one test both positive for each AC

Question 10

Answer 10

See: PS with percentages in answers, no real values given

Think: Smart numbers, avoid 0 and 1
Since % problem, use 100

Do: Solve starting with $100

Question 11

Answer 11

See: Problem Solving, variables in the answers, no real numbers

Think: Smart numbers

Question 12

Answer 12

See: PS with “must” theory language, variables
Exponents, >0

Think: Test Cases… test negatives, fractions between 0 and 1, and 0 and 1 themselves

Solve: make chart to keep AC’s organized

Question 13

Answer 13

See: Percents problem, answers are close together so estimation not a good choice.

Think: percent change formula (change in value / original value * 100%) - typical being original.

Solve: Calculate typical dose per 120 pounds then apply percent change formula

Question 14

Answer 14

See: a^2 + b^2 as a special product

Think: a^2 + b^2 = (a+b)(a-b)

Solve.

Question 15

Answer 15

See: Area (this is a formula question), the potential 3-4-5 triangle at origin

Think: A = 1/2(bXh)

Question 16

Answer 16

See: absolute value and an inequality

Think: two solutions, one negative one positive

Question 17

What number is 108 more than two-thirds of itself?

(A) 72
(B) 144
(C) 162
(D) 216
(E) 324

Answer 17

See: A/Cs that are spread apart. The fact that I don’t understand the question

Think: Work backwards

Solve: Divide each number by /3 then multiply by 2 then 108, are the numbers the same? (E)

Question 18

Answer 18

See: only variables, and variables in the answer choices

Think: Smart Numbers to get the variable then put variable in answer choices until I see my answer

Question 19

Answer 19

Proportions not real numbers!!!

Question 20

Answer 20

Question 21

Answer 21

Question 22

Answer 22