GMAT Quant Questions Explained: 15 Problems from the Video

1. "Last year Shannon listened to a certain public radio station…" (unit conversion)

"Last year Shannon listened to a certain public radio station 10 hours per week and contributed $35 to the station. Of the following, which is closest to Shannon's contribution per minute of listening time last year?"

• $0.001
• $0.010
• $0.025
• $0.058
• $0.067

Correct answer: $0.001

Step by step: convert everything to minutes before dividing. 10 hours per week × 52 weeks = 520 hours in the year. 520 × 60 = 31,200 minutes of listening. Now divide the contribution by the minutes: $35 ÷ 31,200 ≈ $0.00112 per minute, which is closest to $0.001.

GMAT takeaway: convert all units before dividing. The GMAT often hides an easy ratio inside a chain of hours, weeks, and minutes — line up the units first and the arithmetic becomes trivial.

2. "Pat invested x dollars in a fund that paid 8 percent annual interest…" (compound interest)

"Pat invested x dollars in a fund that paid 8 percent annual interest, compounded annually. Which of the following represents the value, in dollars, of Pat's investment plus interest at the end of 5 years?"

Correct answer: x(1.08)⁵

Step by step: "compounded annually" means the balance is multiplied by 1.08 once each year. After year 1 it is x(1.08), after year 2 it is x(1.08)², and after 5 years it is x(1.08)⁵. Do not use the simple-interest form x(1 + 5 × 0.08) = x(1.40); that under-counts the interest earned on prior interest.

GMAT takeaway: compound interest is repeated multiplication (multiply by 1 + rate once per period); simple interest is a single linear add-on. Read the word "compounded" as your signal to use an exponent.

3. "Terry needs to purchase some pipe for a plumbing job…" (cutting and packing)

"Terry needs pipe lengths of 1 ft 4 in, 2 ft 8 in, 3 ft 4 in, 3 ft 8 in, 4 ft 8 in, 5 ft 8 in, and 9 ft 4 in. The store sells pipe only in 10-ft lengths. If each 10-ft length can be cut into shorter pieces, what is the minimum number of 10-ft pipe lengths Terry needs? (Note: 1 ft = 12 in.)"

• 3
• 4
• 5
• 6
• 7

Correct answer: 4

Step by step: convert every length to inches: 16, 32, 40, 44, 56, 68, and 112 inches. One 10-ft pipe is 120 inches. The total needed is 16 + 32 + 40 + 44 + 56 + 68 + 112 = 368 inches, so you need at least ⌈368 ÷ 120⌉ = 4 pipes. Now prove 4 actually works by packing the pieces into four 120-inch pipes: 112; 68 + 44 = 112; 56 + 40 + 16 = 112; and 32 alone. Every piece fits, so the minimum is 4.

GMAT takeaway: for cutting and packing problems, get a lower bound from the total length (divide and round up), then confirm the bound is achievable by exhibiting one valid packing. A lower bound alone is not enough — you must show it can be met.

4. "Consider the following set of inequalities…" (inequality chains)

"Consider the following set of inequalities: p > q, s > r, q > t, s > p, and r > q. Between which two quantities is no relationship established?"

• p and r
• s and t
• s and q
• p and t
• r and t

Correct answer: p and r

Step by step: build the chains. From p > q > t and s > p, you get s > p > q > t. From r > q > t and s > r, you get s > r > q > t. So s sits above both p and r, and both p and r sit above q and t — that settles s vs t, s vs q, p vs t, and r vs t. But nothing forces an order between p and r: p could be larger or r could be larger. So p and r have no established relationship.

GMAT takeaway: chain the inequalities into ordered strings and compare only what is forced. Two quantities on separate branches below a common top are not automatically comparable.

5. "If 3^x minus 3^(x-1) equals 162…" (exponent factoring)

"If 3^x − 3^(x−1) = 162, then x(x − 1) = ?"

• 12
• 16
• 20
• 30
• 81

Correct answer: 20

Step by step: factor out the smaller power. 3^x − 3^(x−1) = 3^(x−1)(3 − 1) = 2 × 3^(x−1). Set that equal to 162: 2 × 3^(x−1) = 162, so 3^(x−1) = 81 = 3⁴. Therefore x − 1 = 4, giving x = 5, and x(x − 1) = 5 × 4 = 20.

GMAT takeaway: when exponential terms are added or subtracted, factor out the common (smallest) power instead of guessing values. That turns the equation into a clean single power you can match by inspection.

6. "The expression n! is defined as the product of the integers…" (factorial cancellation)

"The expression n! is defined as the product of the integers from 1 through n. If p is the product of the integers from 100 through 299 and q is the product of the integers from 200 through 299, which of the following is equal to p/q?"

• 99!
• 199!
• 199!/99!
• 299!/99!
• 299!/199!

Correct answer: 199!/99!

Step by step: write the products before expanding. p = 100 × 101 × … × 199 × 200 × … × 299, and q = 200 × … × 299. When you divide, the entire block 200 × … × 299 cancels, leaving p/q = 100 × 101 × … × 199. That partial product is 199! (all integers 1 through 199) divided by 99! (removing 1 through 99), so p/q = 199!/99!.

GMAT takeaway: factorial questions are cancellation problems. Write each product as a range, line up the overlapping factors, and cancel — never try to compute the giant numbers.

7. "38, 69, 22, 73, 31, 47, 13, 82…" (order statistics and percentile language)

"38, 69, 22, 73, 31, 47, 13, 82. Which of the following numbers is greater than three-fourths of the numbers but less than one-fourth of the numbers in the list above?"

• 56
• 6
• 69
• 71
• 77

Correct answer: 71

Step by step: sort the list first: 13, 22, 31, 38, 47, 69, 73, 82 (eight values). "Greater than three-fourths of the numbers" means greater than 3/4 × 8 = 6 of them, so the value must exceed the 6th-smallest, which is 69. "Less than one-fourth of the numbers" means less than 1/4 × 8 = 2 of them, so it must be below the top two values, 73 and 82. A number greater than 69 but less than 73 is 71.

GMAT takeaway: translate percentile and rank language into counts. Sort the list, turn "three-fourths of" and "one-fourth of" into how many values, and read off the gap.

8. "In a certain medical survey, 45 percent of the people surveyed…" (conditional percentage)

"In a certain medical survey, 45 percent of the people surveyed had the type A antigen in their blood and 3 percent had both the type A antigen and the type B antigen. Which is closest to the percent of those with the type A antigen who also had the type B antigen?"

• 1.35%
• 6.67%
• 13.50%
• 15.00%
• 42.00%

Correct answer: 6.67%

Step by step: the phrase "of those with the type A antigen" tells you to condition on the type A group, so divide the overlap by the A group: 3% ÷ 45% = 3/45 = 1/15 ≈ 0.0667 = 6.67%.

GMAT takeaway: "of those with A" means the A group is your denominator. Conditional percentage is the overlap divided by the group you are conditioning on — not by the whole population.

9. "If the average arithmetic mean of x, y, and z is 7x…" (arithmetic mean and ratio)

"If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0, what is the ratio of x to the sum of y and z?"

• 1:21
• 1:20
• 1:6
• 6:1
• 20:1

Correct answer: 1:20

Step by step: clear the denominator first. The mean is (x + y + z)/3 = 7x, so x + y + z = 21x. Subtract x from both sides: y + z = 20x. Therefore x : (y + z) = x : 20x = 1 : 20.

GMAT takeaway: "average" means total divided by count, so multiply through by the count to clear the fraction before you do anything else. Then isolate the sum the question actually asks about.

10. "If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + 1/4 a…" (fraction arithmetic)

"If a = 1 + 1/4 + 1/16 + 1/64 and b = 1 + (1/4)a, then what is the value of a − b?"

• -85/256
• -1/256
• -1/4
• 125/256
• 169/256

Correct answer: -1/256

Step by step: put a over a common denominator: a = 64/64 + 16/64 + 4/64 + 1/64 = 85/64. Then b = 1 + (1/4)(85/64) = 1 + 85/256 = 341/256. Convert a to 256ths: a = 85/64 = 340/256. Subtract: a − b = 340/256 − 341/256 = -1/256.

GMAT takeaway: with stacked fraction expressions, commit to one common denominator and watch the parentheses — (1/4)a multiplies the whole of a, not just its first term.

11. "When the positive integer k is divided by the positive integer n…" (remainders from a decimal quotient)

"When the positive integer k is divided by the positive integer n, the remainder is 11. If k/n = 81.2, what is the value of n?"

• 9
• 20
• 55
• 70
• 81

Correct answer: 55

Step by step: a quotient of 81.2 means k = 81.2n = 81n + 0.2n. In division language, 81n is the integer-quotient part and 0.2n is the remainder. The remainder is given as 11, so 0.2n = 11, which gives n = 11 ÷ 0.2 = 55. (Check: 0.2 × 55 = 11.)

GMAT takeaway: a decimal quotient splits into an integer quotient plus (remainder ÷ n). The fractional part of the quotient, times the divisor, equals the remainder — set that equal to the given remainder and solve.

12. "If the amount of federal estate tax due on an estate valued…" (tiered tax percent)

"If the amount of federal estate tax due on an estate valued at $1.35 million is $437,000 plus 43 percent of the value of the estate in excess of $1.25 million, then the federal tax due is approximately what percent of the value of the estate?"

• 30%
• 35%
• 40%
• 45%
• 50%

Correct answer: 35%

Step by step: handle the excess portion first. The value in excess of $1.25 million is $1.35M − $1.25M = $0.10 million = $100,000. Then 43% of $100,000 = $43,000. Total tax = $437,000 + $43,000 = $480,000. As a percent of the full estate, $480,000 ÷ $1,350,000 ≈ 0.356 = 35.6%, closest to 35%.

GMAT takeaway: for tiered tax or fee problems, compute the marginal (excess) portion separately, add the fixed base, then divide by the full base the question asks about. Do not apply the marginal rate to the whole amount.

13. "If a certain coin is flipped, the probability that the coin will land heads up…" (independent-event probability)

"If a certain coin is flipped, the probability that the coin will land heads up is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?"

• 3/5
• 1/2
• 1/3
• 1/8
• 1/32

Correct answer: 1/32

Step by step: the question fixes one exact sequence — H, H, H, T, T. Each flip is independent with probability 1/2, so multiply: (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = (1/2)⁵ = 1/32. There is no "choose" multiplier because the order is specified, not free.

GMAT takeaway: when the order of outcomes is specified, just multiply the individual probabilities. Bring in combinations only when the successes can occur in any order.

14. "David and Ron are ordering food for a business lunch…" (system of equations)

"David and Ron are ordering food for a business lunch. David thinks there should be twice as many sandwiches as pastries, but Ron thinks the number of pastries should be 12 more than one-fourth of the number of sandwiches. How many sandwiches should be ordered so David and Ron can agree on the number of pastries?"

• 12
• 16
• 20
• 24
• 48

Correct answer: 48

Step by step: let S be sandwiches and P be pastries, and turn each person's sentence into an equation. David: S = 2P, so P = S/2. Ron: P = 12 + S/4. They agree when the two expressions for P are equal: S/2 = 12 + S/4. Subtract S/4 from both sides: S/4 = 12, so S = 48. (Check: David gives P = 24; Ron gives 12 + 12 = 24.)

GMAT takeaway: translate each person's sentence into its own equation for the shared quantity, then set the two definitions equal. "Agree on the number of pastries" is the signal to equate the two expressions for P.

15. "At a garage sale, all of the prices of the items sold were different…" (rank counting)

"At a garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both the 15th highest price and the 20th lowest price among the prices of the items sold, how many items were sold at the garage sale?"

• 33
• 34
• 35
• 36
• 37

Correct answer: 34

Step by step: "15th highest" means 14 items priced higher than the radio. "20th lowest" means 19 items priced lower. Because all prices are distinct, count the higher items, the radio itself, and the lower items with no overlap: 14 + 1 + 19 = 34.

GMAT takeaway: for rank questions with distinct values, total = (items above) + 1 (the item itself) + (items below). Convert each ordinal rank into a count of items on that side, then add the middle item exactly once.