12 GMAT Quant Questions Solved from the MBA House Video

Correct answer: 23

Step by step: convert the average gap into a total gap. Paul's average is 3 points higher over 3 tests, so Paul's total is 3 × 3 = 9 points higher than Ada's total. On test 1, Paul is 10 lower; on test 2, Paul is 4 lower. Let x be how many points Paul is higher on test 3. Summing the differences (Paul − Ada) gives −10 − 4 + x = 9, so x = 23.

GMAT takeaway: a difference in averages over n items equals n times the per-item gap when applied to the total. Track one person minus the other across all items and set the sum equal to that total gap.

Correct answer: 13

Step by step: evaluate each custom operation from the inside out. For the first term, 98 ◇ 33 = 32 because 98 = 2(33) + 32, then 32 ◇ 17 = 15 because 32 = 1(17) + 15. For the second term, 33 ◇ 17 = 16 because 33 = 1(17) + 16, then 98 ◇ 16 = 2 because 98 = 6(16) + 2. The expression equals 15 − 2 = 13.

GMAT takeaway: a defined-operator symbol is just a rule — substitute the definition and respect the parentheses. Remainders are not associative, so ((a ◇ b) ◇ c) need not equal (a ◇ (b ◇ c)).

Correct answer: 25 min

Step by step: track only the minutes past the hour, since every flight schedule repeats. If the first flight leaves A on the hour (at :00), it arrives at B 2 1/2 hours later, at :30. B flights leave every 20 minutes (at :00, :20, :40), so the next B flight after :30 is at :40 — a wait of 10 minutes at B. The B-to-C flight lasts 1 5/6 hours = 1 hour 50 minutes, so a :40 departure reaches C at :30. C flights leave at :45 each hour, so the wait at C is 15 minutes. Total waiting time is 10 + 15 = 25 minutes.

GMAT takeaway: for repeating-schedule problems, work modulo the hour and only care about minutes past the hour. Add each leg's duration to the departure minute, then find the next scheduled departure to get the wait.

Correct answer: 2

Step by step: a positive integer has exactly three positive factors only when it is the square of a prime — its factors are 1, the prime, and the prime squared. Between 1 and 16, the prime squares are 2² = 4 (factors 1, 2, 4) and 3² = 9 (factors 1, 3, 9). The next prime square, 5² = 25, is out of range, and 16 = 2⁴ has five factors, not three. So there are 2 such integers.

GMAT takeaway: the count of factors comes from the prime factorization: an integer has exactly three factors precisely when it is a prime squared. Memorize that "exactly 3 factors ⇔ p²."

Correct answer: A = {5, 7, 9}, B = {1, 5, 7}

Step by step: first narrow x by the "5-digit" and "units digit 5" conditions. Since 3,305 × 1, × 2, and × 3 give only 4-digit numbers (3,305; 6,610; 9,915), x must be at least 4. Because 3,305 ends in 5, multiplying by an even digit gives a product ending in 0, not 5, so x cannot be 4, 6, or 8. That leaves x ∈ {5, 7, 9}, so A = {5, 7, 9}. Now compute the products to read the hundreds digit: 3,305 × 5 = 16,525 (hundreds digit 5), 3,305 × 7 = 23,135 (hundreds digit 1), and 3,305 × 9 = 29,745 (hundreds digit 7). So B = {1, 5, 7}, giving A = {5, 7, 9}, B = {1, 5, 7}.

GMAT takeaway: use digit conditions to prune before you compute. The units digit of a product depends only on the units digits of the factors, and multiplying a number ending in 5 by an even digit always ends in 0.

Correct answer: 2

Step by step: round every number to something clean. Estimate 39,897 ≈ 40,000, 0.0096 ≈ 0.01, and 198.76 ≈ 200. Then (40,000)(0.01) / 200 = 400 / 200 = 2. Because the answer choices are spread by factors of ten, this rough estimate is more than precise enough to pick 2.

GMAT takeaway: when answer choices differ by orders of magnitude, estimate aggressively. Rounding to one significant figure keeps the arithmetic trivial and still lands on the correct power of ten.

Correct answer: −22

Step by step: translate the sentence phrase by phrase. "2 subtracted from 5x" is 5x − 2; "1/2 the result" is (1/2)(5x − 2); "the sum of 10 and 3x" is 10 + 3x. So (1/2)(5x − 2) = 10 + 3x. Multiply both sides by 2: 5x − 2 = 20 + 6x. Subtract 5x from both sides: −2 = 20 + x. Subtract 20: x = −22.

GMAT takeaway: build the equation left to right exactly as the sentence reads, and keep "subtracted from" in the right order (a subtracted from b is b − a). Clear the fraction first, then isolate x.

Correct answer: 0.03

Step by step: evaluate the left side, then undo the percent. 3 / 10⁴ = 3 / 10,000 = 0.0003. The "%" means divide by 100, so x% = x / 100. Setting x / 100 = 0.0003 gives x = 0.0003 × 100 = 0.03.

GMAT takeaway: "x%" always means x / 100, so solving for x means multiplying the decimal value by 100. Do not confuse the decimal (0.0003) with x itself.

Correct answer: 620

Step by step: factor each candidate and add the prime factors with repetition. 440 = 2³ × 5 × 11, prime sum 2 + 2 + 2 + 5 + 11 = 22. 512 = 2⁹, prime sum 9 × 2 = 18. 620 = 2² × 5 × 31, prime sum 2 + 2 + 5 + 31 = 40. 700 = 2² × 5² × 7, prime sum 2 + 2 + 5 + 5 + 7 = 21. 750 = 2 × 3 × 5³, prime sum 2 + 3 + 5 + 5 + 5 = 20. Only 620 exceeds 35, so the answer is 620.

GMAT takeaway: a large prime factor makes the prime sum jump. Watch for candidates like 620 = 2² × 5 × 31, where the single factor 31 already almost reaches the threshold.

Correct answer: 3

Step by step: convert the rate to milliliters per second. One hour has 3,600 seconds, so 1,200 milliliters per hour is 1,200 / 3,600 = 1/3 milliliter per second. If 1/3 milliliter leaks each second, then the time for 1 milliliter is the reciprocal of the rate: 1 ÷ (1/3) = 3 seconds.

GMAT takeaway: when a question asks "how long for one unit," take the reciprocal of the rate expressed in units-per-time. Convert the time unit first (hours to seconds) so the rate matches the answer's units.

Correct answer: 0

Step by step: write each term in place value. AB = 10A + B and BA = 10B + A, so their sum is 11A + 11B. The three-digit number AAC = 100A + 10A + C = 110A + C. Set them equal: 11A + 11B = 110A + C, which rearranges to 11B = 99A + C. Since B is a single digit, the left side is at most 11 × 9 = 99, so A must be 1 (A = 0 is impossible for a leading digit). Then 11B = 99 + C. The only digit solution is B = 9 and C = 0, because 11 × 9 = 99 forces C = 0. All three digits (A = 1, B = 9, C = 0) are different, so AAC = 110 and the units digit is 0.

GMAT takeaway: convert letter-digit puzzles to place-value algebra (AB = 10A + B). Bounding one variable by "it is a single digit" usually pins down the leading digit fast.

Correct answer: $700

Step by step: find the selling price first, then work back to the retail price. A 12% profit on the $500 wholesale price is 0.12 × 500 = $60, so the selling price was 500 + 60 = $560. The dealer sold at a 20% discount off the suggested retail price, so the selling price is 80% of the retail price R: 0.8R = 560. Solving, R = 560 / 0.8 = $700.

GMAT takeaway: anchor each percent to its stated base — profit is a percent of wholesale cost, while the discount is a percent of retail price. Compute the concrete selling price, then divide by (1 − discount) to recover the retail price.