13 GMAT Quant Questions Solved from the MBA House Class

Correct answer: 35

Step by step: let n, d, q, and h be the numbers of nickels, dimes, quarters, and half-dollars. The three "totals" give n + d = 35, d + q = 45, and n + q = 50. Add all three equations: 2n + 2d + 2q = 130, so n + d + q = 65. Since there are 100 coins in all, h = 100 − 65 = 35.

GMAT takeaway: when three pairwise sums are given, adding them all counts each variable twice — divide by 2 to get the combined total in one step, instead of solving for each variable separately.

Correct answer: I and II only

Step by step: if x − y is odd, then x and y have opposite parity — one is even and the other is odd. I: the product of an even and an odd integer is even, so xy is even (true). II: the square of an even integer is even and the square of an odd integer is odd, so x² + y² = even + odd = odd (true). III: x + y is even + odd = odd, and the square of an odd integer is odd, so (x + y)² is odd, not even (false). Only I and II must be true.

GMAT takeaway: "x − y is odd" is code for "opposite parity." Track even/odd through products and squares (even² is even, odd² is odd) instead of plugging in numbers blindly.

Correct answer: (m − v − 1)/2

Step by step: since v is odd and m is even, the even integers strictly between them begin at v + 1 (the first even number above an odd v) and end at m − 2 (the first even number below an even m). These form an arithmetic sequence with common difference 2, so the count is ((m − 2) − (v + 1))/2 + 1 = (m − v − 3)/2 + 1 = (m − v − 1)/2. Sanity check with m = 8, v = 3: even integers 4 and 6 give a count of 2, and (8 − 3 − 1)/2 = 2. ✓

GMAT takeaway: for evenly spaced counting, use (last − first)/step + 1. Nail down the first and last terms carefully using the parity of the endpoints, then test with small numbers.

Correct answer: 23

Step by step: subtract the first-mile charge: 62.55 − 4.25 = 58.30. Divide by the per-unit rate: 58.30 / 2.65 = 22, so the fare covers the first mile plus 22 additional charged "mile or fraction" units. Because each additional mile or fraction thereof is billed as a full unit, the 22nd unit may represent only a partial mile — the actual distance can be as much as one full mile beyond the 22 complete miles. So the trip was at most 1 + 22 = 23 miles.

GMAT takeaway: "or fraction thereof" signals a ceiling function: you round up to the next whole unit. Separate the flat first-mile charge before dividing, then remember the last unit can be a fraction when the question asks for the maximum distance.

Correct answer: 34

Step by step: four numbers averaging 10 have a total of 4 × 10 = 40. Since 2 is one of them, x + y + z = 38. To make z as large as possible, make x and y as small as possible while keeping all four values different positive integers. The smallest available values (2 is taken) are 1 and 3. Then z = 38 − 1 − 3 = 34.

GMAT takeaway: to maximize one term under a fixed sum, minimize every other term. Honor the constraints — here "different positive integers" forces you to skip 2 and pick 1 and 3.

Correct answer: 6

Step by step: three numbers averaging 3 have a total of 3 × 3 = 9. To maximize z, minimize x and y while keeping them positive integers with x < y < z. The smallest strictly increasing positive integers are x = 1 and y = 2. Then z = 9 − 1 − 2 = 6 (and indeed 1 < 2 < 6). ✓

GMAT takeaway: same tool as the previous problem — fixed sum, maximize one term by minimizing the others. The strict inequality x < y < z just forces distinct increasing values, so use 1 and 2.

Correct answer: 0

Step by step: the expression is 1/x minus x/y, so to maximize it you want the first term large and the subtracted term small. To make 1/x large, take the smallest allowed x: x = 3. For that x, to make x/y small, take the largest allowed y: y = 9. Then 1/x − x/y = 1/3 − 3/9 = 1/3 − 1/3 = 0. Any larger x shrinks 1/x and grows x/y, so nothing beats 0.

GMAT takeaway: to maximize a difference, push the added part up and the subtracted part down — but do it consistently. Once you commit to x = 3, choose the y that helps the second term, rather than optimizing each fraction in isolation.

Correct answer: −2

Step by step: test integer values of k near the cutoff. If k = −1, then 32.45 × 10⁻¹ = 3.245, which is greater than 1 — too big. If k = −2, then 32.45 × 10⁻² = 0.3245, which is less than 1. Making k more negative only shrinks the value further, so the greatest k that still keeps the product below 1 is −2.

GMAT takeaway: multiplying by 10^k just slides the decimal point. For "greatest k" questions, find the boundary by testing consecutive integers rather than solving with logarithms.

Correct answer: (y + z)/x

Step by step: the setup gives two facts: x is a factor of y, so y/x is an integer; x is a multiple of z, so x/z is an integer. Test each choice. (x + z)/z = x/z + 1 — integer. (x + y)/z = x/z + y/z, and y/z = (y/x)(x/z) is a product of integers, so integer. xy/z = y·(x/z) — integer. yz/x = z·(y/x) — integer. But (y + z)/x = y/x + z/x, and z/x need not be an integer since x is a multiple of z, not the other way around. Counterexample: x = 6, y = 6, z = 2 gives (6 + 2)/6 = 8/6, not an integer. So the answer is (y + z)/x.

GMAT takeaway: translate "factor/multiple" into which ratios are integers (y/x and x/z here), then rewrite each option in terms of those known ratios. A single clean counterexample confirms the odd one out.

Correct answer: 936

Step by step: convert the area unit, not the length unit. Since 1 foot = 12 inches, 1 square foot = 12 × 12 = 144 square inches. The area is 6 1/2 = 6.5 square feet, so 6.5 × 144 = 936 square inches.

GMAT takeaway: when converting areas, square the linear conversion factor (12 → 144). Forgetting to square it is the trap that produces the wrong answer 78 (6.5 × 12).

Correct answer: $2,000

Step by step: this is a stacked bar chart, so read only the stocks segment and ignore the other investment types stacked above or below it. In 2000 the stocks portion is $3,000; in 2003 the stocks portion is $5,000. The increase is 5,000 − 3,000 = $2,000.

GMAT takeaway: on stacked-bar graph questions, isolate the single series the question names. Don't read the total height of the bar — read the thickness of the one segment being asked about.

Correct answer: II and III only

Step by step: "24 divided by n leaves remainder 4" means 24 = qn + 4 for some integer quotient q, so qn = 20 — meaning n is a divisor of 20. Also the remainder must be smaller than the divisor, so n > 4. The divisors of 20 that exceed 4 are 5, 10, and 20. Check each statement against {5, 10, 20}: I. n is even — fails, because n could be 5. II. n is a multiple of 5 — true for 5, 10, and 20. III. n is a factor of 20 — true by construction. So II and III only.

GMAT takeaway: convert "remainder r when dividing D" into D − r = qn, so n divides D − r, and always add the hidden constraint n > r. List the finite candidate set, then test each "must be true" statement against every candidate.

Correct answer: $550

Step by step: let H, M, and P be the costs of the hard drive, monitor, and printer. Two facts: P + M = (2/3)H and H + P + M = 2,500. Substitute the first into the second: H + (2/3)H = 2,500, so (5/3)H = 2,500 and H = 1,500. Then P + M = 2,500 − 1,500 = 1,000. The printer costs $100 more than the monitor, so P = M + 100. Substituting: (M + 100) + M = 1,000, giving 2M = 900, M = 450, and P = 450 + 100 = $550.

GMAT takeaway: reduce a three-variable word problem by substitution — use the "part equals a fraction of the whole" relationship to solve for one variable first (here H), then split the remaining total with the "$100 more" condition.