Quant practice set 1
Twelve generated questions in the GMAT Problem Solving format, in three batches of four. Each question hides behind its own button: click to reveal it and start its clock; click an answer and the clock stops. Nothing else is live while you work, exactly like the test.
How to run this set
Start by pressing a question's button when you are ready for it: the question appears and its clock starts. One click on an answer stops the clock, writes your time into the question's header, and wakes the next button. One question at a time mirrors the real test, which is linear: you cannot move on without answering, and a fast guess on a monster is a legitimate move. When four are done, the gate to the next batch opens.
Ideal times, item by item
| Item | Type | Ideal now | |
|---|---|---|---|
| Q1 | Successive percents | 1:00 | |
| Q2 | Ratios and multiples | 1:00 | |
| Q3 | Counting factors | 1:15 | |
| Q4 | Exponent equations | 0:45 | |
| Q5 | Difference of squares | 1:00 | |
| Q6 | Fill and drain rates | 1:30 | |
| Q7 | Median equals mean | 2:00 | |
| Q8 | Units digit cycle | 1:30 | |
| Q9 | Net percent change | 1:00 | |
| Q10 | Remainder on division by 10 | 2:00 | |
| Q11 | Consecutive even integers | 1:00 | |
| Q12 | Weighted average | 2:00 | |
| Total | 16:00 |
Batch 1 of 3: warm-up, the foundations the book assumes
1. A laptop priced at $800 is discounted 25%, and the sale price is then discounted a further 10%. What is the final price?
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Answer: (B).
800 becomes 600 after 25% off; 10% off 600 is 540. Successive discounts multiply (0.75 × 0.90 = 0.675), they never add to 35%. If this took over 1:15, the percents reflex is the first foundations win.
2. At a firm, the ratio of managers to analysts is 3 to 7. If there are 24 fewer managers than analysts, how many analysts are there?
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Answer: (D).
Write managers = 3k, analysts = 7k; the gap is 4k = 24, so k = 6 and analysts = 42. The multiplier k is the whole game in ratio questions.
3. How many positive integers are factors of 210?
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Answer: (C).
210 = 2 × 3 × 5 × 7, four distinct primes each to the first power, so the factor count is 2 × 2 × 2 × 2 = 16. This exact number is the star of Chapter 1's problem set in the book; the divisor-counting formula is a foundations-week pickup and then it is a 45-second question forever.
4. If 4^x = 64, then 3^(x+1) =
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Answer: (C).
4³ = 64, so x = 3, and 3⁴ = 81. Rewriting numbers as powers of a common base is Chapter 4's common-terms idea in miniature.
Batch 1 done when all four are answered. The next four are waiting.
Batch 2 of 3: building, where the book starts picking up
5. If x + y = 10 and x − y = 4, then x² − y² =
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Answer: (B).
x² − y² = (x + y)(x − y) = 10 × 4 = 40, no solving for x and y needed. Spotting the template makes this 30 seconds; grinding x and y out makes it 90. That trade is the whole Advanced Quant book.
6. A hose can fill a pool in 6 hours; a drain, open at the same time, can empty the full pool in 12 hours. With both open and the pool empty, how many hours does it take to fill?
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Answer: (D).
Net rate = 1/6 − 1/12 = 1/12 of a pool per hour, so 12 hours. Averaging 6 and 12 to get 9 is the trap: rates add, times do not. If the setup took over 1:30, put work-rate translation on the foundations list.
7. The set {3, 7, x, 15} has median equal to mean. What is x?
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Answer: (C).
Guess x sits between 7 and 15, so the median is (7 + x)/2 and the mean is (25 + x)/4. Setting them equal gives x = 11. Check: {3, 7, 11, 15} has mean 9 and median 9. This hides a case decision inside algebra; Chapter 5's number-line pictures make the case decision visual.
8. What is the units digit of 7²²?
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Answer: (E).
Units digits of powers of 7 cycle 7, 9, 3, 1 with period 4. 22 = 4 × 5 + 2, so take the second member of the cycle: 9. Meeting it cold and still getting it inside 2 minutes is a genuinely good sign.
Batch 2 done when all four are answered. The last four are waiting.
Batch 3 of 3: the book's flavors
9. A stock rises 20% one month and falls 20% the next. The net change over the two months is:
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Answer: (B).
1.20 × 0.80 = 0.96, so the stock ends at 96% of where it began: a 4% decrease. Percent down never undoes percent up; the multiplier view makes it visible instantly.
10. What is the remainder when 7¹⁰⁰ + 3¹⁰⁰ is divided by 10?
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Answer: (C).
A remainder on division by 10 is just the units digit. Both 7 and 3 have four-member cycles ending in 1, and 100 is a multiple of 4, so both powers end in 1. The sum ends in 2. Two ideas stacked: that stacking is exactly what Chapter 3 drills.
11. The sum of five consecutive even integers is 260. What is the largest of them?
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Answer: (D).
In an evenly spaced set, mean = median = the middle term: 260/5 = 52. The five terms are 44, 48, 52, 56, 60. No algebra needed, and that is the point. The pushup problem on the intake page is this idea wearing a costume.
12. A class of 20 students averaged 84 on a test. The 12 girls averaged 86. What did the 8 boys average?
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Answer: (C).
Total points: 20 × 84 = 1680; girls: 12 × 86 = 1032; boys: 648 over 8 = 81. Think in totals, never in average-of-averages. Chapter 5's teeter-totter picture solves it with zero algebra.
Pacing post-mortem
Press the button whenever you like: it scores everything you have answered so far, on each question's own clock.