Quantitative Aptitude — Practice Q&A

Walkthrough-style questions focused on approach and reasoning, not just the final answer — useful for building the underlying method before switching to pure speed drilling (see Advanced).

Q: A shopkeeper marks an item 40% above cost price, then offers a 25% discount. What's the actual profit percentage?

A: Let cost price = 100. Marked price = 140 (40% above cost). Selling price after 25% discount on marked price = 140 × 0.75 = 105. Profit = 105 − 100 = 5, so profit % = 5%. The key reasoning point: the discount is applied to the marked price, not the cost price — a common error is discounting from cost price directly, which gives a wrong answer.

Q: Two pipes can fill a tank in 12 and 15 hours respectively. A third pipe can empty it in 20 hours. If all three are opened together, how long to fill the tank?

A: Combined rate = 1/12 + 1/15 − 1/20 (the outlet pipe is subtracted, per Intermediate's work-rate framework). Common denominator 60: 5/60 + 4/60 − 3/60 = 6/60 = 1/10. So the tank fills in 10 hours. The reasoning point: correctly identifying which pipe is an inlet (positive rate) vs. outlet (negative rate) is the actual skill being tested — the arithmetic itself is straightforward once the rates are set up correctly.

Q: A sum of money becomes ₹5,290 in 2 years and ₹6,083.50 in 3 years at compound interest. What's the rate of interest?

A: The interest earned in the 3rd year alone = 6083.50 − 5290 = 793.50, and this represents the interest on the 2-year amount (5290) for one year. Rate = (793.50 / 5290) × 100 = 15%. The reasoning point: the difference between consecutive years' compound amounts directly gives you that year's interest, which is a faster path than trying to solve for principal and rate simultaneously from the two given amounts.

Q: In a Data Sufficiency question: "What is the value of x?" Statement I: x² = 25. Statement II: x > 0. Are the statements individually or jointly sufficient?

A: Statement I alone: x² = 25 gives x = 5 or x = −5 — not sufficient alone, two possible values. Statement II alone: x > 0 gives no specific value — not sufficient alone. Both together: x² = 25 AND x > 0 together give exactly x = 5 — sufficient jointly. The reasoning point, directly connecting to Intermediate's Data Sufficiency note: the task is judging sufficiency, not computing the answer for its own sake — here, the "answer" (x = 5) is really just the mechanism for determining sufficiency, not something you'd report as a final numeric answer the way a standard question requires.

Q: A DI caselet states: "Company A's revenue grew by 20% each year for 3 years, starting from ₹10 lakh." What was the revenue at the end of year 3?

A: This is compound growth, same mechanics as Compound Interest: 10 × 1.2 × 1.2 × 1.2 = 10 × 1.728 = ₹17.28 lakh. The reasoning point: recognizing that a "grows by X% each year" caselet is structurally identical to a compound interest problem — once recognized, the same formula/approach applies directly, rather than treating it as an unfamiliar new problem type.

Q: A number series: 3, 8, 15, 24, 35, ? — what's the next term?

A: Differences between consecutive terms: 5, 7, 9, 11 — an arithmetic pattern in the differences themselves (each difference increases by 2), a second-order pattern (see Intermediate's systematic check order, step 3). Next difference = 13, so next term = 35 + 13 = 48. The reasoning point: checking first-order constant difference (fails here) before moving systematically to second-order differences is what makes this solvable quickly rather than by trial and error.