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Free CA Quantitative Aptitude Practice Questions & Answers
500 exam-style Quantitative Aptitude questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 121
The arithmetic mean of two numbers is 10 and their geometric mean is 8. The numbers are:
Select an option first.
Correct answer: C — 4 and 16
Explanation: The arithmetic mean gives a + b = 20 and the geometric mean gives ab = 64, so the numbers are the roots of x squared - 20x + 64 = 0, namely 4 and 16. Note that the AM of 10 exceeds the GM of 8, as it always must unless the two numbers are equal.
Question 122
In a linear programming problem, the objective function is:
Select an option first.
Correct answer: D — A linear function of the decision variables to be maximised or minimised
Explanation: The objective function states the goal - maximum profit or minimum cost - as a linear expression in the decision variables. The inequalities are the CONSTRAINTS, the region they define is the FEASIBLE REGION, and non-negativity is one particular constraint. Keeping the four terms distinct is itself a theory question.
Question 123
In how many years will Rs.10,000 amount to Rs.13,310 at 10% per annum compound interest?
Select an option first.
Correct answer: D — 3
Explanation: The ratio is 13,310/10,000 = 1.331, which is 1.1 cubed, so the period is 3 years. As with all such questions, the figures are constructed around a whole-number power of (1 + i) - test the square and the cube of the growth factor before resorting to logarithms.
Question 124
The number of ways of choosing a president and a secretary from 8 members is:
Select an option first.
Correct answer: D — 56
Explanation: The president can be any of 8 and the secretary any of the remaining 7, giving 8 x 7 = 56. Order MATTERS here because the two posts are distinct, so this is a permutation. Distractor A is C(8,2) = 28, which would be right if a committee of two with no distinction of office were being chosen.
Question 125
The number of 4-digit numbers that can be formed from the digits 1, 2, 3, 4 and 5 without repetition is:
Select an option first.
Correct answer: A — 120
Explanation: This is the number of arrangements of 5 digits taken 4 at a time: 5 x 4 x 3 x 2 = 120. Order matters here, since 1234 and 4321 are different numbers, so permutations apply rather than combinations. Distractor B, 5 to the power 4, would be the answer if repetition were allowed.
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Question 126
In how many ways can 5 boys and 3 girls be arranged in a row so that no two girls sit together?
Select an option first.
Correct answer: B — 14,400
Explanation: Seat the 5 boys first in 5! = 120 ways, creating 6 gaps including the two ends. Place the 3 girls into 3 of those gaps in 6 x 5 x 4 = 120 ways. Total = 120 x 120 = 14,400. The gap method is the standard technique for a no-two-together restriction: arrange the unrestricted group first, then slot the restricted one into the spaces.
Question 127
The number of distinct arrangements of the letters of the word ACCOUNT is:
Select an option first.
Correct answer: D — 2,520
Explanation: ACCOUNT has 7 letters, of which C appears twice, so the count is 7! / 2! = 5,040 / 2 = 2,520. Dividing by the factorial of each repetition removes the arrangements that merely swap identical letters. Distractor A forgets the repetition entirely - always count the letters and check for repeats before applying any formula.
Question 128
The number of distinct arrangements of the letters of the word LEVEL is:
Select an option first.
Correct answer: C — 30
Explanation: LEVEL has 5 letters, with L repeated twice and E repeated twice, so the count is 5! divided by (2! x 2!) = 120/4 = 30. Divide by the factorial of EACH repetition separately and then multiply the divisors - dividing by 2! only once, which gives 60, is the standard error.
Question 129
The present value of a perpetuity of Rs.6,000 per annum at a discount rate of 8% is:
Select an option first.
Correct answer: B — Rs.75,000
Explanation: Present value of a perpetuity = annual cash flow / rate = 6,000 / 0.08 = Rs.75,000. Although the payments continue for ever, their present value is finite because each successive payment is discounted more heavily. Distractor C divides the wrong way round; a quick sanity check is that the answer must be many times the annual payment.
Question 130
The present value of Rs.1,000 receivable at the end of every year for ever, the first receipt one year hence, at 10% per annum, is:
Select an option first.
Correct answer: B — Rs.10,000
Explanation: Present value = 1,000 / 0.10 = Rs.10,000. The result is finite despite the infinite stream because each successive receipt is discounted more heavily. Sense check: Rs.10,000 invested at 10% throws off exactly Rs.1,000 a year for ever without touching the capital.
Question 131
A point of inflexion on a curve is a point at which:
Select an option first.
Correct answer: D — The second derivative is zero and changes sign
Explanation: At a point of inflexion the curvature reverses, from concave upwards to concave downwards or the reverse, which requires the second derivative to be zero AND to change sign there. A zero second derivative alone is not sufficient. A stationary point, where the first derivative vanishes, is a different idea and need not be an inflexion.
Question 132
The derivative of x raised to the power n with respect to x is:
Select an option first.
Correct answer: D — n x raised to the power (n - 1)
Explanation: The power rule brings the index down as a multiplier and reduces the index by one, giving n times x to the power (n - 1). It holds for any real n, including negative and fractional values, which is why 1 over x squared differentiates to -2 over x cubed. Reducing rather than raising the index is the point to fix in memory.
Question 133
The number of elements in the power set of a set having 5 elements is:
Select an option first.
Correct answer: C — 32
Explanation: The power set contains every subset, and there are 2 to the power 5 = 32 of them, counting the empty set and the set itself. Distractor D, 31, excludes the set itself and is the number of PROPER subsets. The formula follows from each element being independently either in or out of a given subset.
Question 134
Of two equal sums receivable, one after 2 years and one after 5 years, discounted at the same rate:
Select an option first.
Correct answer: C — The sum receivable after 2 years has the higher present value
Explanation: Discounting divides by (1 + i) raised to the number of years, so a longer wait means a larger divisor and a smaller present value. Money has time value: a rupee today can be invested, so a rupee promised sooner is always worth more than the same rupee promised later.
Question 135
An annuity of Rs.1,200 per year continuing for ever, discounted at 6%, has a present value of:
Select an option first.
Correct answer: C — Rs.20,000
Explanation: Present value of a perpetuity = cash flow / rate = 1,200 / 0.06 = Rs.20,000. Distractor D inverts the division. A useful cross-check: the present value of a perpetuity is always the amount which, invested at the given rate, would yield the annual payment - and 6% of Rs.20,000 is indeed Rs.1,200.
Question 136
The present value of Rs.10,000 receivable at the end of 3 years, discounted at 10% per annum, is:
Select an option first.
Correct answer: B — Rs.7,513.15
Explanation: Present value = 10,000 / (1.1)^3 = 10,000 / 1.331 = Rs.7,513.15. Distractor C compounds forward instead of discounting back, and distractor D discounts for only one year. Discounting and compounding are exact inverses, so multiplying the answer by 1.331 should return Rs.10,000 - a five-second check.
Question 137
The present value of Rs.5,000 due in 2 years, discounted at 8% per annum compounded annually, is:
Select an option first.
Correct answer: C — Rs.4,286.69
Explanation: Present value = 5,000 divided by (1.08) squared = 5,000/1.1664 = Rs.4,286.69. Distractor B compounds forward instead of discounting back, and distractor D discounts for one year only. Multiply the answer by 1.1664 to recover Rs.5,000 - a five-second verification.
Question 138
The present value of an annuity of Rs.5,000 payable at the end of each year for 4 years at 10% per annum, given that the PV annuity factor is 3.1699, is:
Select an option first.
Correct answer: B — Rs.15,849.50
Explanation: Present value = annual payment x annuity factor = 5,000 x 3.1699 = Rs.15,849.50. Distractor A is the undiscounted total of the four payments, which must always exceed the present value because money received later is worth less. If a computed present value ever exceeds the simple total, the arithmetic is wrong.
Question 139
The present value of an annuity DUE of Rs.4,000 for 5 years at 10%, the ordinary annuity PV factor being 3.7908, is:
Select an option first.
Correct answer: D — Rs.16,679.52
Explanation: Multiply the ordinary annuity present value by (1 + i): 4,000 x 3.7908 x 1.1 = Rs.16,679.52. Because each payment arrives one period EARLIER, it is discounted less and the present value is higher than for an ordinary annuity - distractor A, the ordinary annuity figure, must therefore be too low.
Question 140
The present value of Rs.1,000 receivable at the end of each year for 10 years at 10%, the annuity factor being 6.1446, is:
Select an option first.
Correct answer: A — Rs.6,144.60
Explanation: Present value = 1,000 x 6.1446 = Rs.6,144.60. Distractor B is the undiscounted total of the ten receipts, which must always exceed the present value. Distractor C is the FUTURE value of the same annuity - present and future value factors are easily confused, so check which the question supplies.
Question 141
The simple interest on a sum for 3 years at 5% per annum is Rs.1,200. The principal is:
Select an option first.
Correct answer: A — Rs.8,000
Explanation: Rearranging the formula, P = SI x 100 / (r x t) = 1,200 / (0.05 x 3) = Rs.8,000. Check by working forwards: 5% of 8,000 is 400 a year, and 400 x 3 = Rs.1,200. Rearranging the standard formula rather than memorising four versions of it is the safer habit.
Question 142
log a plus log b equals:
Select an option first.
Correct answer: C — log(ab)
Explanation: Logarithms convert multiplication into addition, so the sum of two logs is the log of the PRODUCT. Distractor A is the commonest error in the topic: there is no rule for the log of a sum. Similarly, subtraction of logs gives the log of a quotient, never the log of a difference.
Question 143
The value of log(a/b) + log(b/c) + log(c/a) is:
Select an option first.
Correct answer: C
Explanation: Using log(m/n) = log m - log n, the expression becomes (log a - log b) + (log b - log c) + (log c - log a), in which every term cancels, leaving 0. The same result follows in one step from the product rule, since (a/b)(b/c)(c/a) = 1 and log 1 = 0 for any base. Look for the telescoping pattern before expanding.
Question 144
If a : b = c : d, then (a + c) : (b + d) equals:
Select an option first.
Correct answer: B — a : b
Explanation: If each ratio equals k, then a = bk and c = dk, so (a + c)/(b + d) = k(b + d)/(b + d) = k, which is a : b. This is the addendo property of proportion, and it is why adding matching terms of equal ratios leaves the ratio unchanged - useful for simplifying before computing.
Question 145
The fourth proportional to 5, 8 and 15 is:
Select an option first.
Correct answer: D — 24
Explanation: If 5 : 8 :: 15 : x, then 5x = 8 x 15, so x = 24. Keep the three related ideas apart: the FOURTH proportional to a, b, c is bc/a; the THIRD proportional to a and b is b squared over a; and the MEAN proportional between a and b is the square root of ab. Most errors here come from applying the wrong one of the three.
Question 146
If the roots of x^2 - px + 12 = 0 differ by 1 and p is positive, then p equals:
Select an option first.
Correct answer: B — 7
Explanation: For roots a and b, a + b = p and ab = 12. Since (a - b)^2 = (a + b)^2 - 4ab, we get 1 = p^2 - 48, so p^2 = 49 and p = 7 (taking the positive value). Verify: the roots are 3 and 4, which differ by 1 and multiply to 12. The identity linking the difference of roots to the sum and product is worth memorising - it avoids solving the quadratic at all.
Question 147
A sum of money doubles itself in 8 years under simple interest. The rate per annum is:
Select an option first.
Correct answer: C — 12.5%
Explanation: Doubling means the interest earned equals the principal: P = P x r x 8, so r = 1/8 = 12.5% per annum. Under COMPOUND interest the same doubling would need only about 9% - simple interest requires a higher rate for the same result, because no interest is earned on interest.
Question 148
A sum of money triples itself in 20 years under simple interest. The rate per annum is:
Select an option first.
Correct answer: A — 10%
Explanation: Tripling means the interest earned is TWICE the principal: 2P = P x r x 20, so r = 2/20 = 10% per annum. The common slip is to use 3P instead of 2P - the amount triples, but the interest is only the increase, which is twice the principal.
Question 149
Rs.4,000 becomes Rs.4,410 in 2 years under compound interest. The rate per annum is:
Select an option first.
Correct answer: C — 5%
Explanation: The growth factor is 4,410/4,000 = 1.1025, which is 1.05 squared, so the rate is 5%. As always in these questions the ratio is a whole power of (1 + i) - test the square first when the period is two years. Verify: 4,000 to 4,200 to 4,410.
Question 150
A nominal rate of 12% per annum compounded monthly gives a rate per period of:
Select an option first.
Correct answer: C — 1%
Explanation: Divide the nominal annual rate by the number of compounding periods in the year: 12/12 = 1% per month. The number of periods becomes 12 for a one-year investment. Distractor D is the quarterly rate. Divide the rate and multiply the periods together - doing one without the other is the standard error.
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