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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 1
If x + 1/x = 5, then the value of x squared plus 1 over x squared is:
Select an option first.
Correct answer: D — 23
Explanation: Squaring both sides gives x squared + 2 + 1 over x squared = 25, so the required value is 23. The middle term is 2 because x multiplied by 1/x is 1. This identity family recurs constantly - squaring the given expression and subtracting the cross term is the whole method.
Question 2
The amount of an annuity DUE of Rs.1,000 for 3 years at 10% per annum, the ordinary annuity future value factor being 3.31, is:
Select an option first.
Correct answer: C — Rs.3,641
Explanation: In an annuity due each payment is made at the BEGINNING of the period, so every one earns interest for one extra period: 1,000 x 3.31 x 1.1 = Rs.3,641. The rule is general - multiply the ordinary annuity result by (1 + i), whether computing a present value or a future value. Distractor A is the ordinary annuity answer.
Question 3
The area under the curve y = x squared between x = 0 and x = 2 is:
Select an option first.
Correct answer: D — 8/3
Explanation: Integrate x squared to get x cubed over 3, then evaluate between the limits: 8/3 - 0 = 8/3, or about 2.67. As a check, the region sits inside a rectangle of width 2 and height 4, whose area is 8 - and the curve fills exactly one third of it. Any answer above 8 would be impossible.
Question 4
Which term of the arithmetic progression 7, 11, 15, ... is equal to 107?
Select an option first.
Correct answer: D — The 26th
Explanation: The nth term is a + (n - 1)d, so 7 + (n - 1)4 = 107 gives (n - 1) = 25 and n = 26. The commonest error is to stop at 25, forgetting that the difference is added one time FEWER than the term number. Substituting back - 7 + 25 x 4 = 107 - settles it in a few seconds.
Question 5
The sum of the first 20 terms of the arithmetic progression 5, 9, 13, ... is:
Select an option first.
Correct answer: D — 860
Explanation: Here a = 5, d = 4 and n = 20. Sum = (n/2)[2a + (n - 1)d] = 10[10 + 76] = 860. As a check, the 20th term is 5 + 19 x 4 = 81, and the average of the first and last terms is (5 + 81)/2 = 43, which times 20 gives 860. Two independent routes to the same figure is the safest use of spare time in an objective paper.
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Question 6
In an arithmetic progression the 5th term is 17 and the 9th term is 33. The first term is:
Select an option first.
Correct answer: C — 1
Explanation: The four steps from the 5th to the 9th term add 16, so d = 4. The first term is then 17 - 4 x 4 = 1. Subtracting one term from another eliminates the first term and isolates the common difference - the standard opening move when two terms are given.
Question 7
The number of distinct arrangements of the letters of the word BANANA is:
Select an option first.
Correct answer: A — 60
Explanation: BANANA has 6 letters with A appearing three times and N twice, so the count is 6! divided by (3! x 2!) = 720/12 = 60. Divide by the factorial of EACH repetition and multiply those divisors together - handling only one of the two repeats gives 120, which is distractor B.
Question 8
The number of distinct arrangements of the letters of the word MISSISSIPPI is:
Select an option first.
Correct answer: D — 34,650
Explanation: The word has 11 letters, with I appearing 4 times, S 4 times and P twice. The count is 11! divided by (4! x 4! x 2!) = 39,916,800 / 1,152 = 34,650. Divide by the factorial of EVERY repeated letter - distractor A is 11! with no division at all.
Question 9
The number of ways of arranging 3 books chosen from 7 different books on a shelf is:
Select an option first.
Correct answer: A — 210
Explanation: Order on a shelf matters, so this is a permutation: 7 x 6 x 5 = 210. Distractor B is C(7,3) = 35, the number of SELECTIONS without regard to order, and the two differ by the 3! = 6 ways of arranging each selection. Ask whether arrangement matters before choosing the tool.
Question 10
The region defined by 3x + 2y less than or equal to 12, with x and y both non-negative, is:
Select an option first.
Correct answer: B — A bounded triangle in the first quadrant
Explanation: The non-negativity conditions confine the region to the first quadrant and the constraint caps it along the line joining (4, 0) and (0, 6), giving a closed triangle with the origin. A feasible region is BOUNDED when it can be enclosed in a circle - and only then is a maximum of a linear objective guaranteed to exist.
Question 11
A firm's total revenue is TR = 50q and its total cost is TC = 2,000 + 30q. The break-even quantity is:
Select an option first.
Correct answer: C — 100
Explanation: Break-even occurs where TR = TC: 50q = 2,000 + 30q, so 20q = 2,000 and q = 100 units. The 20 is the CONTRIBUTION per unit - selling price 50 less variable cost 30 - and the break-even quantity is always fixed cost divided by contribution per unit. Distractor A divides fixed cost by the selling price instead.
Question 12
The capital recovery factor is the reciprocal of the:
Select an option first.
Correct answer: D — Present value annuity factor
Explanation: The present value annuity factor converts an annual payment into a lump sum; its reciprocal does the reverse, converting a loan into the equal annual instalment that repays it. This is exactly the calculation performed when a loan is divided by its annuity factor to find the instalment.
Question 13
If n(A) = 20, n(B) = 15 and n(A intersection B) = 5, then n(A union B) is:
Select an option first.
Correct answer: B — 30
Explanation: By the addition rule for sets, n(A union B) = n(A) + n(B) - n(A intersection B) = 20 + 15 - 5 = 30. Subtracting the intersection removes the double count of elements belonging to both sets. Distractor A omits that subtraction, which is exactly the error the question tests.
Question 14
The characteristic of log 0.0034 is:
Select an option first.
Correct answer: D — -3
Explanation: For a number less than 1, the characteristic is negative and equals one more than the number of zeros immediately after the decimal point, taken with a minus sign. Here there are two such zeros, so the characteristic is -3, usually written as 3 with a bar. The mantissa, from the digits 34, stays positive.
Question 15
The number of ways of seating 6 people around a circular table is:
Select an option first.
Correct answer: B — 120
Explanation: In a circular arrangement one person may be fixed to remove the rotational duplicates, leaving (6 - 1)! = 120 arrangements. Distractor A, 6! = 720, is the answer for a straight ROW. If the arrangements are also indistinguishable when reflected, as with a necklace, the answer halves again to 60.
Question 16
The value of C(12,10) is:
Select an option first.
Correct answer: C — 66
Explanation: Use symmetry: C(12,10) = C(12,2) = (12 x 11)/2 = 66. Computing it directly with ten factors would be laborious and error-prone. Whenever r is close to n, switch to n - r first - the answer is identical and the arithmetic is trivial.
Question 17
A committee of 3 men and 2 women is to be formed from 7 men and 5 women. The number of ways is:
Select an option first.
Correct answer: C — 350
Explanation: Choose the men in C(7,3) = 35 ways and the women in C(5,2) = 10 ways; since both choices must be made, multiply: 35 x 10 = 350. Selection uses COMBINATIONS because the order within the committee does not matter; had the members been assigned distinct offices, permutations would apply instead.
Question 18
The number of diagonals in a decagon is:
Select an option first.
Correct answer: B — 35
Explanation: A diagonal joins two non-adjacent vertices, so the count is C(n,2) minus the n sides = 45 - 10 = 35, which is the formula n(n - 3)/2 = 10 x 7 / 2 = 35. Distractor A is C(10,2), the total number of lines joining any two vertices, which includes the sides.
Question 19
The number of ways of selecting 5 cards from a standard pack of 52 is:
Select an option first.
Correct answer: B — 2,598,960
Explanation: This is C(52,5) = 52 x 51 x 50 x 49 x 48 divided by 5! = 2,598,960. Distractor A is the corresponding PERMUTATION, which is 120 times larger because it counts each hand in every possible order. A hand of cards is a selection, not an arrangement, so combinations are correct.
Question 20
A committee of 5 is to be formed from 6 men and 4 women, and must include AT LEAST 3 women. The number of ways is:
Select an option first.
Correct answer: A — 66
Explanation: Split into cases. Three women and two men: C(4,3) x C(6,2) = 4 x 15 = 60. Four women and one man: C(4,4) x C(6,1) = 6. Total 66. Cases must be mutually exclusive and then ADDED - the phrase 'at least' always signals this case-by-case treatment.
Question 21
If x is greater than 5 and y is greater than 3, then it necessarily follows that:
Select an option first.
Correct answer: D — x + y is greater than 8
Explanation: Inequalities in the same direction may be ADDED, so x + y exceeds 5 + 3 = 8. They may not be subtracted: x could be 5.1 and y could be 100, making x - y deeply negative, which disposes of distractor C. Multiplication is safe only when both quantities are known to be positive.
Question 22
If log x = 3 log 2 + 2 log 3, then x is:
Select an option first.
Correct answer: C — 72
Explanation: By the power rule the right side is log(2 cubed) + log(3 squared) = log 8 + log 9, and by the product rule that is log 72. Hence x = 72. Distractor A adds the bases and distractor D uses only the second term - apply the power rule to each term BEFORE combining, never after.
Question 23
If the sum of n terms of an arithmetic progression is 3n squared + 5n, the common difference is:
Select an option first.
Correct answer: C — 6
Explanation: The first term is S(1) = 8. Since S(2) = 12 + 10 = 22, the second term is 22 - 8 = 14, so d = 14 - 8 = 6. In general, when the sum is a quadratic in n, the common difference is twice the coefficient of n squared - here 2 x 3 = 6, which confirms the answer instantly.
Question 24
In an arithmetic progression the first term is 5 and the 20th term is 62. The common difference is:
Select an option first.
Correct answer: B — 3
Explanation: The 20th term is a + 19d, so 5 + 19d = 62, giving 19d = 57 and d = 3. The divisor is 19, not 20, because the common difference is added one time fewer than the term number. Distractor D divides by 20, which is precisely the off-by-one this question tests.
Question 25
In a geometric progression the first term is 3 and the fourth term is 81. The common ratio is:
Select an option first.
Correct answer: C — 3
Explanation: The fourth term is ar cubed, so 3 r cubed = 81, giving r cubed = 27 and r = 3. The index is 3, not 4, because the first term already carries r to the power zero. Miscounting that index by one is the single commonest error in geometric progression questions.
Question 26
If the universal set has 50 elements and n(A) = 18, then the number of elements not in A is:
Select an option first.
Correct answer: C — 32
Explanation: The complement contains everything in the universal set that A does not: 50 - 18 = 32. A set and its complement always partition the universal set, so their counts must add back to 50 - a check that immediately rejects distractor D.
Question 27
The complement of the universal set is:
Select an option first.
Correct answer: C — The empty set
Explanation: The complement of a set contains everything in the universal set that is NOT in it. Since the universal set contains everything, nothing remains, so its complement is the empty set. Correspondingly, the complement of the empty set is the universal set - the two results are mirror images.
Question 28
The amount of Rs.9,000 at 20% per annum compounded annually for 2 years is:
Select an option first.
Correct answer: D — Rs.12,960
Explanation: Amount = 9,000 x (1.2) squared = 9,000 x 1.44 = Rs.12,960. Distractor A is the simple interest amount of Rs.12,600, and the Rs.360 difference is the second year's interest on the first year's Rs.1,800 - which is precisely what compounding adds.
Question 29
The compound interest on Rs.20,000 for 3 years at 10% per annum, compounded annually, is:
Select an option first.
Correct answer: A — Rs.6,620
Explanation: The amount is 20,000 x (1.1) cubed = 20,000 x 1.331 = Rs.26,620, and the INTEREST is that less the principal, Rs.6,620. Distractor C is the amount rather than the interest, which is the commonest misreading. The simple interest for comparison would be Rs.6,000 - the Rs.620 excess is interest earned on interest.
Question 30
The amount of Rs.6,000 at 5% per annum compound interest for 3 years is:
Select an option first.
Correct answer: B — Rs.6,945.75
Explanation: Amount = 6,000 x (1.05) cubed = 6,000 x 1.157625 = Rs.6,945.75. Distractor A is the SIMPLE interest amount, which must always be the smaller of the two beyond the first year. The Rs.45.75 difference is the interest earned on interest over the three years.
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