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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 61
The value of x satisfying x/2 + x/3 = 10 is:
Select an option first.
Correct answer: A — 12
Explanation: Multiply throughout by the LCM of the denominators, 6, to clear the fractions: 3x + 2x = 60, so 5x = 60 and x = 12. Check: 6 + 4 = 10. Clearing denominators first avoids the arithmetic slips that come from adding fractions mid-solution.
Question 62
The value of C(10,3) is:
Select an option first.
Correct answer: D — 120
Explanation: C(10,3) = (10 x 9 x 8)/(3 x 2 x 1) = 720/6 = 120. Distractor A is the corresponding PERMUTATION, P(10,3) = 720, which is 3! times larger because it counts each selection in every order. Cancel before multiplying to keep the arithmetic small.
Question 63
The value of C(8,5) is:
Select an option first.
Correct answer: A — 56
Explanation: Use the symmetry property: C(8,5) = C(8,3) = (8 x 7 x 6)/(3 x 2 x 1) = 56. Distractor B is the corresponding permutation P(8,3) = 336. Converting to the smaller of r and n - r before computing keeps the arithmetic short and is worth doing automatically.
Question 64
If f(x) = x squared - 3x, then f(4) is:
Select an option first.
Correct answer: A — 4
Explanation: Substitute 4 for every x: 16 - 12 = 4. Distractor B comes from computing (4 squared) - 3, ignoring the x in the second term. Substitution questions look trivial but reward care with signs and with each occurrence of the variable - write the substituted expression out fully before simplifying.
Question 65
If 5 raised to the power (x + 3) equals 125, then x is:
Select an option first.
Correct answer: C
Explanation: Write 125 as 5 cubed, so 5^(x+3) = 5^3. With equal bases the indices must be equal, giving x + 3 = 3 and x = 0. Reducing both sides to the same base is the standard first move for any exponential equation, and it converts the problem into ordinary algebra.
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Question 66
The roots of x squared - 9x + 20 = 0 are:
Select an option first.
Correct answer: C — 4 and 5
Explanation: Look for two numbers with product 20 and sum 9: they are 4 and 5, so the equation factorises as (x - 4)(x - 5) = 0. Distractor D has the right product but a sum of 21, and distractor A has the right product but a sum of 12 - always test BOTH conditions rather than the product alone.
Question 67
In a linear programming problem, the non-negativity restrictions confine the solution to:
Select an option first.
Correct answer: C — The first quadrant
Explanation: Requiring both variables to be zero or positive restricts the solution to the first quadrant, which is natural since the variables usually represent quantities produced or purchased. Without this restriction a mathematically optimal solution might call for a negative output, which has no business meaning.
Question 68
If A : B = 5 : 7 and B is 42, then A is:
Select an option first.
Correct answer: B — 30
Explanation: Each ratio part is worth 42/7 = 6, so A = 5 x 6 = 30. Finding the value of one part first is the reliable method whenever a single term is given. Check the result against the original ratio: 30 : 42 does reduce to 5 : 7.
Question 69
If n(A union B) = 40, n(A) = 25 and n(B) = 20, then n(A intersection B) is:
Select an option first.
Correct answer: D — 5
Explanation: Rearranging the addition rule, n(A intersection B) = n(A) + n(B) - n(A union B) = 25 + 20 - 40 = 5. A sanity check: the intersection can never exceed the smaller of the two sets, so any answer above 20 - such as distractor C - is impossible on its face.
Question 70
The time in which Rs.5,000 amounts to Rs.6,050 at 10% per annum compound interest is:
Select an option first.
Correct answer: A — 2 years
Explanation: The ratio of amount to principal is 6,050/5,000 = 1.21, which is 1.1 squared, so the period is 2 years. Recognising the ratio as a power of (1 + i) avoids logarithms entirely, and the numbers in such questions are always chosen so that it can be recognised - test squares and cubes first.
Question 71
A sum of Rs.8,000 amounts to Rs.9,261 in 3 years at compound interest. The rate per annum is:
Select an option first.
Correct answer: A — 5%
Explanation: The ratio of amount to principal is 9,261/8,000 = 1.157625, whose cube root is 1.05, so the rate is 5%. Recognising 9,261 as 21 cubed and 8,000 as 20 cubed gives the ratio 21/20 directly - the examiner chooses such numbers deliberately, so look for a perfect cube before reaching for logarithms.
Question 72
The quadratic equation whose roots are 2 and -5 is:
Select an option first.
Correct answer: C — x squared + 3x - 10 = 0
Explanation: The equation is x squared - (sum of roots)x + (product of roots) = 0. The sum is 2 + (-5) = -3 and the product is -10, giving x squared + 3x - 10 = 0. Note the sign flip on the sum, which is where most errors occur. Check by factorising: (x + 5)(x - 2) = 0 does give roots -5 and 2.
Question 73
The cube root of 0.008 is:
Select an option first.
Correct answer: D — 0.2
Explanation: Write 0.008 as 8/1000; the cube root of 8 is 2 and of 1000 is 10, giving 2/10 = 0.2. Verify by cubing: 0.2 x 0.2 x 0.2 = 0.008. Counting decimal places is where these go wrong - a cube root has one third as many decimal places as the number itself.
Question 74
The value of 16 raised to the power three-quarters is:
Select an option first.
Correct answer: C — 8
Explanation: Write 16 as 2^4, so 16^(3/4) = 2^(4 x 3/4) = 2^3 = 8. Alternatively take the fourth root of 16, which is 2, then cube it. The denominator of a fractional index is the ROOT and the numerator is the POWER - taking them in either order gives the same result, so choose whichever keeps the numbers small.
Question 75
If f(x) = 2x + 3, then the inverse function f inverse of x is:
Select an option first.
Correct answer: B — (x - 3)/2
Explanation: Put y = 2x + 3, interchange x and y to get x = 2y + 3, then solve for y to obtain y = (x - 3)/2. Distractor A is the RECIPROCAL, not the inverse function - the two are entirely different ideas that share a notation. Verify by composing: f((x - 3)/2) = 2(x - 3)/2 + 3 = x.
Question 76
The amount of Rs.5,000 invested for 4 years at 10% per annum compounded annually is:
Select an option first.
Correct answer: B — Rs.7,320.50
Explanation: Amount = 5,000 x (1.1) to the power 4 = 5,000 x 1.4641 = Rs.7,320.50. Distractor C uses three years and distractor D gives the INTEREST rather than the amount. Read carefully whether the question wants the amount or the interest - they differ by the principal.
Question 77
Rs.2,000 is deposited at the END of each year for 3 years, earning 10% per annum compounded annually. The amount at the end of the third year is:
Select an option first.
Correct answer: A — Rs.6,620
Explanation: The first deposit earns interest for 2 years, the second for 1 year and the third for none: 2,000(1.1^2 + 1.1 + 1) = 2,000 x 3.31 = Rs.6,620. Distractor B is the sum of the deposits with no interest at all, and distractor D would be the answer for an annuity DUE, where each deposit is made at the beginning of the year.
Question 78
Rs.3,000 is deposited at the end of each year for 5 years at 8%, the future value annuity factor being 5.8666. The amount accumulated is:
Select an option first.
Correct answer: C — Rs.17,599.80
Explanation: Amount = 3,000 x 5.8666 = Rs.17,599.80. Distractor A is the sum of the deposits with no interest, which the true answer must exceed. Distractor B would be the PRESENT value of the same annuity - present and future value factors are easily transposed, so check which one the question gives.
Question 79
If the third term of a geometric progression is 12 and the sixth term is 96, the common ratio is:
Select an option first.
Correct answer: D — 2
Explanation: Dividing the sixth term by the third eliminates the first term: ar^5 / ar^2 = r^3 = 96/12 = 8, so r = 2. The gap between the terms is 6 - 3 = 3, which is why the cube appears. This ratio-of-terms technique works for any two terms of a GP and avoids solving for the first term.
Question 80
The sum of an infinite geometric progression whose first term is 8 and common ratio is 1/2 is:
Select an option first.
Correct answer: B — 16
Explanation: For an infinite GP the sum is a/(1 - r), valid only when the absolute value of r is less than 1. Here 8/(1 - 0.5) = 16. Always test the ratio before applying the formula: with r of 1 or more the terms do not shrink and the series diverges, which is when distractor D would be correct.
Question 81
The equation 2x + 3y = 12 represents:
Select an option first.
Correct answer: B — A straight line
Explanation: Any equation of the first degree in x and y plots as a straight line - here through (6, 0) and (0, 4). A squared term would be needed for a parabola and equal squared terms in both variables for a circle. Degree one in both variables is the test, and it is why the constraints of a linear programming problem are all straight lines.
Question 82
Rs.12,000 is borrowed at 10% per annum compounded HALF-YEARLY for 2 years. The amount repayable is:
Select an option first.
Correct answer: D — Rs.14,586.08
Explanation: The rate per half year is 5% and there are 4 half years, so the amount is 12,000 x (1.05) to the power 4 = Rs.14,586.08. Distractor C is the annually compounded figure, which must be smaller. Halve the rate and double the periods together - doing only one is the standard error.
Question 83
A function whose first derivative is positive throughout an interval is:
Select an option first.
Correct answer: B — Increasing on that interval
Explanation: A positive rate of change means the function rises as x rises, so it is increasing. A negative derivative means decreasing and a zero derivative a stationary point. This sign test identifies the intervals of increase and decrease before any turning point is classified.
Question 84
If 2^x = 8^(y+1) and 9^y = 3^(x-9), then the value of x + y is:
Select an option first.
Correct answer: B — 27
Explanation: Express both sides to a common base. 2^x = 2^(3y+3) gives x = 3y + 3. 9^y = 3^(2y) = 3^(x-9) gives 2y = x - 9, so x = 2y + 9. Solving, 3y + 3 = 2y + 9, hence y = 6 and x = 21, so x + y = 27. Whenever an indices question mixes bases, first rewrite every term as a power of the smallest base.
Question 85
If 2 raised to the power x equals 3 raised to the power y equals 6 raised to the power z, then 1/x + 1/y equals:
Select an option first.
Correct answer: D — 1/z
Explanation: Let the common value be k. Then x = log k / log 2, so 1/x = log 2 / log k, and likewise 1/y = log 3 / log k. Adding gives (log 2 + log 3)/log k = log 6 / log k = 1/z. Taking logarithms of all three equal expressions is the standard opening move for this whole family of questions.
Question 86
If a to the power x equals b to the power y equals c to the power z, and b squared equals ac, then y equals:
Select an option first.
Correct answer: B — 2xz divided by (x + z)
Explanation: Let the common value be k. Then log a = log k / x and similarly for b and c. The condition b squared = ac gives 2 log b = log a + log c, so 2/y = 1/x + 1/z, whence y = 2xz/(x + z). Note that y is the HARMONIC mean of x and z - a neat consequence of b being the geometric mean of a and c.
Question 87
If 2 raised to the power (2x - 1) equals 32, then x is:
Select an option first.
Correct answer: D — 3
Explanation: Write 32 as 2 to the power 5, so 2x - 1 = 5, giving 2x = 6 and x = 3. Equating indices is valid only once both sides share a base, which is why converting 32 comes first. Distractor C stops at 2x = 6 without halving. Substitute back to check: 2(3) - 1 = 5, and 2 to the power 5 is indeed 32.
Question 88
The solution of -2x + 6 is greater than or equal to 0 is:
Select an option first.
Correct answer: D — x is less than or equal to 3
Explanation: Rearranging gives 6 is greater than or equal to 2x, so x is less than or equal to 3. Had we divided the original inequality by -2 directly, the sign would have to be REVERSED, giving the same answer. Moving the negative term across instead of dividing by a negative avoids the reversal rule altogether - the safer habit.
Question 89
The sum of the infinite series 9 + 3 + 1 + ... is:
Select an option first.
Correct answer: D — 13.5
Explanation: The common ratio is 1/3, so the sum is 9/(1 - 1/3) = 9 x 3/2 = 13.5. The series converges because the ratio is below 1 in absolute value. The sum must exceed the first term of 9 but stay finite - a bracket that rules out two options at once.
Question 90
A loan of Rs.50,000 is repayable in 5 equal annual instalments at 5%, the present value annuity factor being 4.3295. Each instalment is:
Select an option first.
Correct answer: B — Rs.11,548.68
Explanation: Instalment = 50,000 / 4.3295 = Rs.11,548.68. Distractor A repays the principal in five equal parts with no interest at all, so the true instalment must exceed it. The total repaid, about Rs.57,743, less the Rs.50,000 borrowed, is the interest cost of the loan.
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