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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 181
The sum of 2 + 6 + 18 + ... to 5 terms is:
Select an option first.
Correct answer: C — 242
Explanation: With a = 2 and r = 3, the sum is a(r^n - 1)/(r - 1) = 2(243 - 1)/2 = 242. Distractor A is the fifth TERM alone rather than the sum of the series. Where r exceeds 1 use this form; where r is less than 1 the form a(1 - r^n)/(1 - r) avoids negative signs, though both give the same result.
Question 182
The sum of the first 6 terms of the progression 5, 10, 20, ... is:
Select an option first.
Correct answer: C — 315
Explanation: With a = 5 and r = 2, the sum is 5(2 to the power 6 minus 1)/(2 - 1) = 5 x 63 = 315. Distractor A is the sixth TERM alone, 160, rather than the sum of the six. A quick check on any doubling series: its sum is always one less than twice the last term, and 2 x 160 - 5 = 315.
Question 183
The sum of the first 12 terms of the progression 3, 7, 11, ... is:
Select an option first.
Correct answer: B — 300
Explanation: With a = 3, d = 4 and n = 12, the sum is (12/2)[2(3) + 11(4)] = 6[6 + 44] = 300. As a cross-check the 12th term is 3 + 44 = 47, and the average of the first and last terms, (3 + 47)/2 = 25, multiplied by 12 also gives 300.
Question 184
The sum of the infinite series 1 + 1/3 + 1/9 + ... is:
Select an option first.
Correct answer: D — 3/2
Explanation: With a = 1 and r = 1/3, the sum is a/(1 - r) = 1/(2/3) = 3/2. The series converges because the absolute value of r is less than 1. Note that the sum, 1.5, must exceed the first term and stay below the sum of the first few terms extended generously - a quick plausibility bracket.
Question 185
If the sum of the first n natural numbers is 210, then n equals:
Select an option first.
Correct answer: B — 20
Explanation: n(n + 1)/2 = 210 gives n(n + 1) = 420, so n squared + n - 420 = 0 and n = 20, since 20 x 21 = 420. Look for the factor pair of two consecutive integers rather than applying the quadratic formula - the numbers in such questions are always chosen to make that possible.
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Question 186
The sum of the first 15 odd numbers is:
Select an option first.
Correct answer: A — 225
Explanation: The sum of the first n odd numbers is n squared, so the answer is 15 squared = 225. Checking with the arithmetic progression formula, with a = 1, d = 2 and n = 15: (15/2)(2 + 28) = 225. The n squared result is worth memorising - it recurs in series questions.
Question 187
If x = 3 + 2 root 2, then the value of x + 1/x is:
Select an option first.
Correct answer: B — 6
Explanation: Rationalise 1/(3 + 2 root 2) by multiplying numerator and denominator by (3 - 2 root 2). The denominator becomes 9 - 8 = 1, so 1/x = 3 - 2 root 2. Adding, the irrational parts cancel and x + 1/x = 6. Whenever a surd of the form a + b root c appears with its reciprocal, expect the irrational part to vanish - that is the whole design of the question.
Question 188
If alpha and beta are the roots of x squared - 5x + 6 = 0, the value of 1/alpha + 1/beta is:
Select an option first.
Correct answer: C — 5/6
Explanation: Combine the fractions: 1/alpha + 1/beta = (alpha + beta)/(alpha x beta) = 5/6, using the sum of the roots 5 and the product 6. The roots themselves - 2 and 3 - need never be found, which is the point of the sum and product relations. Check: 1/2 + 1/3 = 5/6.
Question 189
The identity C(n, r) = C(n, n - r) reflects the fact that:
Select an option first.
Correct answer: C — Choosing r objects is the same as rejecting the remaining n - r
Explanation: Every selection of r objects automatically determines the n - r left behind, so the two counts must be equal. The property is a practical labour saver: C(20,18) is far quicker computed as C(20,2) = 190. Recognising the shortcut is what the question rewards.
Question 190
The third proportional to 9 and 12 is:
Select an option first.
Correct answer: A — 16
Explanation: The third proportional to a and b is b squared divided by a = 144/9 = 16, so 9, 12 and 16 are in continued proportion. Distinguish it from the FOURTH proportional, which needs three given numbers, and from the MEAN proportional, which is the square root of the product.
Question 191
If the total cost of producing 10 units is Rs.500, the AVERAGE cost is:
Select an option first.
Correct answer: B — Rs.50
Explanation: Average cost is total cost divided by quantity: 500/10 = Rs.50 per unit. Marginal cost, by contrast, is the derivative of the total cost function and would need that function, not just one point on it. Average needs division; marginal needs differentiation.
Question 192
The sum of two numbers is 20 and their product is 96. The numbers are:
Select an option first.
Correct answer: A — 8 and 12
Explanation: The numbers are the roots of x squared - 20x + 96 = 0, which factorises as (x - 8)(x - 12) = 0. So they are 8 and 12. Every 'sum and product' word problem is a disguised quadratic, and framing it that way is faster than trial and error - distractor B has the right sum but a product of 96 is not obtained.
Question 193
In a linear programming problem with an unbounded feasible region, the objective function:
Select an option first.
Correct answer: A — May have a minimum but no maximum
Explanation: If the region extends without limit in the direction in which the objective increases, no maximum exists; but a minimum may still be attained at a corner point. This is why an unbounded region requires a check of whether the optimum actually exists, rather than simply evaluating the corners.
Question 194
If A and B are disjoint sets, then n(A union B) equals:
Select an option first.
Correct answer: A — n(A) + n(B)
Explanation: Disjoint means the intersection is empty, so the correction term in the general addition rule is zero and the counts simply add. Distractor B is the general rule, which is not wrong here but is not the simplified form the question asks for - disjointness is the given that removes the third term.
Question 195
If n(A) = 30, n(B) = 25, n(C) = 20, with the pairwise intersections 10, 8 and 6 and all three overlapping in 3, then n(A union B union C) is:
Select an option first.
Correct answer: C — 54
Explanation: Add the individual counts, subtract each pairwise intersection, then add back the triple intersection: 30 + 25 + 20 - 10 - 8 - 6 + 3 = 54. The triple overlap is added back because subtracting all three pairs removed it twice too often - the alternating pattern is the whole of the inclusion-exclusion principle.
Question 196
A bond of face value Rs.1,000 pays interest at 9% annually and is redeemable at par after one year. If the required yield is 12%, its value today is:
Select an option first.
Correct answer: D — Rs.973.21
Explanation: The holder receives interest of Rs.90 plus the redemption of Rs.1,000 at the end of the year, so the value is 1,090 / 1.12 = Rs.973.21. Because the required yield of 12% EXCEEDS the coupon rate of 9%, the bond must trade at a discount to par - a direction check that eliminates the first three options at a glance.
Question 197
Simple interest and compound interest on the same sum at the same rate are equal for:
Select an option first.
Correct answer: A — One year, where compounding is annual
Explanation: Compound interest exceeds simple interest only because interest is earned on interest, and that cannot happen within the first compounding period. For annual compounding the two are therefore identical for one year and diverge thereafter. With half-yearly compounding they would already differ within a year.
Question 198
A two-digit number has digits whose sum is 9. When 27 is subtracted from the number, its digits are reversed. The number is:
Select an option first.
Correct answer: C — 63
Explanation: Let the number be 10a + b with a + b = 9. The condition gives 10a + b - 27 = 10b + a, so 9a - 9b = 27 and a - b = 3. Solving with a + b = 9 gives a = 6 and b = 3, so the number is 63. Check: 63 - 27 = 36, which is 63 reversed. Always verify a word-problem answer against the original wording, not against your own equation.
Question 199
The 5th term of a geometric progression whose first term is 2 and common ratio 3 is:
Select an option first.
Correct answer: C — 162
Explanation: The nth term is a r raised to (n - 1), so the 5th term is 2 x 3 to the power 4 = 2 x 81 = 162. Distractor B uses 3 to the power 5, an off-by-one in the index; distractor D is 3 to the power 5 alone, ignoring the first term. Write out the terms - 2, 6, 18, 54, 162 - if in any doubt.
Question 200
The 10th term of the arithmetic progression 2, 5, 8, ... is:
Select an option first.
Correct answer: D — 29
Explanation: The nth term is a + (n - 1)d = 2 + 9 x 3 = 29. The multiplier is 9, not 10, because the first term already exists before any common difference is added. Distractor B uses 10 instead of 9 - an off-by-one that accounts for most errors on this formula.
Question 201
Find the next letter of the series: C, F, I, L, ___
Select an option first.
Correct answer: A — O
Explanation: The positions are 3, 6, 9 and 12, rising by 3 each time, so the next is 15 - the letter O. Converting to position numbers is always faster than counting letters, and it makes the constant gap of 3 immediately visible.
Question 202
Doctor is to Patient as Lawyer is to:
Select an option first.
Correct answer: D — Client
Explanation: The relationship is that of a professional to the person he serves: a doctor treats a patient, a lawyer represents a client. Court, judge and law all relate to a lawyer, but through place, counterpart and subject rather than through the service relationship. State the relationship in words before looking at the options - the trap is always an option related by a different link.
Question 203
Book is to Author as Painting is to:
Select an option first.
Correct answer: B — Artist
Explanation: The relation is between a work and the person who creates it: an author writes a book, an artist paints a painting. Canvas is the material, brush the instrument and gallery the place - each connected to painting, but by a different relation. Naming the relationship in words before scanning the options is what keeps you out of the near-miss traps.
Question 204
At exactly 3 o'clock, the angle between the hour hand and the minute hand is:
Select an option first.
Correct answer: C — 90 degrees
Explanation: The dial of 360 degrees is divided into 12 hour spaces of 30 degrees each. At 3 o'clock the hands are three spaces apart, giving 3 x 30 = 90 degrees. The general formula for any time is the absolute value of 30H minus 5.5M, which at H = 3 and M = 0 also gives 90 degrees.
Question 205
A father is three times as old as his son. In 12 years he will be twice as old. The son's present age is:
Select an option first.
Correct answer: A — 12 years
Explanation: Let the son be x, so the father is 3x. In 12 years, 3x + 12 = 2(x + 12), giving 3x + 12 = 2x + 24 and x = 12. Check: 12 and 36 now; 24 and 48 in twelve years, which is exactly double. Set up one unknown and translate each sentence into an equation.
Question 206
Pointing to a photograph, a man said, 'She is the daughter of my grandfather's only son.' How is the woman in the photograph related to him?
Select an option first.
Correct answer: C — His sister
Explanation: His grandfather's only son must be his own father. The daughter of his father is therefore his sister. Work these puzzles from the INSIDE out, resolving the innermost description first and substituting it before moving outward - attempting the whole chain in one step is where errors arise.
Question 207
A is B's sister. C is B's mother. D is C's father. E is D's mother. How is A related to D?
Select an option first.
Correct answer: D — Granddaughter
Explanation: C is B's mother, and since A is B's sister, C is also A's mother. D is C's father, so D is A's mother's father - that is, A's grandfather. A is therefore D's granddaughter. E is a red herring, introduced only to tempt the great-granddaughter answer. Draw a vertical family tree and mark each generation before answering.
Question 208
Showing a photograph, Ram said, 'He is the son of my mother's only son.' Who is in the photograph?
Select an option first.
Correct answer: C — Ram's son
Explanation: Ram's mother's only son must be Ram himself. The person in the photograph is therefore Ram's son. The phrase 'only son' is the whole of the clue: it forces the identification with the speaker, and without it the answer would be a nephew - which is exactly what distractor D tests.
Question 209
A is the brother of B. C is the father of A. D is the brother of C. How is D related to B?
Select an option first.
Correct answer: B — Uncle
Explanation: C is A's father, and since A and B are brothers, C is also B's father. D is C's brother, so D is B's father's brother - that is, B's uncle. The sibling link transfers the parent: whatever is true of A's father is true of B's father.
Question 210
Introducing a man, a woman said, 'His wife is the only daughter of my father.' How is the man related to the woman?
Select an option first.
Correct answer: A — Husband
Explanation: The only daughter of the woman's father is the woman herself. So the man's wife is the speaker, which makes him her husband. These self-referential clues are the standard difficulty in this topic: resolve the innermost phrase into a named person - here 'me' - before reading the rest of the sentence.
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