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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 421
The odds in favour of an event are 3 : 2. The probability of the event is:
Select an option first.
Correct answer: A — 0.6
Explanation: Odds in favour of 3 : 2 mean 3 favourable outcomes against 2 unfavourable, giving 3 out of a total of 5, that is 0.6. Distractor C, 3/2, is the odds ratio itself, which cannot be a probability since it exceeds 1. Odds compare favourable with unfavourable, while probability compares favourable with the TOTAL.
Question 422
For a frequency distribution with open-ended classes, the most appropriate measure of central tendency is the:
Select an option first.
Correct answer: B — Median
Explanation: An open-ended class such as 'below 10' or '60 and above' has no definite class mark, so any measure requiring one - the arithmetic or geometric mean - cannot be computed without an arbitrary assumption. The median depends only on the position of the middle observation, which usually falls in a closed class, so it can still be found.
Question 423
For a negatively skewed distribution:
Select an option first.
Correct answer: D — Mode is greater than median, which is greater than mean
Explanation: A long tail to the LEFT drags the mean furthest down, the median less so, while the mode remains at the peak - giving mode above median above mean. Sketch the curve with its tail on the left and read the order off the horizontal axis; it is faster and safer than recalling the inequality.
Question 424
Paasche's price index uses as weights the quantities of the:
Select an option first.
Correct answer: A — Current year
Explanation: Paasche uses CURRENT year quantities, so the basket is re-weighted every period to reflect what people actually buy now. That makes it more up to date than Laspeyres but far more laborious, since quantity data must be collected afresh each time, and it tends to have a downward bias.
Question 425
In sampling theory, a PARAMETER is:
Select an option first.
Correct answer: A — A measure describing the population
Explanation: A parameter describes the population - the population mean or standard deviation, for instance - and is usually unknown. The corresponding measure computed from a sample is a STATISTIC, and is used to estimate the parameter. Sampling theory is entirely about how good that estimate is.
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Question 426
The Poisson distribution has:
Select an option first.
Correct answer: D — One parameter
Explanation: The Poisson is fully specified by its mean m, which is also its variance, so a single parameter determines the whole distribution. The binomial needs two, n and p, and the normal needs two, the mean and the standard deviation. Counting parameters is a standard one-mark discriminator between the three.
Question 427
The parameters of a normal distribution are:
Select an option first.
Correct answer: D — The mean and the standard deviation
Explanation: A normal distribution is completely specified once its mean, which fixes its location, and its standard deviation, which fixes its spread, are known. Distractor B gives the parameters of the BINOMIAL. Every distribution is defined by its own parameters, and naming them correctly is a standard one-mark question.
Question 428
For a standard normal distribution the mean and the standard deviation are respectively:
Select an option first.
Correct answer: D — 0 and 1
Explanation: Standardisation subtracts the mean and divides by the standard deviation, producing a distribution centred at 0 with a spread of 1. Every normal distribution reduces to this one, which is why a single table of areas serves them all - and why the z value is read as 'number of standard deviations from the mean'.
Question 429
The values that divide a distribution into 100 equal parts are called:
Select an option first.
Correct answer: C — Percentiles
Explanation: Percentiles divide the data into 100 equal parts, deciles into 10 and quartiles into 4, while the median is the single value dividing it into 2. Note the correspondences: the 50th percentile, the 5th decile, the 2nd quartile and the median are all the same value.
Question 430
Karl Pearson's coefficient of skewness is given by:
Select an option first.
Correct answer: B — (Mean minus Mode) divided by the standard deviation
Explanation: Pearson's measure divides the gap between mean and mode by the standard deviation, making it a pure number. Where the mode is ill-defined, the empirical relation converts it to 3(Mean minus Median) divided by SD. Distractor A is BOWLEY'S coefficient, based on quartiles - keep the two apart.
Question 431
In a Poisson distribution the mean is 3. The variance is:
Select an option first.
Correct answer: A — 3
Explanation: The defining property of the Poisson distribution is that its mean and variance are both equal to the parameter m, here 3. This makes it the limiting case of the binomial when n is large and p is small, with np held constant, and it is the distribution used for rare events such as accidents or printing errors per page.
Question 432
In a Poisson distribution, P(X = 1) equals P(X = 2). The mean is:
Select an option first.
Correct answer: D — 2
Explanation: Setting the two probabilities equal, m times e to the minus m equals m squared times e to the minus m divided by 2. The exponential and one factor of m cancel, leaving 1 = m/2, so m = 2. Cancelling the common exponential term first is what makes this a two-line answer rather than a numerical hunt.
Question 433
For a Poisson distribution with mean 1, the probability of exactly one occurrence is approximately:
Select an option first.
Correct answer: D — 0.3679
Explanation: P(X = 1) = e to the minus 1, multiplied by 1 to the power 1, divided by 1 factorial = 0.3679. Note that P(X = 0) is also 0.3679 when the mean is 1 - the only value of the parameter for which the first two probabilities are equal.
Question 434
For a Poisson distribution with mean 2, the probability of no occurrence is:
Select an option first.
Correct answer: A — 0.1353
Explanation: The Poisson probability of x occurrences is e to the power minus m, multiplied by m to the power x, divided by x factorial. For x = 0 this reduces to e to the power minus 2 = 0.1353. Distractor B is the probability of exactly one occurrence, which for m = 2 happens to be twice as large.
Question 435
For a positively skewed distribution:
Select an option first.
Correct answer: B — Mean is greater than median, which is greater than mode
Explanation: A long tail to the RIGHT pulls the mean furthest in that direction, the median less so, while the mode stays at the peak - giving mean above median above mode. Negative skewness reverses the order exactly. Sketching the curve with its tail is faster and safer than memorising the inequality.
Question 436
Primary data are those which are:
Select an option first.
Correct answer: B — Collected by the investigator for the first time, for the purpose in hand
Explanation: Primary data are original and gathered directly for the enquiry, so the investigator controls the definitions, coverage and accuracy. The same figures become SECONDARY data when reused by someone else for another purpose - the classification depends on the relationship between the user and the collection, not on the data themselves.
Question 437
The method of least squares fits a line by minimising:
Select an option first.
Correct answer: C — The sum of the squares of the deviations of the observed values from the line
Explanation: Squaring removes the signs, so positive and negative deviations cannot cancel, and it penalises large errors more heavily than small ones. Minimising the plain sum of deviations, as distractor A proposes, would be satisfied by infinitely many lines, since those deviations sum to zero for any line through the means.
Question 438
One card is drawn from a well-shuffled pack of 52. The probability that it is a king OR a heart is:
Select an option first.
Correct answer: B — 4/13
Explanation: P(king or heart) = P(king) + P(heart) - P(king of hearts) = 4/52 + 13/52 - 1/52 = 16/52 = 4/13. The king of hearts must be subtracted because it belongs to both sets and would otherwise be counted twice. Distractor A is exactly the answer obtained by omitting that subtraction.
Question 439
Two fair dice are thrown together. The probability that the sum of the numbers shown is 9 is:
Select an option first.
Correct answer: B — 1/9
Explanation: The favourable outcomes are (3,6), (4,5), (5,4) and (6,3) - four out of 36 equally likely outcomes - giving 4/36 = 1/9. Note that (3,6) and (6,3) are DIFFERENT outcomes because the dice are distinguishable; treating them as one is the classic error and would give 2/36.
Question 440
A card is drawn at random from a standard pack of 52. The probability that it is a face card is:
Select an option first.
Correct answer: D — 3/13
Explanation: The face cards are the jack, queen and king in each of the four suits, that is 12 cards, giving 12/52 = 3/13. Distractor A would be the probability of a specific rank such as a king, and distractor B that of a particular suit. Count the favourable cards explicitly rather than relying on memory.
Question 441
A number is chosen at random from 1 to 20. The probability that it is a multiple of 3 is:
Select an option first.
Correct answer: A — 3/10
Explanation: The multiples of 3 up to 20 are 3, 6, 9, 12, 15 and 18 - six numbers - so the probability is 6/20 = 3/10. Distractor B assumes that a third of any range must be divisible by 3, which fails whenever the range is not an exact multiple of 3. Count the favourable cases explicitly.
Question 442
The probability that a leap year selected at random contains 53 Sundays is:
Select an option first.
Correct answer: D — 2/7
Explanation: A leap year has 366 days, that is 52 complete weeks plus 2 odd days. The seven equally likely pairs of odd days are Sunday-Monday, Monday-Tuesday and so on, and 2 of them contain a Sunday. The probability is therefore 2/7. For an ORDINARY year, with only 1 odd day, it would be 1/7.
Question 443
Two fair dice are rolled together. The probability of obtaining a doublet is:
Select an option first.
Correct answer: C — 1/6
Explanation: The doublets are (1,1) through (6,6), that is 6 outcomes out of 36, giving 1/6. Distractor B, 1/36, is the probability of one SPECIFIED doublet such as two sixes. Read whether the question asks for any doublet or a particular one - the answers differ by a factor of six.
Question 444
Two fair dice are thrown. The probability that the sum is 7 is:
Select an option first.
Correct answer: C — 1/6
Explanation: The favourable outcomes are (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1) - six of the 36 equally likely results - giving 1/6. Seven is the most likely total with two dice, which is a useful sanity anchor: no other sum has six combinations.
Question 445
The probability of an impossible event is:
Select an option first.
Correct answer: A
Explanation: An impossible event contains no favourable outcome, so its probability is 0; a certain event has probability 1, and every probability lies between the two. A probability can never be negative or exceed 1, so an answer outside that range always signals an arithmetical error.
Question 446
A card is drawn from a well-shuffled pack of 52. The probability that it is a king or a queen is:
Select an option first.
Correct answer: C — 2/13
Explanation: There are 4 kings and 4 queens, and no card is both, so the events are mutually exclusive: 8/52 = 2/13. No overlap needs subtracting here, unlike the king-or-heart case where the king of hearts must be removed once. Ask whether the two categories can overlap before applying the addition rule.
Question 447
Three fair coins are tossed. The probability of getting exactly two heads is:
Select an option first.
Correct answer: C — 3/8
Explanation: There are 8 equally likely outcomes, of which HHT, HTH and THH give exactly two heads, so the probability is 3/8. The count of 3 is C(3,2), which is why this is a binomial situation with n = 3 and p = 1/2. Note that 'exactly two' is not 'at least two', which would also include HHH and give 4/8.
Question 448
Two cards are drawn one after another WITH replacement from a pack of 52. The probability that both are aces is:
Select an option first.
Correct answer: C — 1/169
Explanation: With replacement the pack is restored, so the draws are independent and the probability is (4/52) x (4/52) = (1/13) squared = 1/169. Distractor A is the WITHOUT replacement answer, (4/52) x (3/51). The single word 'replacement' decides which of the two applies.
Question 449
A bag contains 5 red and 3 blue balls. Two balls are drawn at random without replacement. The probability that both are red is:
Select an option first.
Correct answer: B — 5/14
Explanation: Favourable ways = C(5,2) = 10; total ways = C(8,2) = 28; probability = 10/28 = 5/14. Equivalently, 5/8 for the first ball multiplied by 4/7 for the second. Distractor A is the WITH replacement answer - after a draw without replacement both the numerator and the denominator fall by one.
Question 450
The probable error of the coefficient of correlation is used to:
Select an option first.
Correct answer: B — Test the significance of the observed correlation
Explanation: Probable error sets limits within which the true correlation is expected to lie. The working rules are that r is not significant if it is less than its probable error, and is significant if it exceeds six times the probable error. It is a test of reliability, not a correction to the value of r itself.
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