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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 361
Deflating a series of money values by a price index yields:
Select an option first.
Correct answer: C — The real value of the series, at constant prices
Explanation: Dividing money values by the price index and multiplying by 100 strips out the effect of price change, leaving the series expressed in constant prices - the real value. The identical procedure converts money wages into real wages, and it is the standard use of a cost of living index.
Question 362
The most appropriate diagram for showing the components of a total is a:
Select an option first.
Correct answer: A — Pie chart
Explanation: A pie chart divides a circle into sectors proportional to each component, so it displays parts of a whole directly - each 1% of the total corresponds to 3.6 degrees. A histogram shows a frequency DISTRIBUTION and a scatter diagram the relationship between two variables.
Question 363
The measure of dispersion least affected by extreme values is the:
Select an option first.
Correct answer: A — Quartile deviation
Explanation: Quartile deviation depends only on the middle half of the data, so values in either tail cannot influence it at all. The range is determined entirely by the two extremes, and the standard deviation squares deviations, which magnifies the effect of outliers rather than reducing it.
Question 364
If every observation in a data set is increased by 5, the standard deviation:
Select an option first.
Correct answer: B — Remains unchanged
Explanation: Standard deviation measures SPREAD about the mean. Adding a constant shifts every value and the mean by the same amount, so every deviation is unaltered and the standard deviation does not change. The mean, by contrast, increases by 5 - measures of location move with a change of origin while measures of dispersion do not.
Question 365
If every observation is multiplied by 3, the standard deviation is:
Select an option first.
Correct answer: A — Multiplied by 3
Explanation: Standard deviation is measured in the same units as the data, so multiplying every value by 3 multiplies it by 3. The VARIANCE, being in squared units, is multiplied by 9 - which is distractor C, offered to catch a confusion between the two. Dispersion is independent of a change of origin but not of a change of scale.
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Question 366
In the data set 10, 12, 14, 16 and 500, the measure LEAST distorted by the extreme value is the:
Select an option first.
Correct answer: B — Median
Explanation: The median is 14, sitting comfortably among the bulk of the data, whereas the mean is 110.4 - a figure no observation is anywhere near. The range and standard deviation are both driven almost entirely by the outlier. This is why the median is preferred for skewed data such as incomes.
Question 367
If every observation in a data set is divided by 5, the arithmetic mean is:
Select an option first.
Correct answer: A — Divided by 5
Explanation: The mean responds to a change of scale in exactly the same proportion as the data, so it too is divided by 5. This is the property underlying the step deviation method, in which a common factor is divided out to simplify the arithmetic and then multiplied back at the end.
Question 368
Which measure of central tendency is most affected by extreme values?
Select an option first.
Correct answer: C — Arithmetic mean
Explanation: The arithmetic mean uses every observation, so a single very large or very small value pulls it noticeably. The median depends only on position and the mode only on frequency, so both are resistant. This is why median income is reported rather than mean income - a few very high earners would distort the mean.
Question 369
The mean of 20 observations is 12. If every observation is multiplied by 3, the new mean is:
Select an option first.
Correct answer: A — 36
Explanation: Multiplying every value by a constant multiplies the mean by the same constant, giving 36. Contrast ADDING a constant, which adds it to the mean. Measures of location respond to both changes of origin and changes of scale, which is precisely what distinguishes them from measures of dispersion.
Question 370
If the sample size is increased fourfold, the standard error of the mean is:
Select an option first.
Correct answer: C — Halved
Explanation: The standard error varies inversely with the square root of the sample size, and the square root of 4 is 2, so it is halved. This is the law of diminishing returns in sampling: quadrupling the cost of the survey only doubles the precision, which is why very large samples are rarely worth it.
Question 371
For a moderately skewed distribution the mean is 35 and the median is 33. The mode is:
Select an option first.
Correct answer: D — 29
Explanation: The empirical relation is Mode = 3 Median - 2 Mean = 99 - 70 = 29. Since the mean exceeds the median, the distribution is positively skewed and the mode must be the smallest of the three - a check that rules out distractors B and D immediately. The relation is approximate and applies only to moderately skewed distributions.
Question 372
If A and B are mutually exclusive AND exhaustive events, then P(A) + P(B) equals:
Select an option first.
Correct answer: D — 1
Explanation: Exhaustive means one of them must occur, and mutually exclusive means they cannot both occur, so between them they account for the entire sample space and their probabilities sum to 1. A and its complement are the standard example of such a pair.
Question 373
The expected value of a constant k is:
Select an option first.
Correct answer: B — k
Explanation: A constant takes the value k with probability 1, so its expectation is k. Two related results follow and are frequently examined: E(kX) = k E(X), and the variance of a constant is zero, since a constant does not vary at all.
Question 374
Fisher's ideal index is:
Select an option first.
Correct answer: A — The geometric mean of Laspeyres' and Paasche's indices
Explanation: Fisher's index is the square root of the product of the Laspeyres and Paasche indices, that is their GEOMETRIC mean. By combining base year and current year weights it balances the upward bias of the one against the downward bias of the other, which is a large part of why it is called ideal.
Question 375
When the class intervals of a distribution are UNEQUAL, the histogram must be drawn using:
Select an option first.
Correct answer: D — Frequency density as the height of each rectangle
Explanation: In a histogram it is the AREA of each rectangle that represents the frequency, so with unequal widths the height must be frequency divided by class width. Using raw frequencies as heights would exaggerate the wider classes and give a misleading picture of the distribution's shape.
Question 376
A frequency polygon is obtained by joining:
Select an option first.
Correct answer: B — The mid-points of the tops of the histogram rectangles
Explanation: Plotting each class mark against its frequency and joining the points gives the polygon, which is usually closed by extending to the class marks of the empty classes at either end. Its advantage over the histogram is that two or more distributions can be superimposed for comparison.
Question 377
The geometric mean of 4 and 9 is:
Select an option first.
Correct answer: A — 6
Explanation: The geometric mean of two values is the square root of their product: the square root of 36 = 6. Distractor B is the arithmetic mean, which is always the larger of the two unless the values are equal. The geometric mean is the correct average for ratios and rates of growth, such as an average rate of return over several years.
Question 378
The geometric mean of 3 and 27 is:
Select an option first.
Correct answer: C — 9
Explanation: The geometric mean is the square root of the product: the square root of 81 = 9. Distractor A is the arithmetic mean, which is always the larger unless the two values are equal. Note that 3, 9 and 27 form a geometric progression with ratio 3.
Question 379
The mode of a frequency distribution can be located graphically from:
Select an option first.
Correct answer: B — A histogram
Explanation: The modal class is the tallest rectangle of the histogram; joining its top corners to the corresponding corners of the adjacent rectangles and dropping a perpendicular from the intersection gives the mode. An ogive locates the median and quartiles instead - the two graphs answer different questions.
Question 380
The harmonic mean of 2 and 6 is:
Select an option first.
Correct answer: A — 3
Explanation: The harmonic mean of two values is 2ab/(a + b) = (2 x 2 x 6)/8 = 3. It is the reciprocal of the mean of the reciprocals and is the right average for rates expressed per unit, such as speed over equal distances. Note the ordering that always holds: harmonic mean 3, geometric mean 3.46, arithmetic mean 4.
Question 381
The expression (Q3 + Q1 - 2 Median) divided by (Q3 - Q1) is:
Select an option first.
Correct answer: C — Bowley's coefficient of skewness
Explanation: This is Bowley's measure, built entirely on positional values and therefore usable with open-ended classes. It lies between -1 and +1 and is zero when the median sits midway between the quartiles. Pearson's coefficient uses the mean, mode and standard deviation instead.
Question 382
The regression coefficients of y on x and of x on y are given as 0.9 and 1.2 respectively. This is:
Select an option first.
Correct answer: C — Impossible, since their product exceeds 1 and r squared cannot exceed 1
Explanation: The product of the two regression coefficients equals r squared, and here 0.9 x 1.2 = 1.08, which exceeds 1 - impossible, since the correlation coefficient lies between -1 and +1. Multiplying the two coefficients is the quickest validity check on any question that supplies both, and examiners set such data deliberately.
Question 383
The inclusive and exclusive methods of forming classes differ in their treatment of:
Select an option first.
Correct answer: D — The class limits
Explanation: Under the exclusive method the upper limit of one class is the lower limit of the next and is excluded from it; under the inclusive method both limits belong to the class and a gap appears between classes. That gap must be closed by converting to class BOUNDARIES before computing a median or mode.
Question 384
A and B are independent events with P(A) = 0.4 and P(B) = 0.5. The probability that both occur is:
Select an option first.
Correct answer: C — 0.2
Explanation: For independent events the probabilities multiply: 0.4 x 0.5 = 0.2. Distractor A adds them, which would apply to the probability of A OR B for mutually exclusive events. Independence and mutual exclusiveness are opposite ideas - two events with non-zero probabilities cannot be both.
Question 385
If A and B are independent events, then A and the complement of B are:
Select an option first.
Correct answer: B — Also independent
Explanation: If knowing that B occurred tells you nothing about A, then knowing that B did NOT occur tells you nothing either - independence carries over to the complements. Formally P(A and not B) = P(A) x P(not B). This lets 'at least one' problems be solved through the complement without losing independence.
Question 386
Laspeyres' price index uses as weights the quantities of:
Select an option first.
Correct answer: B — The base year
Explanation: Laspeyres uses BASE year quantities, so the same basket is priced in both years and the index is easy to compute from period to period. Its weakness is that it ignores substitution away from goods that have become dearer, which tends to give an upward bias. Paasche, using current year quantities, has the opposite bias.
Question 387
The regression coefficient of y on x measures:
Select an option first.
Correct answer: A — The change in y for a unit change in x
Explanation: The regression coefficient is the slope of the line of y on x, giving the average change in the DEPENDENT variable y for a unit change in the independent variable x. It carries units, unlike the correlation coefficient, which is a pure number measuring the strength of the relationship - distractor C describes that instead.
Question 388
If the coefficient of correlation is zero, the two variables are:
Select an option first.
Correct answer: A — Uncorrelated - there is no LINEAR relationship, though a non-linear one may exist
Explanation: The correlation coefficient measures the strength of a LINEAR association only. A value of zero rules out a straight-line relationship but not, for example, a parabolic one, in which y depends entirely on x yet r comes out at zero. Zero correlation therefore does not prove independence - a distinction examiners test directly.
Question 389
The relationship between the heights of fathers and the heights of their sons is an example of:
Select an option first.
Correct answer: B — Positive correlation
Explanation: Taller fathers tend to have taller sons, so the two variables move in the same direction, giving positive correlation. It is not PERFECT, since the relationship is a tendency rather than a rule - the distinction between a positive correlation and a perfect one is what distractor D tests.
Question 390
If the price index for 2026, with 2020 as base, is 145, then prices have:
Select an option first.
Correct answer: C — Risen by 45%
Explanation: The base year index is 100, so an index of 145 represents an increase of 45 points, that is a rise of 45%. Distractor A confuses the index LEVEL with the percentage CHANGE - the index says prices are 1.45 times the base level, not that they rose by 145%. Always subtract 100 before quoting a percentage increase.
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