EPFO APFC 2023 General Studies · Question 106 of 120

Correct — B, (b) Y. Like the item before it, this question prints only its own sentence; the Directions block and the table of earnings and profits were printed once above the first question of the set and govern all three. Two words fix what has to be computed. 'Absolute' means the jump is measured in the table's own units, not as a proportion of anything — so this is a subtraction and not a division, the exact opposite of the previous item. 'Over the previous year' fixes the comparison as 2017 against 2016. And the row is the profit row, not the earnings row. So take the four profit figures for 2016 and 2017 and subtract. Company X made 20·5 in 2016 and 22·4 in 2017, a jump of 1·9. Company Y made 8·5 and then 9·5, a jump of 1·0. Company Z made 7·5 and then 8·8, a jump of 1·3. Company W made 4 in 2016 and 5·5 in 2017, a jump of 1·5. The four jumps are 1·9, 1·0, 1·3 and 1·5, and the smallest of them is company Y's, which is option (b). It is the only whole-number jump in the set and the only one below one and a quarter. Two habits make this reliable rather than lucky. The first is to write all four subtractions down before comparing any of them; the numbers are close enough that stopping after two — say at Y's 1·0 and Z's 1·3 — leaves a real risk that an uncomputed company is smaller still. The second is to watch the decimals. Three of the four subtractions cross a decimal boundary, 22·4 minus 20·5 and 8·8 minus 7·5 and 5·5 minus 4, and the 2016 profit of company W is printed as a bare 4 with no decimal at all, which is easy to read as 4·0 in one glance and as something else in a hurried one. Note also how completely this item inverts the one before it. There, the measure was relative and the direction was maximum, and the answer was company Y because its small base magnified a modest gain. Here, the measure is absolute and the direction is minimum, and the answer is company Y again — but for the opposite reason, because in absolute units a company with small profits also tends to move in small steps. The same letter is correct in both items and the reasoning that gets there is entirely different, which is exactly the trap a shared table allows an examiner to set.

• (a)X — Company X is where a candidate lands who computes proportions instead of differences, and it is the single most likely wrong answer here. In relative terms X did have the smallest jump in 2017: its profit rose by 1·9 on a base of 20·5, about 9·3 per cent, against Y's 11·8 per cent, Z's 17·3 per cent and W's 37·5 per cent. So a candidate who read the previous item, worked in percentages there and carried the habit across will find a defensible-looking answer waiting. But 'absolute' is printed in the stem, and in absolute units X's jump of 1·9 is the largest of the four, not the smallest — the exact opposite of what is asked. This is the clearest illustration in the set of why the adjective must be read: on these numbers the relative and absolute orderings are almost perfectly reversed at the top and bottom, and confusing them turns a right answer into the most wrong one available.
• (c)Z — Company Z's profit rose from 7·5 in 2016 to 8·8 in 2017, a jump of 1·3. That is the second smallest of the four and it is close enough to Y's 1·0 to be chosen by a candidate who has done the subtraction carelessly. The likeliest route here is a decimal slip: 8·8 minus 7·5 is 1·3, but read against the neighbouring row it is easy to subtract the wrong pair, and 8·8 minus 8·5 gives 0·3, which would make Z look like the minimum by a wide margin. A second route is stopping early — Z's figures sit directly below X's large ones, so a candidate scanning down the column meets a small difference for the first time at Z and may not carry on to Y and W at all. The safeguard is mechanical: compute all four differences, then compare. Four subtractions on a table this size take about fifteen seconds.
• (d)W — Company W has the smallest profits in the table — 4 in 2016 and 5·5 in 2017, the two lowest figures in that column — so it is the natural choice for a candidate who reads 'minimum' as being about the size of the company rather than the size of the change. Its jump is 1·5, third smallest of the four and half as large again as company Y's 1·0. In relative terms W is not merely wrong but the furthest possible from right: a rise of 1·5 on a base of 4 is 37·5 per cent, the largest proportional jump of any company in 2017. So whichever measure is used, W is not the minimum — smallest in absolute level, third in absolute change, first in relative change. The lesson is that a table's smallest numbers and its smallest movements are unrelated questions, and the stem here asks about the movement.

An absolute change is a subtraction, carried out in the units the table uses; a relative change is that difference divided by the value it started from. Because the two use different denominators — one has none at all, the other has the base value — they rank the same set of entities differently whenever the bases differ, which in a table of companies of different sizes they always do. In these 2017 profit figures the two orderings are close to reversed: by absolute change the ranking from smallest to largest runs Y, Z, W, X, while by relative change it runs X, Y, Z, W. Company X is the smallest mover in proportional terms and the largest in absolute terms, and company W is the largest proportionally and only the third largest absolutely. Neither ordering is more correct than the other; they answer different questions, and the examiner's job in a data-interpretation set is to make sure the candidate answers the one printed. There is a structural reason absolute and relative measures diverge like this. Large entities move in large absolute steps and small proportional ones, small entities in the reverse, so absolute comparisons tend to be dominated by the size of the entity and relative comparisons by its volatility. Analysts therefore report both, and a table that shows only one is incomplete. For an exam, the practical rule is short: the words 'absolute', 'difference', 'more than' and 'by how much' call for a subtraction; the words 'relative', 'percentage', 'proportional', 'growth rate' and 'times' call for a division.

This is the last of the three questions governed by the table printed above the first of them, and the notes record that the table itself is on an earlier page — this item's page carries neither the Directions block nor the data, only the sentence. A candidate who has not held the table in view has nothing at all to work from, which is the practical reason a shared-context set must be attempted together and in order. The set's design is worth studying as a whole because it is the only one of its kind outside the English Language section of this booklet. Its three items switch the row from earnings to profits, the years from 2016-to-2020 to 2019-to-2020 to 2016-to-2017, the measure from a percentage threshold to a relative jump to an absolute jump, and the direction from a count to a maximum to a minimum. Nothing carries across except familiarity with the table. Most tellingly, this item and the one before it have the same answer, company Y, arrived at by opposite reasoning — Y is the biggest relative riser in 2020 because it starts from the smallest base, and the smallest absolute riser in 2017 for the same underlying reason, that small profits move in small steps. A candidate who notices the repeat and doubts it may talk themselves out of a correct answer; the repetition is a property of the data, not a signal.

• The 2017 profit jumps over 2016, read from the table's profit rows: company X 22·4 minus 20·5 = 1·9; company Y 9·5 minus 8·5 = 1·0; company Z 8·8 minus 7·5 = 1·3; company W 5·5 minus 4 = 1·5. The smallest absolute jump is company Y's 1·0, and it is the only one of the four that is a whole number.
• Absolute change is a subtraction in the table's own units; relative change is that difference divided by the earlier value. The two orderings differ here almost completely: by absolute jump the order from smallest is Y, Z, W, X, while by relative jump it is X at 9·3 per cent, Y at 11·8, Z at 17·3 and W at 37·5.
• Company X has the largest absolute jump in 2017 and the smallest relative one, so a candidate who computes percentages when the stem says 'absolute' does not merely miss the answer — they select the company that is furthest from it on the measure actually asked for. Reading the adjective is worth more here than any arithmetic.
• Company W holds the two smallest profit figures in the 2016 and 2017 columns, 4 and 5·5, but its jump of 1·5 is neither the smallest absolute change nor anywhere near the smallest relative one — at 37·5 per cent it is the largest proportional jump in that year. The smallest values in a table and the smallest changes in it are unrelated.
• The three items of this set change the row, the years, the measure and the direction between them, and the second and third happen to share the same answer for opposite reasons. A repeated answer inside a shared-context set is a property of the data and not evidence that a question has been misread.

• Computing percentages when the stem says 'absolute'. That produces company X, whose relative jump of about 9·3 per cent is the smallest of the four while its absolute jump of 1·9 is the largest — the furthest possible answer from the one asked for.
• Choosing the company with the smallest profits. Company W's figures of 4 and 5·5 are the lowest in those two columns, but its jump of 1·5 is larger than company Y's 1·0, and in proportional terms it is the biggest riser of the year at 37·5 per cent.
• Stopping the subtraction early. The four differences 1·9, 1·0, 1·3 and 1·5 lie close together, so a candidate who computes two and picks the smaller of them has a real chance of missing the true minimum; all four have to be written down before any comparison.
• Subtracting the wrong pair of cells. Each year occupies two rows, earnings and profit, for five consecutive years, so the eye slips easily between adjacent rows; 8·8 minus 8·5 gives a spurious 0·3 and would put company Z in first place by a wide margin.

The closing item of a shared-context set is usually the one that reverses something in the item before it — maximum becomes minimum, relative becomes absolute, or the year of comparison shifts — because that is the cheapest way for an examiner to test whether the table was understood or merely used once. Expect the pair to be adjacent and expect the second to look almost identical to the first at a glance. Beyond this reversal, the standard closing forms are a difference or total across a row, a ratio between two cells, an average over the years shown, and a question about the year in which some quantity peaked. All of them are two or three operations at most, so accuracy rather than technique decides the mark. The routine that works is the same every time: read the adjective and the year before looking at the table, identify exactly which cells are needed, write the small number of arithmetic results down in full, and only then compare them.

No directly related past PYQ was found.

• practice — not a real PYQ

  The output of four units changed over a year as follows: unit P from 18 to 20, unit Q from 45 to 49, unit R from 6 to 9 and unit S from 70 to 75. Which unit showed the smallest absolute increase in output?

  • (a)P
  • (b)Q
  • (c)R
  • (d)S

  Answer(a) P — the absolute increases are P 2, Q 4, R 3 and S 5, so P is the smallest. The item is built so that the relative ordering disagrees: in percentage terms P rose 11·1, Q 8·9, R 50 and S 7·1 per cent, making S the smallest relative riser. A candidate who computes percentages when the stem says 'absolute' will choose S and be wrong on the measure printed.

• practice — not a real PYQ

  A company's annual profit over four consecutive years was ₹4.0 crore, ₹6.4 crore, ₹9.0 crore and ₹12.0 crore. In which year was the absolute increase over the preceding year the greatest?

  • (a)The second year
  • (b)The third year
  • (c)The fourth year
  • (d)The increase was the same in each of the three years

  Answer(c) The fourth year — the year-on-year increases are 2.4, 2.6 and 3.0 crore, so the largest absolute rise is the last of them. In relative terms the ordering is reversed: the increases are 60 per cent, 40.6 per cent and 33.3 per cent, so the greatest proportional rise came in the second year, when the base was smallest. The same series can give opposite answers depending on which measure the stem names.