EPFO APFC 2023 General Studies · Question 104 of 120

Correct — C, (c) 3. The Directions block printed above this item carries a table of earnings and profits for four companies, X, Y, Z and W, over the years 2016 to 2020, and that table governs this question and the two that follow it. This item uses only the earnings rows for the first and last of those years, and it asks a threshold question rather than a computation: for how many of the four companies is the 2020 earning at least twenty per cent above the 2016 earning? Read the two rows off the table. Company X earned 100 in 2016 and 130 in 2020; company Y earned 95 and 96; company Z earned 74 and 89; company W earned 50 and 95. A rise of at least twenty per cent means the later figure is at least 1·2 times the earlier one, so the test on each company is whether the 2020 earning reaches 1·2 times its 2016 earning. For X, 1·2 × 100 = 120 and the company earned 130, so X qualifies — the rise is thirty per cent. For Y, 1·2 × 95 = 114 and the company earned only 96, so Y fails badly; its earnings rose by one unit in five years, barely one per cent. For W, 1·2 × 50 = 60 and the company earned 95, so W qualifies with room to spare — its earnings nearly doubled, a rise of ninety per cent. That leaves company Z, which is the whole point of the question. Its earnings went from 74 to 89, a rise of 15. Twenty per cent of 74 is 14·8, and 15 exceeds 14·8, so Z qualifies — but only just, by two tenths of a unit. Three companies clear the threshold and one does not, so the count is 3. Decimals can be avoided altogether, and on a boundary case like Z that is the safer route. A rise of at least twenty per cent means the ratio of later to earlier is at least 6/5, so cross-multiplying, the test is whether five times the 2020 earning is at least six times the 2016 earning. For Z: 5 × 89 = 445 and 6 × 74 = 444, and 445 is greater than 444, so Z clears the bar by a single unit in that comparison. For X: 650 against 600, clear. For W: 475 against 300, clear. For Y: 480 against 570, nowhere near. Whole numbers, no rounding, no ambiguity — and on a question decided by a margin this thin, no rounding is exactly what is wanted.

• (a)1 — A count of one is what a candidate produces who reads 'increased by at least 20%' as though it meant a dramatic increase, and therefore notices only company W, whose earnings went from 50 to 95 and nearly doubled. It is also where a candidate lands who compares absolute increases rather than proportional ones and concludes that only the largest jump counts. Both readings ignore the words the stem actually uses. 'At least 20%' is a floor, not a description of magnitude, and three of the four companies clear it: X rose thirty per cent, W rose ninety per cent, and Z rose a little over twenty. The absolute-increase reading is doubly misleading here, because W's rise of 45 units is larger than X's rise of 30 in absolute terms but smaller than X's in no sense at all once expressed as a percentage — the two orderings happen to agree for these companies, which makes the wrong method look safe until the data changes.
• (b)2 — This is the serious distractor, and it is where the item does its work. A count of two is what a candidate gets who accepts X and W but rejects company Z, and there are two ways to reject Z wrongly. The first is to take twenty per cent of the wrong base: twenty per cent of 89, the 2020 figure, is 17·8, and Z's rise of 15 falls short of that, so the company appears to fail. But a percentage increase is always measured against the earlier value, so the base is 74, twenty per cent of which is 14·8, and 15 clears it. Using the later figure as the base understates every growth rate and is the single commonest error in data interpretation. The second way to reject Z is to estimate: 15 out of 74 looks like 'about a fifth' and a candidate who cannot tell which side of a fifth it falls on may play safe and exclude it. The cross-multiplication settles it without decimals — 5 × 89 = 445 against 6 × 74 = 444 — and Z is in.
• (d)4 — A count of four means company Y has been admitted, and Y is the one company that plainly fails. Its earnings were 95 in 2016 and 96 in 2020: a rise of a single unit, which is about one per cent over five years. The error behind this option is reading the word 'increased' and stopping there, without applying the twenty per cent qualifier — all four companies did earn more in 2020 than in 2016, so the count of companies that merely increased is indeed four, and that is the question a hurried candidate answers. Y's row is also the flattest in the table, dipping to 90 in 2019 before recovering to 96, so it is the one company whose earnings show no trend at all. A second route to this option is reading down the wrong column pair or drifting between the earning and profit rows, which is easy in a table that alternates two rows per year for five consecutive years.

Percentage change is measured against the earlier value, always. If a quantity moves from an old value to a new one, the percentage change is (new − old) divided by old, times a hundred, and the denominator is the old value even when the change is a fall. Dividing by the new value instead is the most frequent error in the whole of data interpretation, and it is systematically biased: it understates every increase and overstates every decrease, so a candidate who makes it consistently will still get many questions right and will fail exactly the boundary cases the examiner builds the item around. Threshold questions of the form 'how many rose by at least p per cent' are best handled without computing any percentage at all. A rise of at least p per cent means new ≥ (1 + p/100) × old, and for the round thresholds that papers use, that multiplier is a simple fraction: 6/5 for twenty per cent, 11/10 for ten per cent, 5/4 for twenty-five per cent, 3/2 for fifty per cent. Cross-multiplying turns the test into a comparison of two whole numbers, which is faster than dividing and cannot go wrong by rounding. The other habit a table rewards is deciding which rows are relevant before touching any arithmetic. A table like this one holds forty numbers; this question needs eight of them, and every one of the other thirty-two is a chance to read the wrong cell.

This is the opening item of the only shared-context set outside the English Language section of the paper: one Directions block and one table, printed once above this question, govern this item and the next two. That layout has a practical consequence worth planning for. The table has to be understood once and then used three times, so the time spent orienting in it — which rows are earnings and which are profits, which columns are companies, what the unit is — is amortised across three questions and should be spent deliberately rather than skipped. The unit here is thousand crore rupees, and it never matters: every question in the set compares figures within the table, so the unit cancels and no conversion is ever required. The examiner's lever in this particular item is a single boundary. Two companies clear the twenty per cent bar by a mile and one fails by a mile; the item is decided entirely by company Z, whose rise of 15 on a base of 74 is 20·27 per cent, clearing the threshold by about a quarter of a unit. An examiner who wanted an easy question would not have chosen 74 and 89. One warning about self-checking on this item: reading the profit rows by mistake instead of the earnings rows also yields three companies above twenty per cent, so arriving at the printed answer is no proof that the right rows were read. Confirm the row labels, not just the count.

• Percentage increase is (new − old)/old × 100, and the base is always the earlier figure. Using the later figure as the base understates every increase — twenty per cent of Z's 2020 earning of 89 is 17·8, which would wrongly exclude it, whereas twenty per cent of its 2016 earning of 74 is 14·8, which its rise of 15 clears.
• A rise of at least twenty per cent means the later value is at least 6/5 of the earlier one, so the test can be run entirely in whole numbers: 5 × later against 6 × earlier. For company Z that is 5 × 89 = 445 against 6 × 74 = 444, so Z qualifies by a margin of one in the cross-product. No decimals and no rounding are involved.
• The earnings rows for 2016 and 2020 are the only data this item needs: X 100 to 130, a rise of thirty per cent; Y 95 to 96, a rise of about one per cent; Z 74 to 89, a rise of 20·27 per cent; W 50 to 95, a rise of ninety per cent. Three of the four clear the twenty per cent threshold, so the answer is three.
• The Directions block and the table are printed once, above this question, and govern the next two items as well. Neither of those prints the table again, so the reader who skips the block cannot answer them at all. In this booklet the arrangement occurs only here outside the English Language section.
• The common threshold multipliers, worth memorising as fractions for cross-multiplication: ten per cent is 11/10, twenty per cent is 6/5, twenty-five per cent is 5/4, thirty-three and a third per cent is 4/3, fifty per cent is 3/2 and one hundred per cent is 2. Each turns a percentage test into a comparison of two integers.

• Measuring the percentage rise against the later figure instead of the earlier one. That is what excludes company Z, and it is the error the whole item is constructed around; twenty per cent of 74 is 14·8, not twenty per cent of 89, which is 17·8.
• Reading 'increased by at least 20%' as merely 'increased'. All four companies earned more in 2020 than in 2016, so ignoring the qualifier gives a count of four; company Y's rise was from 95 to 96, about one per cent over five years.
• Estimating on a boundary case. Fifteen on a base of seventy-four is 20·27 per cent, which no eyeball estimate can be trusted to place on the right side of twenty; the whole-number test 5 × 89 against 6 × 74 settles it in one line.
• Drifting between the earning and profit rows in a table that alternates them for five consecutive years. Here the mistake is unusually well hidden, because the profit rows also give three companies above twenty per cent, so the count alone will not reveal the misreading.

Table-based data interpretation in EPFO papers comes as a set of two or three items sharing one Directions block, and the items within a set are deliberately of different kinds so that the table has to be understood rather than scanned. A counting item like this one — how many rows or columns satisfy a stated condition — is the usual opener, because it forces the candidate across the whole table once. It is typically followed by a comparison item asking which entity did best or worst on some derived measure, and often by a third asking for a ratio, an average or a difference. The recurring levers are always the same three: the choice between absolute and relative change, the choice of base year, and a boundary case placed so that estimation fails. Preparation is procedural rather than mathematical — read the Directions and the row labels before the first question, identify precisely which cells each item needs, and convert every percentage threshold into a fraction so the comparisons can be done in whole numbers.

No directly related past PYQ was found.

• practice — not a real PYQ

  A shop's annual sales over four consecutive years were 60, 66, 72 and 75 units. In how many of the last three of those years did sales rise by at least 10 per cent over the preceding year?

  • (a)0
  • (b)1
  • (c)2
  • (d)3

  Answer(b) 1 — a rise of at least ten per cent means the later figure is at least 11/10 of the earlier one. From 60 to 66 the rise is exactly ten per cent, and 'at least' includes it. From 66 to 72 the rise is 6 on a base of 66, about 9·1 per cent, and 11 × 66 = 726 exceeds 10 × 72 = 720, so it fails. From 72 to 75 the rise is about 4·2 per cent. Only one year qualifies, and the boundary year is included because the condition says 'at least'.

• practice — not a real PYQ

  A company's earnings rose from 250 units in one year to 295 units in a later year. Which one of the following statements about that change is correct?

  • (a)The earnings rose by more than 20 per cent
  • (b)The earnings rose by exactly 20 per cent
  • (c)The earnings rose by less than 20 per cent
  • (d)The percentage rise cannot be determined from the figures given

  Answer(c) The earnings rose by less than 20 per cent — the rise is 45 on a base of 250, which is 18 per cent. The whole-number test gives the same result without dividing: a rise of twenty per cent requires 5 × later to be at least 6 × earlier, and 5 × 295 = 1475 falls short of 6 × 250 = 1500. Choosing the later figure as the base would give 45/295, about 15·3 per cent, which is also below twenty and so hides the error on this particular pair of numbers.