Study the given table and answer the question that follows. The table represents the number of scooters (in thousands) manufactured by four companies A, B, C and D from the period 2012 to 2015. The average number of scooters produced by company D is what per cent (rounded off to 2 decimal places) more than the combined average number of scooters produced by the three companies A, B, and C?
- (a)52.75%
- (b)35.35%
- (c)44.66%
- (d)27.25%
Answer
Why
Correct — B. Take the four column totals off the table first.
A = 360+580+1000+1240 = 3180
B = 420+940+780+950 = 3090
C = 380+570+1020+1180 = 3150
D = 520+980+1090+1660 = 4250
D's average = 4250 ⁄ 4 = 1062.5
A, B and C together = 9420 spread over 12 entries = 9420 ⁄ 12 = 785
Excess = 1062.5 − 785 = 277.5
277.5 ⁄ 785 = 0.353503… → 35.35% → option (b)
Why the others are wrong
- (a)52.75% — For 52.75% the base would have to be about 695.6, since 1062.5 ⁄ 1.5275 = 695.6. The three companies' twelve figures average 785, so the excess is nothing like that large.
- (c)44.66% — 44.66% needs a base of about 734.5 (1062.5 ⁄ 1.4466). No reading of the table produces 734.5 — the A, B and C figures give exactly 785.
- (d)27.25% — 27.25% needs a base near 835. Even the commonest base error, dividing the 277.5 gap by D's own 1062.5, comes to 26.12% rather than 27.25%.
Concept
Two ideas meet here, and the arithmetic is the easy half.
"X is p% more than Y" always puts the quantity named after "than" in the denominator. The base is the combined A-B-C average, never D's.
The combined average of three companies over four years is their grand total divided by all twelve entries: 9420 ⁄ 12 = 785. Dividing by 4 instead would give the combined annual output of the three, a different quantity altogether.
The phrase "combined average" can be read two ways, and here both give the same number.
Total over twelve entries is 9420 ⁄ 12 = 785. Averaging the three companies' own averages — 795, 772.5 and 787.5 — also gives 785, because each company has the same four years behind it. The ambiguity costs you nothing on this question.
Key facts
- "X is p% more than Y" means p = (X − Y) ⁄ Y × 100, so the quantity named after "than" is the base.
- Company D averages 4250 ⁄ 4 = 1062.5 thousand scooters over 2012 to 2015.
- The combined average of A, B and C is 9420 ⁄ 12 = 785, not 9420 ⁄ 4 = 2355.
- The table is in thousands throughout, and a percentage comparison is unaffected by a shared unit.
Study next
Common traps
- Dividing the A+B+C total by 4 instead of 12, which turns a 35.35% rise into a 54.88% fall.
- Using D's own average as the base, which gives 26.12%.
- Rounding to 35.4% and then failing to find it among four two-decimal options.
SSC builds a small table, then asks one derived comparison from it — which company has the highest average at 9 Sep 2024, 16:00, Quant Q.11, and one total as a percentage of another at Quant Q.15 of this paper. The reading is never the difficulty. The denominator the wording asks for is.
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