SSC CGL 2024 Tier-I · 11 September 2024, Shift 2 · Quantitative Aptitude · Question 18 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

Find the average of the prime numbers lying between 50 and 76.

(a)64
(b)60
(c)66
(d)62

Answer

Why

Correct — A. First list the primes, then take a plain mean.

Primes strictly between 50 and 76: 53, 59, 61, 67, 71, 73 — six numbers.
Every other value in 51–75 carries a factor of 2, 3, 5 or 7.

Add them, showing the running total:
53 + 59 = 112
112 + 61 = 173

173 + 67 = 240
240 + 71 = 311
311 + 73 = 384

Divide by the count: 384 ÷ 6 = 64 → option (a).

Why the others are wrong

(b)
60 — 60 sits below the true mean. The two primes under 60 (53 and 59) fall short of it by only 8 in total, while the four above it (61, 67, 71, 73) exceed it by 32 — a net surplus of 24 over six terms, which lifts the mean to 64.
(c)
66 — 66 demands a total of 66 × 6 = 396. The six primes add to 384, twelve less. Recount the sum before dividing rather than eyeballing the middle of the range.
(d)
62 — 62 is what you get by stopping the list at 71: 53 + 59 + 61 + 67 + 71 = 311, and 311 ÷ 5 = 62.2. 73 is prime too, so the list has six entries, not five.

Concept

A prime has exactly two divisors, 1 and itself. To settle any number below 100 you only need to try 2, 3, 5 and 7 — the next prime is 11, and 11 × 11 = 121 is already past 100.

That trial division is the whole first half of this question. The second half is an ordinary mean: add the values, divide by how many there are.

The examiner's leverage is the list, not the arithmetic. Miss one prime and both the total and the count change, so the mean moves twice.

"Between 50 and 76" is read here as exclusive, but neither 50 nor 76 is prime, so an inclusive reading returns the same six numbers and the same answer.

Key facts

The primes between 50 and 76 are 53, 59, 61, 67, 71 and 73 — six numbers totalling 384.
51 = 3 × 17, 57 = 3 × 19 and 69 = 3 × 23 are composite even though each reads as prime at a glance.
Testing a number below 100 for primality needs trial division by 2, 3, 5 and 7 only, because 11² = 121 > 100.

Study next

Primality testing by trial division up to √nMean of an ungrouped list of valuesPrimes and composites between 1 and 100

Common traps

Counting 51, 57 or 69 as prime because they are odd and not obviously factorable.
Dividing by 5 after having correctly listed six primes.
Averaging the two endpoints of the range instead of the primes inside it.

The arithmetic is deliberately light so the marks turn on the list. Write the six primes down before adding anything — a recount costs seconds, a wrong list costs the mark.

Related PYQs

No directly related past PYQ was found.