SSC CGL 2024 Tier-I · 17 September 2024, Shift 3 · Quantitative Aptitude · Question 3 of 98

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.

If x is an integer such that x + 1⁄x = 65⁄8, then find the value of x − 1⁄x.

Answer

Why

Correct — C. The stem is an image: if x is an integer with x + 1⁄x = 65⁄8, find x − 1⁄x.

Read 65⁄8 as a mixed number:
65⁄8 = 8 + 1⁄8, which is exactly the shape x + 1⁄x when x = 8.

Substitute:
x − 1⁄x = 8 − 1⁄8 = (64 − 1)⁄8 = 63⁄8 → option (c), the picture showing 63 over 8.

Why the others are wrong

(a)
63⁄6 has the right numerator over the wrong denominator. The quantity subtracted is 1⁄8, so the common denominator can only be 8.
(b)
36⁄8 is 4.5, far below 8 − 1⁄8. The subtraction removes only one-eighth, so the numerator falls from 64 to 63, not to 36.
(d)
32⁄6 changes numerator and denominator at once. Neither 32 nor 6 can come out of 8 − 1⁄8, whose value is just under 8.

Concept

Two routes reach the same place, and knowing both saves a minute.

Reading route: 65⁄8 is the mixed number 8 + 1⁄8, and x + 1⁄x has that same shape, so x = 8 can be read straight off. This works only because the stem promises x is an integer.

Identity route: (x − 1⁄x)² = (x + 1⁄x)² − 4, so the square is 4225⁄64 − 256⁄64 = 3969⁄64, and its root is 63⁄8.

The identity route produces ±63⁄8. Only the positive value is printed, and it is the one x = 8 gives — the other root of the equation, x = 1⁄8, is not an integer.

Key facts

65⁄8 read as a mixed number is 8 + 1⁄8, which fixes x = 8.
(x + 1⁄x)² − (x − 1⁄x)² = 4 for every non-zero x.
8 − 1⁄8 = 63⁄8 = 7.875.

Study next

The identity pair (x + 1⁄x)² and (x − 1⁄x)² differing by 4Finding x² + 1⁄x² and x³ + 1⁄x³ from x + 1⁄xRecognising a mixed number as a value plus its own reciprocal

Common traps

Solving 8x² − 65x + 8 = 0 by formula when the mixed number can be read in one glance
Ignoring the integer condition, taking x = 1⁄8 and answering with the negative value

The options for this item are pictures, so the last step is matching a computed fraction to an image rather than to text. Value-finding by structure is also asked at 12 Sep 2024, 09:00, Quant Q.19, where 28.9 : x :: x : 36.1 has to be solved for x.

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