SSC CGL 2025 Tier-I · 15 September 2025, Shift 3 · Quantitative Aptitude · Question 3 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 11 September 2026.

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Which of the following represents the correct simplified value of the continued fraction:x = 1 + 1⁄(2+1⁄(2+1⁄2))

(a)8⁄5
(b)17⁄12
(c)7⁄5
(d)9⁄7

Answer

Why

Correct — B. Work from the innermost fraction outwards.

Innermost level: 2 + 1⁄2 = 5⁄2
Take its reciprocal: 1 ÷ 5⁄2 = 2⁄5

Next level: 2 + 2⁄5 = 12⁄5
Take its reciprocal: 1 ÷ 12⁄5 = 5⁄12

Add the leading 1: 1 + 5⁄12 = 17⁄12 → option (b)

Why the others are wrong

(a)
8⁄5 — 8⁄5 = 1.6, but the part after the leading 1 is 1 ÷ 12⁄5 = 5⁄12 ≈ 0.42, so x is about 1.42.
(c)
7⁄5 — 7⁄5 = 1 + 2⁄5 skips the middle layer. 2⁄5 is the first reciprocal. It must still be added to 2 and inverted again before the leading 1 goes on.
(d)
9⁄7 — 9⁄7 = 1 + 2⁄7, which would need the denominator under the top 1 to be 7⁄2. That denominator is 2 + 2⁄5 = 12⁄5.

Concept

A continued fraction is evaluated from the bottom up. Each layer has the shape 'number + 1⁄(what is below it)', so you compute the lowest piece, take its reciprocal, add, and repeat.

The reciprocal of a⁄b is b⁄a, which is why 1 ÷ 5⁄2 becomes 2⁄5 in one step.

This expression is the start of the continued fraction for √2, which runs 1 + 1⁄(2 + 1⁄(2 + …)) without end.

Stopping it gives 3⁄2, 7⁄5, 17⁄12 in turn, and 17⁄12 ≈ 1.4167 against √2 ≈ 1.4142. The stage before the answer, 7⁄5 = 1.4, is the value of option (c).

Key facts

Evaluate a continued fraction from the innermost level outward.
1 ÷ (a⁄b) = b⁄a, so 1 ÷ 12⁄5 = 5⁄12.
Cut off after one, two and three '2' layers, 1 + 1⁄(2 + 1⁄(2 + …)) gives 3⁄2, 7⁄5 and 17⁄12, closing in on √2 ≈ 1.4142.

Study next

Continued fractions with other entries, such as 1 + 1⁄(1 + 1⁄(1 + 1⁄2))Simplifying nested brackets of fractions with ÷ and ×Reciprocals of mixed numbers and improper fractions

Common traps

Inverting a sum term by term: 1⁄(2 + 2⁄5) is 5⁄12, not 1⁄2 + 5⁄2.
Adding the leading 1 too early and stopping at 1 + 2⁄5 = 7⁄5.

12 Sep 2025, 09:00, Quant Q.3 needs the same inside-out order on brackets: 3⁄4 − 1⁄4 = 1⁄2, half of that is 1⁄4, 1⁄3 − 1⁄4 = 1⁄12, 5⁄6 ÷ 1⁄12 = 10, and 7 1⁄4 − 10 = −2 3⁄4.

Related PYQs

No directly related past PYQ was found.

Topic: Basic algebraic identities of School Algebra & Elementary surds — all 147 SSC CGL questions on it, every solved shift.