SSC CGL 2025 Tier-I · 19 September 2025, Shift 2 · Quantitative Aptitude · Question 2 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 13 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

Which of the following is the least 6-digit number, which is a perfect square?

(a)100489
(b)100588
(c)100688
(d)100788

Answer

Why

Correct — A.
The least 6-digit number is 100000, so find the first square at or above it.

Estimate the root: √100000 ≈ 316.2
Square 316: 316² = 99856, still only 5 digits
Square 317: 317² = 100489, which has 6 digits

So the least 6-digit perfect square is 100489 → option (a)

Why the others are wrong

(b)
100588 — It ends in 8, and no perfect square ends in 2, 3, 7 or 8. It also lies between 317² = 100489 and 318² = 101124.
(c)
100688 — It ends in 8, so it cannot be a square. It falls between 317² = 100489 and 318² = 101124, with no whole-number root.
(d)
100788 — It ends in 8 as well, which rules it out on sight. Its root would lie between 317 and 318, so it is not a perfect square.

Concept

The least n-digit perfect square is the square of the smallest whole number whose square has n digits.

When the smallest n-digit number is an even power of 10, such as 100 or 10000, it is already a square. 100000 = 10⁵ is an odd power, so its root, about 316.2, must be rounded up to 317.

Squaring 317 then gives the answer directly.

A unit-digit check settles this even before any squaring: options (b), (c) and (d) all end in 8, and no square ends in 8.

Key facts

316² = 99856 and 317² = 100489
The greatest 6-digit perfect square is 999² = 998001
A perfect square never ends in 2, 3, 7 or 8

Study next

Least number to add to, or subtract from, a number to make it a perfect squareGreatest n-digit perfect square, such as 999² = 998001Unit-digit tests for squares and cubes

Common traps

Rounding √100000 ≈ 316.2 down to 316, which gives 99856, a 5-digit number
Square-rooting every option instead of first striking out those that end in 8

The same rounding-up step decides 21 Sep 2025, 09:00, Quant Q.1: 48² = 2304 is below 2378, so the next square is 49² = 2401 and the number to add is 23.

Related PYQs

No directly related past PYQ was found.

Topic: Square roots — all 48 SSC CGL questions on it, every solved shift.