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SSC CGL 2025 PYQ — Question 75

SSC CGL - 12 Sep 2025 - Shift 2 • Quantitative Aptitude • Q75

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Let x=2+5x=\sqrt{2}+\sqrt{5} and y=7+3y=\sqrt{7}+\sqrt{3}. Which is greater?
 

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Correct answer: C

Explanation

The correct answer is option 3 i.e. x < y.

(a + b)2 = a2 + b2 + 2ab

x2 = 2 + 5 + 2√10 = 7 + 2√10

y2 = 7 + 3 + 2√21 = 10 + 2√21

x2 - y2 = (7 + 2√10) - (10 + 2√21) = -3 + 2(√10 - √21)

Since √10 < √21, √10 - √21 < 0

So x2 - y2 < 0

⇒ x2 < y2

Since x, y > 0, then x < y