GATE 2015 CS (CS2) – Question 9

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

P,R,S,T,U form an arithmetic progression. Which lists must also be arithmetic progressions?
I: 2P,2R,2S,2T,2U
II: P−3,R−3,S−3,T−3,U−3
III: P²,R²,S²,T²,U²

I only
I and II
II and III
I and III

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Show answer and explanation

Correct answer: (B) I and II

Explanation

Multiplying all terms by two multiplies the common difference by two, preserving an arithmetic progression. Subtracting three from every term leaves the difference unchanged. Squaring generally makes the differences vary; for example squares of one,two,three are one,four,nine. Thus I and II, B.

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