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Data sufficiency: two statements on powers of x, y or r decide the sign or size of an expression

This type of question, asked 3 times: CDS 1 2022, CDS 2 2022, CDS 1 2026. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2022

    41
    Consider a question and two statements : Question : Is 3x+2y3x + 2y positive? Statement-I : x3=−29.8x^3 = -29.8 Statement-II : y3=3xy^3 = 3x Which one of the following is correct in respect of the question and the statements?

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  2. Question 2

    CDS 2 2022

    30
    Consider the question and two statements given below : Let x and y be two real numbers. Question : Is xy>0xy > 0 ? Statement-1 : x8y9<0x^8 y^9 < 0. Statement-2 : x9y10<0x^9 y^{10} < 0. Which one of the following is correct in respect of the question and the statements ?

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  3. Question 3

    CDS 1 2026

    76
    A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : Is rnr^n less than 1, where r is a real number and n is a natural number ? Statement-I : 0<r2<10 < r^2 < 1 Statement-II : 0<r3<20 < r^3 < 2 Which one of the following is correct in respect of the above Question and the Statements ?

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