XAT 2022 Progression Question (Hard)

Question

If both the sequences x, a_1, a_2, y and x, b_1, b_2, z are in A.P. and it is given that y z and z x, then which of the following values can b_1 - b_2 possibly take?

Optima Learn · Accepted Answer

Let the common differences of the A.P.s x, a_1, a_2, y and x, b_1, b_2, z be d_1 and d_2 respectively. Then a_1 x d_1, a_2 x 2d_1, y x 3d_1 and b_1 x d_2, b_2 x 2d_2, z x 3d_2. Thus, b_1 - b_2 -d_2 d_2 . From z x, d_1 0. Therefore, d_2 must be negative. The only negative value among the options is -

XAT 2022 Progression — Previous Year Question

XAT 2022

Quantitative

Progression

Hard

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