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Arithmetic Progressions Common Difference Ratio

XAT 2022 · Quantitative Ability & Data Interpretation · Medium · Progression

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If both the sequences x,a1,a2,yx, a_1, a_2, y and x,b1,b2,zx, b_1, b_2, z are in A.P. and it is given that y>xy > x and z<xz < x, then which of the following values can a1−a2b1−b2\frac{a_1 - a_2}{b_1 - b_2} possibly take?

  1. A.

    2

  2. B.

    5

  3. C.

    -3

  4. D.

    1

  5. E.

    0

Answer

C

Explanation

In an A.P., a1−a2=−d1a_1 - a_2 = -d_1. Since y>xy > x, common difference d1>0d_1 > 0, so a1−a2<0a_1 - a_2 < 0. For second A.P., b1−b2=−d2b_1 - b_2 = -d_2. Since z<xz < x, d2<0d_2 < 0, so b1−b2>0b_1 - b_2 > 0. Therefore, a1−a2b1−b2=negativepositive<0\frac{a_1 - a_2}{b_1 - b_2} = \frac{\text{negative}}{\text{positive}} < 0. The only negative option is -3.

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