CAT 2021 Question Paper | Quant Slot 2

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 10 : Three positive integers x, y and z are in arithmetic progression. If y - x > 2 and xyz = 5(x + y + z), then z - x equals

Video Explanation

Explanatory Answer

Given that, x, y, z are in arithmetic progression.
Also given that xyz = 5(x + y + z).
xyz = 5(3y). Since x, y, z are in arithmetic progression.
xz = 15.
The possible combinations for x and z are (3, 5) (1, 15).
 z - x > 4 (Since y - x > 2).
Therefore,
x = 1, y = 8, z = 15
Hence, z - x = 14.

The question is " Three positive integers x, y and z are in arithmetic progression. If y - x > 2 and xyz = 5(x + y + z), then z - x equals "

Hence, the answer is '14'

Choice C is the correct answer.