# Moderate Number System Solved QuestionAptitude Discussion

 Q. If $a$ and $b$ are positive integers, and $x = 2×3×7×a$ , and $y = 2×2×8×b$ , and the values of both $x$ and $y$ lie between 120 and 130 (not including the two), then $a – b =$
 ✖ A. -2 ✔ B. -1 ✖ C. 1 ✖ D. 2

Solution:
Option(B) is correct

We are given that $x = 2×3×7×a = 42a$ and $y = 2×2×8×b = 32b$

We are given that the values of both $x$ and $y$ lie between 120 and 130 (not including the two).

The only multiple of 42 in this range is $42×3 = 126$.

Hence, $x = 126$ and $a = 3.$
The only multiple of 32 in this range is $32×4 = 128$.

Hence, $y = 128$ and $b = 4$.

Hence, $a - b = 3 - 4 =$ -1