If aa and bb are positive integers, and x=2×3×7×ax=2×3×7×a , and y=2×2×8×by=2×2×8×b , and the values of both xx and yy lie between 120 and 130 (not including the two), then a–b=a–b=
We are given that x=2×3×7×a=42ax=2×3×7×a=42a and y=2×2×8×b=32by=2×2×8×b=32b
We are given that the values of both xx and yy lie between 120 and 130 (not including the two).
The only multiple of 42 in this range is 42×3=12642×3=126.
Hence, x=126x=126 and a=3.a=3.
The only multiple of 32 in this range is 32×4=12832×4=128.
Hence, y=128y=128 and b=4b=4.
Hence, a−b=3−4=a−b=3−4= -1