Problem:
Find the smallest positive number from the numbers below.
Answer Choices:
A. 10−311
B. 311−10
C. 18−513
D. 51−1026
E. 1026−51
Solution:
Since 102=100>99=(311)2,
182=324<325=(513)2,512=2601>2600=(1026)2,
only (A) and (D) are positive numbers.
Moreover, since a−b=a+ba2−b2, 10−311=10+3111≈201 and 51−1026=51+10261≈1021.
So (D) is the answer.