The remainder when positive integer nn (n>1n>1) is divided by 25 is 1 and the remainder when nn is divided by 7 is also 1. What is the least value of nn?
Select the correct option:
A) 76
B) 101
C) 126
D) 151
E) 176

Rationale: we ' re asked to find the least number that gives us a remainder of 1 when divided by 25 and gives us a remainder of 1 when divided by 7 . you might notice , rather quickly , that all of the answers gives us a remainder when divided by 25 . . . 76 = 75 + 1 101 = 100 + 1 126 = 125 + 1 151 = 150 + 1 176 = 175 + 1 so the real question is ` ` which of these 5 is the least number that has a remainder of 1 when divided by 7 ? ' ' from here , you can just do the ` ` brute force ' ' math : a : 76 / 7 = 10 r 6 not a match b : 101 / 7 = 14 r 3 not a match c : 126 / 7 = 18 r 0 not a match d : 151 / 7 = 21 r 4 not a match none of these numbers ` ` fits ' ' the description , so the answer must be e . e : 176 / 7 = 25 r 1 ; answer : e
Answer: E