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? Pick one: A) 76 B) 101 C) 126 D) 151 E) 176
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 = 10r6 NOT a match   B: 101/7 = 14r3 NOT a match   C: 126/7= 
<gadget id="calculator">126/7</gadget>
<output>18</output>
18r0 NOT a match   D: 151/7= 21r4 NOT a match   NONE of these numbers "fits" the description, so the answer MUST be E.   176: 176/7 = 25r1;   ANSW176R:176
<result>E</result>
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?