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The remainder when positive integer \(n\) (\(n>1\)) is divided by 25 is 1 and the remainder when \(n\) is divided by 7 is also 1. What is the least value of \(n\)?
The remainder when positive integer \(n\) (\(n>1\)) is divided by 25 is 1 and the remainder when \(n\) is divided by 7 is also 1. What is the least value of \(n\)?
A. 76 B. 101 C. 126 D. 151 E. 176
Notice that \(n-1\) is divisible by both 7 and 25. So, the least value of \(n-1\) is the least common multiple of 7 and 25 which is \(7*25=175\). Hence \(n-1=175\) and \(n=176\).
You don't have to mention n>1. The moment the question says positive integer, it's implied that n>1
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Not really, positive integer is n>0, in that case the answer could be 1 (although if it is not in the answer choices that would discard it). To have another possible "lower value" than the one in the options diminishes the quality of the question as a whole.
1/25 = 0*(25) + 1
1/7 = 0*(7) + 1
1 is a possible value that satisfies both options.
The remainder when positive integer \(n\) (\(n>1\)) is divided by 25 is 1 and the remainder when \(n\) is divided by 7 is also 1. What is the least value of \(n\)?
A. 76 B. 101 C. 126 D. 151 E. 176
Hi Banuel,
Thanks for this! What does the M11-34 refer to? What is the source of this question if you don't mind me asking?
The remainder when positive integer \(n\) (\(n>1\)) is divided by 25 is 1 and the remainder when \(n\) is divided by 7 is also 1. What is the least value of \(n\)?
A. 76 B. 101 C. 126 D. 151 E. 176
Hi Banuel,
Thanks for this! What does the M11-34 refer to? What is the source of this question if you don't mind me asking?
Thank you.
M11-34 is the ID of the question in GMAt Club Test. The source is GMAT Club.
_________________
Ans: E I solved this question working backwards from the options. We need to find least value N from which when 1 is reduced (N-1) it becomes multiple of both 25 and 7. working backward: N-1 divisible by 25 divisible by 7 75 Y N 100 Y N 125 Y N 150 Y N 175 Y Y ---- Ans. Note: if we just look at the N-1 we will know in first instant without solving much that these are divisible by because they all end up with Unit digit 0 or 5. so we actually need to know which one is divisible by 7.
Bunuel wrote:
The remainder when positive integer \(n\) (\(n>1\)) is divided by 25 is 1 and the remainder when \(n\) is divided by 7 is also 1. What is the least value of \(n\)?
A. 76 B. 101 C. 126 D. 151 E. 176
_________________
-------------------------------------------------------------------- The Mind is Everything, What we Think we Become.