The remainder when positive integer n (n1) is divided by 25 is 1 and

Question

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 OA is E, but I disagree.

I don't think the logic is correct in this question. I interpreted the question as "If N/25 leaves a remainder of 1" OR "If N/7 leaves a remainder of 1". An "OR" operator indicates that only one condition has to pass, therefore the answer should be A.

76 / 25 = 3 with a remainder of 1
76 is the smallest digit available.

M11-34

Bunuel · Accepted Answer

Since  n  yields a remainder of 1 when divided by both 25 and 7, then that  n-1  must be a multiple of both 7 and 25. This means the smallest value of  n-1  is the least common multiple (LCM) of 7 and 25, which is  7*25=175 . Consequently, if  n-1=175 , the smallest possible value for  n  would be  176 .

Answer: E.

GyanOne · Answer

The question is actually asking - what is the least integer that leaves a remainder of 1, whether it is divided by 25 or by 7? The only other option is to use 'and' instead of 'or' here which would again amount to unclear usage - it could mean division by 25 followed by division with 7.

In such questions, divided by A or divided by B, if used as is used above, means the result when it is divided by both individually and considers the result of both operations, not just one.

puneet478 · Answer

The question means that if you divide the number N by either 25 or 7, it should leave a remainder of '1'. The number should satisfy both the conditions.

puneet478 · Answer

Further to add, since 25 & 7 are prime to each other, so LCM will be 175, adding remainder 1, we get 176 as the smallest number which satisfies above conditions.

Prajakta750 · Answer

If the q says number divided by a and b then it means that it shud be divided by both a then the remaining quotient divided by b. 
For eg. 200 divided by 25 and 7 means that 200/25 = 8 and then 8/7 = 1 with remainder 1.

EMPOWERgmatRichC · Answer

Hi All,

Since the answers to this question are all numbers, we can TEST THE ANSWERS.

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 = 18r0 NOT a match
D: 151/7 = 21r4 NOT a match

NONE of these numbers "fits" the description, so the answer MUST be E.

E: 176/7 = 25r1

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

GMATDemiGod · Answer

i put it into a formula

n=25b+1
n=7b+1

equate got 25b=7a

So tested this proportion (25*7) and (7*25) to get 175 each. Therefore with +1 remainder answer is E

This method okay?

EMPOWERgmatRichC · Answer

Hi GMATDemiGod,

Your approach does work here. You just have to be careful about similar questions - 25 and 7 have no prime factors in common, so your approach works perfectly. If the numbers DID have prime factors in common though (say 6 and 8), then using your approach would not get you the correct answer (the smallest value would be 25, not 49).

GMAT assassins aren't born, they're made,
Rich

GMATDemiGod · Answer

how would it work with 6 and 8? I would cancel out to bring it to the lowest terms.

Ok with 6 and 8 you would just find the standard GCF, as the same as 25 and 7 (but since nothing in common they are just multiplied)

EMPOWERgmatRichC · Answer

Hi GMATDemiGod,

With 6 and 8, you'd have to find the Least Common Multiple (which would NOT happen if you just multiplied 6 and 8 together) - the LCM is 24 (not 48). As long as you realized that point, then you could complete the math from there and get the correct answer.

GMAT assassins aren't born, they're made,
Rich

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The remainder when positive integer n (n>1) is divided by 25 is 1 and

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