If m is 3 more than a multiple of 5 and 2 more than a multiple of 6,

Question

If m is 3 more than a multiple of 5 and 2 more than a multiple of 6, which of the following could be m?

A. 14
B. 28
C. 58
D. 68
E. 74

GMATinsight · Answer

m is 3 more than a multiple of 5 i.e. m = 5a+3
 m is 2 more than a multiple of 6 i.e. m = 6b+2

Just check option

A. 14 when divided by 5 leaves  remainder 4 instead of 3  hence incorrect option
B. 28 when divided by 5 leaves remainder 3 and when divided by  6 leaves remainder 4 instead of 2 h ence Incorrect option
C. 58 when divided by 5 leaves remainder 3 and when divided by  6 leaves remainder 4 instead of 2  hence Incorrect option
 D. 68 when divided by 5 leaves remainder 3 and when divided by 6 leaves remainder 2 hence Correct option 
E. 74

Answer: Option C

Abhishek009 · Answer

(A) 14 - 3 is 11 not multiple of 5

(B) 28 - 2 is 26 not multiple of 6

(C) 55 - 2 is 53 not multiple of 6

(D) 68 - 2 is 66 multiple of 6 and 68 - 3 = 65 multiple of 5

(D) 74 - 3 is 71 not multiple of 5 
  
Hence, Correct answer must be (D)

AnisMURR · Answer

Here is my detailed solution,

Hope you like it,

Anis

Vinayak Shenoy · Answer

IMO D
m=5k+3 and m=6l+2
only option D satisfies the given condition.

gracie · Answer

lowest value of m is 8
8+5*6=38 (not a choice)
38+5*6=68 
D

ScottTargetTestPrep · Answer

Since m is 3 more than a multiple of 5, we can say the following:

m = 3 + 5k (where k is an integer)

Since m is 2 more than a multiple of 6, we can say the following:

m = 2 + 6x (where x is an integer)

At this point, it may be easiest to check the answer choices to determine which could be m.

A) 14

Since 14 IS NOT 3 more than a multiple of 5, 14 cannot be m.

B) 28

Since 28 IS NOT 2 more than a multiple of 6, 28 cannot be m.

C) 58

Since 58 IS NOT 2 more than a multiple of 6, 58 cannot be m.

D) 68

Since 68 IS 2 more than a multiple of 6, and 3 more than a multiple of 5, 68 CAN BE m.

Answer: D

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If m is 3 more than a multiple of 5 and 2 more than a multiple of 6,

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If m is 3 more than a multiple of 5 and 2 more than a multiple of 6,

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