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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,  [#permalink]

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New post 01 Nov 2016, 04:46
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

86% (01:26) correct 14% (01:36) wrong based on 95 sessions

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Re: If m is 3 more than a multiple of 5 and 2 more than a multiple of 6,  [#permalink]

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New post 01 Nov 2016, 06:02
Bunuel wrote:
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


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 hence 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
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Re: If m is 3 more than a multiple of 5 and 2 more than a multiple of 6,  [#permalink]

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New post 01 Nov 2016, 07:52
Bunuel wrote:
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


(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)

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Re: If m is 3 more than a multiple of 5 and 2 more than a multiple of 6,  [#permalink]

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New post 01 Nov 2016, 08:18
Here is my detailed solution,

Hope you like it,

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Re: If m is 3 more than a multiple of 5 and 2 more than a multiple of 6,  [#permalink]

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New post 02 Nov 2016, 05:55
Bunuel wrote:
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


IMO D
m=5k+3 and m=6l+2
only option D satisfies the given condition.
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Re: If m is 3 more than a multiple of 5 and 2 more than a multiple of 6,  [#permalink]

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New post 02 Nov 2016, 15:36
Bunuel wrote:
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


lowest value of m is 8
8+5*6=38 (not a choice)
38+5*6=68
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Re: If m is 3 more than a multiple of 5 and 2 more than a multiple of 6,  [#permalink]

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New post 04 Nov 2016, 09:37
Bunuel wrote:
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


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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Re: If m is 3 more than a multiple of 5 and 2 more than a multiple of 6,   [#permalink] 04 Nov 2016, 09:37
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