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# If integer m is 3 more than a multiple of 5 and 2 more than a multiple

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
If integer m is 3 more than a multiple of 5 and 2 more than a multiple  [#permalink]

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05 Dec 2016, 02:26
00:00

Difficulty:

45% (medium)

Question Stats:

69% (02:23) correct 31% (02:45) wrong based on 52 sessions

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If integer m is 3 more than a multiple of 5 and 2 more than a multiple of 6, which of the following could be 7m + 4?

A. 65
B. 104
C. 158
D. 270
E. 291

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Posts: 1682
Location: India
Re: If integer m is 3 more than a multiple of 5 and 2 more than a multiple  [#permalink]

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05 Dec 2016, 08:12
m = 5x + 3
n = 6y + 2

Find the first intersection --> Happens when x = y = 1 --> m = 8

Successive intersections can be found out by taking the LCM(5, 6) and adding 8 to it --> LCM(5,6) + 8 --> 30a + 8 --> 8, 38, 68, 98, .......

When m = 8 --> 7m + 4 = 60
When m = 38 --> 7m + 4 = 266 + 4 = 270

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

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05 Dec 2016, 10:14
1
1
Bunuel wrote:
If integer m is 3 more than a multiple of 5 and 2 more than a multiple of 6, which of the following could be 7m + 4?

A. 65
B. 104
C. 158
D. 270
E. 291

$$\frac{Correct \ Option \ - \ 4}{7} = Remainder \ 0$$

Now, check the options to find the value of m -

(A) 65 - 4 = 61 ( Not divisible by 7 )
(B) 104 - 4 = 101 ( Not divisible by 7 )
(C) 158 - 4 = 154 ( Divisible by 7 ) ; m = 22
(D) 270 - 4 = 266 ( Divisible by 7 ) ; m = 38
(E) 291 - 4 = 287 ( Divisible by 7 ) ; m = 41

Now , check among the given option only (D) satisfies....

38 = 5*7 + 3 ( m is 3 more than a multiple of 5 )
38 = 6*6 + 2 ( m is 2 more than a multiple of 6 )

Hence, with Vyshak Correct answer must be (D)
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Abhishek....

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

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04 Feb 2019, 19:45
Hello from the GMAT Club BumpBot!

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Re: If integer m is 3 more than a multiple of 5 and 2 more than a multiple   [#permalink] 04 Feb 2019, 19:45
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