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# If 5n + 4 is divisible by 3 and 6m + 2 is divisible by 5 (m and n are

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VP
Joined: 31 Oct 2013
Posts: 1492
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If 5n + 4 is divisible by 3 and 6m + 2 is divisible by 5 (m and n are  [#permalink]

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01 Oct 2018, 12:20
1
00:00

Difficulty:

55% (hard)

Question Stats:

61% (02:18) correct 39% (02:36) wrong based on 25 sessions

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If 5n + 4 is divisible by 3 and 6m + 2 is divisible by 5 (m and n are non negative integers), what is the lowest common value for m and n ?

A) 4
B) 7
C) 8
D) 13
E) 15
Intern
Joined: 14 Aug 2018
Posts: 20
Location: United States (WA)
GMAT 1: 670 Q43 V40
GMAT 2: 750 Q47 V47
GPA: 3.3
WE: Education (Education)
Re: If 5n + 4 is divisible by 3 and 6m + 2 is divisible by 5 (m and n are  [#permalink]

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01 Oct 2018, 12:46
1
There is a math way to get to the right answer, but it is probably a to faster to work backward from the answer choices. Substitute the answer choices into the equations and see which is the lowest answer choice that works.

Before you start this method, pause and think - is it easier and faster to check for divisibility by 5 or by 3? Notice how the testmaker put the divisible by 5 equation second - this is on purpose. Most students will work with the first equation first - work smarter by doing the easier and faster thing first.

A number is divisible by 5 if it ends in either 0 or 5. So, for 6m+2 we only need to check the units digit

A. 6(4) + 2 ends in 6 eliminate
B. 6(7) + 2 ends in 4 eliminate
C. 6(8) + 2 ends in 0. keep. Do second equation. 5(8)+ 4 = 44. Not divisible by 3. (Div by three if digits add to a number divisible by 3. 4+4 = 8, which is not divisible by 3)
D. 6(13) + 2 ends in 0. Keep. Do second equation 5(13) + 4 = 69. Is divisible by 3. Is right.
_________________
Jayson Beatty
Indigo Prep
http://www.indigoprep.com
Re: If 5n + 4 is divisible by 3 and 6m + 2 is divisible by 5 (m and n are   [#permalink] 01 Oct 2018, 12:46
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# If 5n + 4 is divisible by 3 and 6m + 2 is divisible by 5 (m and n are

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