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# If F, G and H are positive integers. F/6 + G/4 = H/12, do H and 12 hav

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Intern
Joined: 06 May 2015
Posts: 46
Location: India
Schools: Darden '21
GPA: 4
If F, G and H are positive integers. F/6 + G/4 = H/12, do H and 12 hav  [#permalink]

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Updated on: 03 Oct 2018, 19:59
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Difficulty:

85% (hard)

Question Stats:

41% (02:00) correct 59% (02:15) wrong based on 46 sessions

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If F, G and H are positive integers. F/6 + G/4 = H/12, do H and 12 have a common factor greater than 1?

(1) F is a multiple of 3
(2) G is a multiple of 3

Originally posted by reynaldreni on 03 Oct 2018, 18:49.
Last edited by Bunuel on 03 Oct 2018, 19:59, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Aug 2009
Posts: 7095
Re: If F, G and H are positive integers. F/6 + G/4 = H/12, do H and 12 hav  [#permalink]

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03 Oct 2018, 21:55
1
reynaldreni wrote:
If F, G and H are positive integers. F/6 + G/4 = H/12, do H and 12 have a common factor greater than 1?

(1) F is a multiple of 3
(2) G is a multiple of 3

$$\frac{F}{6} + \frac{G}{4} = \frac{H}{12}.........2F+3G=H$$

(1) F is a multiple of 3
$$F=3X$$..
$$2F+3G=H......2*3X+3G=H....3(2X+G)=H$$
So H is a multiple of 3
suff

(2) G is a multiple of 3
$$G=3X$$..
$$2F+3G=H......2F+3*3x=H....2F+9x=H$$
If F is a multiple of 3, h is a multiple of 3
If G is a multiple of 2, H is a multiple of 2
But many ways in which say F and G are 1 and 3, H is 11...
insuff

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If F, G and H are positive integers. F/6 + G/4 = H/12, do H and 12 hav &nbs [#permalink] 03 Oct 2018, 21:55
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