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# Let G and H be positive integers. 2G - 10 > -H and 3H - 20 < -G. If L

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Intern
Joined: 06 May 2015
Posts: 45
Location: India
Schools: Darden '21
GPA: 4
Let G and H be positive integers. 2G - 10 > -H and 3H - 20 < -G. If L  [#permalink]

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Updated on: 28 Sep 2018, 07:50
00:00

Difficulty:

55% (hard)

Question Stats:

52% (02:10) correct 48% (02:26) wrong based on 33 sessions

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Let G and H be positive integers. $$2G - 10 > -H$$ and $$3H - 20 < -G$$. If L is the minimum value of G and M is the maximum value of H, then which of the following pair is (L,M) ?

A) (2,6)
B) (6,2)
C) (5,5)
D) (3,5)
E) (11,1)

Originally posted by reynaldreni on 28 Sep 2018, 07:11.
Last edited by Bunuel on 28 Sep 2018, 07:50, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Aug 2009
Posts: 7207
Re: Let G and H be positive integers. 2G - 10 > -H and 3H - 20 < -G. If L  [#permalink]

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28 Sep 2018, 09:37
reynaldreni wrote:
Let G and H be positive integers. $$2G - 10 > -H$$ and $$3H - 20 < -G$$. If L is the minimum value of G and M is the maximum value of H, then which of the following pair is (L,M) ?

A) (2,6)
B) (6,2)
C) (5,5)
D) (3,5)
E) (11,1)

2G-10>-H....(I)
3H-20<-G ......-G>3H-20 or -2G>6H-40....(II)

2G-10-2G>-H+6H-40.........-10>5H-40.......5H<30....H<6
So max value of H is 5

Now
2G-10>-H.......6G-30>-3H(I)
3H-20<-G ......-..(II)

3H-20-3H<6G-30-G......-20<5G-30........5G>10.......G>2
So minimum value of G is 3

So (L,M) is (3,5)

D
_________________

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: Let G and H be positive integers. 2G - 10 > -H and 3H - 20 < -G. If L &nbs [#permalink] 28 Sep 2018, 09:37
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