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Let G and H be positive integers. 2G  10 > H and 3H  20 < G. If L
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Updated on: 28 Sep 2018, 08:50
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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)
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Originally posted by reynaldreni on 28 Sep 2018, 08:11.
Last edited by Bunuel on 28 Sep 2018, 08:50, edited 1 time in total.
Renamed the topic and edited the question.



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Re: Let G and H be positive integers. 2G  10 > H and 3H  20 < G. If L
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28 Sep 2018, 10:37
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) 2G10>H....(I) 3H20<G ......G>3H20 or 2G>6H40....(II) Add I and II 2G102G>H+6H40.........10>5H40.......5H<30....H<6 So max value of H is 5 Now 2G10>H.......6G30>3H(I) 3H20<G ........(II) Add I and II 3H203H<6G30G......20<5G30........5G>10.......G>2 So minimum value of G is 3 So (L,M) is (3,5) D
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Re: Let G and H be positive integers. 2G  10 > H and 3H  20 < G. If L
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18 Aug 2019, 08:40
An alternative solution to the one provided by chetan2u is trying out the given points in the two given inequations. Point (L,M) A) (2,6) (i) 2*210>6; 6>6 (This is not possible, Move on to the next given solution) B) (6,2) (i) 2*610>2; 2>2 (This is not possible, Move on to the next given solution) C) (5,5) (i) 2*510>5; 0>5 (This is OK. Try next inequation) (ii) 3*520<5; 5<5 (This is not possible, Move on to the next given solution) D) (3,5) (i) 2*310>5; 4>5 (This is OK. Try next inequation) (ii) 3*520<3; 5<3 (This is OK. This is the solution) OPTION D
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Let G and H be positive integers. 2G  10 > H and 3H  20 < G. If L
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Updated on: 18 Aug 2019, 09:04
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) Given: Let G and H be positive integers. \(2G  10 > H\) and \(3H  20 < G\). Asked: 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) ? 2G > 10  H. G > 5  H/2. (1) 3H < 20 G 3H > G 20 (2) Adding (1) & (2) G  3H > G  H/2  15 3H  H/2 < 15 5H/2 < 15 H < 15 * 2/5 = 6 H< 6 (3) M = 5 since M is maximum value of H and is a positive integer H > 6 10  H > 10 6 = 4 2G> 10  H > 4 G > 2 (4) L = 3 since L is minimum value of G and is a positive integer (L,M) = (3, 5) IMO D
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"Success is not final; failure is not fatal: It is the courage to continue that counts." Please provide kudos if you like my post. Kudos encourage active discussions. My GMAT Resources:  Efficient LearningAll you need to know about GMAT quantTele: +911140396815 Mobile : +919910661622 Email : kinshook.chaturvedi@gmail.com
Originally posted by Kinshook on 18 Aug 2019, 08:48.
Last edited by Kinshook on 18 Aug 2019, 09:04, edited 1 time in total.



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Let G and H be positive integers. 2G  10 > H and 3H  20 < G. If L
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18 Aug 2019, 09:02
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) Given: Let G and H be positive integers. \(2G  10 > H\) and \(3H  20 < G\). Asked: 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) ? 2G + H > 10 (1) G + 3H < 20 (2) 2G + 6H < 40 2G  6H > 40 (3) Adding (1) & (3) 5H >  30 H<6 (4) M = 5 Maximum positive integer value of H Putting H<6 in (1) H>6 2G > 10  H > 10 6 =4 G>2 (5) L=3 Minimum positive integer value of G (L, M) = (3, 5) IMO D
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"Success is not final; failure is not fatal: It is the courage to continue that counts." Please provide kudos if you like my post. Kudos encourage active discussions. My GMAT Resources:  Efficient LearningAll you need to know about GMAT quantTele: +911140396815 Mobile : +919910661622 Email : kinshook.chaturvedi@gmail.com




Let G and H be positive integers. 2G  10 > H and 3H  20 < G. If L
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18 Aug 2019, 09:02






