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

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

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New post 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)

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  [#permalink]

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New post 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)



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

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Re: Let G and H be positive integers. 2G - 10 > -H and 3H - 20 < -G. If L  [#permalink]

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New post 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*2-10>-6; -6>-6 (This is not possible, Move on to the next given solution)

B) (6,2)

(i) 2*6-10>-2; -2>--2 (This is not possible, Move on to the next given solution)

C) (5,5)

(i) 2*5-10>-5; 0>-5 (This is OK. Try next inequation)
(ii) 3*5-20<-5; -5<-5 (This is not possible, Move on to the next given solution)

D) (3,5)

(i) 2*3-10>-5; -4>-5 (This is OK. Try next inequation)
(ii) 3*5-20<-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  [#permalink]

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New post 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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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  [#permalink]

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New post 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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Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
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Let G and H be positive integers. 2G - 10 > -H and 3H - 20 < -G. If L   [#permalink] 18 Aug 2019, 09:02
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Let G and H be positive integers. 2G - 10 > -H and 3H - 20 < -G. If L

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