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If a+b=200 and a<b , is a+b>c+d ? (1) c+d<200 (2)

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If a+b=200 and a<b , is a+b>c+d ? (1) c+d<200 (2)  [#permalink]

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New post 08 Nov 2011, 19:49
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Question Stats:

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If \(a+b=200\) and \(a<b\), is \(a+b>c+d\)?

(1) \(c+d<200\)
(2) \(b+c+d=300\)
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Re: Is (a+b) > (c+d)  [#permalink]

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New post 08 Nov 2011, 23:39
1
Statement 1: If a+b=200 and c+d<200, then a+b>c+d. Sufficient.
Statement 2: If a+b = 200 and a<b => b>100. Therefore if b+c+d = 300 => c+d <200 which translates into the same case as in statement 1. Sufficient.

(D) is the answer.
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Re: If a+b=200 and a<b , is a+b>c+d ? (1) c+d<200 (2)  [#permalink]

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New post 27 Nov 2016, 14:10
kostyan5 wrote:
If \(a+b=200\) and \(a<b\), is \(a+b>c+d\)?

(1) \(c+d<200\)
(2) \(b+c+d=300\)


\(a+b=200\) and \(a<b\)

Thus, \(a + b < 2b\)

Or, \(200 < 2b\)

Or, \(b > 100\)

FROM STATEMENT - I ( SUFFICIENT )

Given , \(a+b=200\) & \(c+d<200\)

Thus, we can safely conclude - \(a+b>c+d\)

FROM STATEMENT - II ( SUFFICIENT )

I will try to plug in some value and check here, \(a+b=200\) & \(b > 100\)

Say \(b = 110\) & \(a = 90\)

Given, \(b+c+d=300\) , if \(b = 110\) , \(c + d = 190\)

It is given, \(a+b=200\) & we have \(c + d = 190\)

So, we can safely conclude here as well that \(a+b>c+d\)

Thus, EACH statement ALONE is sufficient to answer the question asked, answer will be (D)

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Re: If a+b=200 and a<b , is a+b>c+d ? (1) c+d<200 (2)  [#permalink]

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New post 26 Jul 2018, 05:49
kostyan5 wrote:
If \(a+b=200\) and \(a<b\), is \(a+b>c+d\)?

(1) \(c+d<200\)
(2) \(b+c+d=300\)


Imo D

From 1 we have \(c+d<200\) sufficient.

From 2 we have b+c+d=300
Now add a to both sides then a+b+c+d=300+a
a+b=200 so above equation becomes 200+c+d=300+a
solving this we have c+d=100+a
From the question stem we have a<b then suppose a=99 and b=101 then above equation becomes
c+d=100+99=199 still less than 200 so it is sufficient.
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Re: If a+b=200 and a<b , is a+b>c+d ? (1) c+d<200 (2) &nbs [#permalink] 26 Jul 2018, 05:49
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