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

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

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28 Jan 2008, 12:39
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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
CEO
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Re: DS - a + b [#permalink]

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28 Jan 2008, 12:53
D

a + b = 200 and a < b

b is $$(100,+\infty)$$

1) c + d < 200.
a + b > c + d
200 > c + d. true
sufficient

2) b + c + d = 300
a + b > c + d
200 > 300-b
300-b is $$(-\infty,200)$$
200 > 300-b is true
sufficient.

simple and tricky. Good Q!
+1
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Re: DS - a + b [#permalink]

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28 Jan 2008, 13:37
Walker can you explain the second condition..?
CEO
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Re: DS - a + b [#permalink]

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28 Jan 2008, 13:55
2) b + c + d = 300 -------> c + d = 300 - b
a + b > c + d
200 > 300-b
300-b is $$(-\infty,200)$$ ------->$$300 - (100,+\infty)=(-\infty,200)$$
200 > 300-b is true -------> a + b > c + d is true
sufficient.
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Manager
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Re: DS - a + b [#permalink]

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28 Jan 2008, 14:38
Hi walker, I am still lost on how statement two is sufficient.

Any other way to explain it?

walker wrote:
2) b + c + d = 300 -------> c + d = 300 - b
a + b > c + d
200 > 300-b
300-b is $$(-\infty,200)$$ ------->$$300 - (100,+\infty)=(-\infty,200)$$
200 > 300-b is true -------> a + b > c + d is true
sufficient.
Director
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Re: DS - a + b [#permalink]

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28 Jan 2008, 14:43
1
KUDOS
what walker is saying is this:

from the stem a+b = 200 and a<b
therefore b>100 and a<100

so lets take b a little more than 100, eg 101 for arguments sake

now lets plug it into the second piece of data.

c + d = 300 - b = 300 - 101 = 199

therefore c + d < 200, sufficient

AVakil wrote:
Hi walker, I am still lost on how statement two is sufficient.

Any other way to explain it?

walker wrote:
2) b + c + d = 300 -------> c + d = 300 - b
a + b > c + d
200 > 300-b
300-b is $$(-\infty,200)$$ ------->$$300 - (100,+\infty)=(-\infty,200)$$
200 > 300-b is true -------> a + b > c + d is true
sufficient.
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Re: DS - a + b [#permalink]

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29 Jan 2008, 11:55
sonibubu wrote:
If a + b = 200 and a < b, is a + b > c + d ?

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

200>c+d?

1: says this Suff.

2: c+d=300-b 200>300-b --> -100>-b ---> 100<b? Yes b/c a<b and a+b=200. Thus B>=101 (assuming a and b are integers, we could have b=100.000000000000001 etc...) Either way B>100 so 2 is suff.

D
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Re: DS - a + b [#permalink]

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29 Jan 2008, 15:36
sonibubu wrote:
If a + b = 200 and a < b, is a + b > c + d ?

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

Since a + b = 200 and b > a,
b is atleast 101

1) This states c+d < 200, hence c+d < a+b, as a+b=200. Sufficient

2) Since b is atleast 101, substituting its lowest value (to maximize c+d), we get
c+d = 199
Sufficient

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Re: DS - a + b   [#permalink] 29 Jan 2008, 15:36
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