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

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

by VJesus12 » Thu Dec 28, 2017 4:40 am
If a+b=200 and a<b, is a+b>c+d?

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

The OA is the option D.

I know how to prove that the statement (1) is sufficient, but how can I show that the statement (2) is sufficient?

Experts, may you give me some help?
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by ceilidh.erickson » Sat Dec 30, 2017 3:05 pm
If a+b=200 and a<b, is a+b>c+d?

(1) c+d<200
(2) b+c+d=300
Rephrase using the given information in the question stem:

a + b = 200 -->
is 200 > c + d?

(1) gives us exactly this, so it's clearly sufficient.

(2) First, let's unpack what we know about a & b:
if a + b = 200, and one is larger than the other, than one must be greater than 100 and the other less than 100:
b > 100
a < 100

We can apply this to the information given in statement 2:
b + c + d = 300
(>100) + c + d = 300
c + d = (<200)

This looks funny algebraically, but think: if we subtract some number that's larger than 100 from 300, we'll be left with something less than 200. Since this answers our target question, it's sufficient.

The answer is D.
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by ceilidh.erickson » Sat Dec 30, 2017 3:25 pm
Also, here's a good rule of thumb: if one statement is very obviously sufficient, as (1) was here, the answer is often D. If the answer had just been A here, that would have meant that the test writer gave us information that we didn't use (a < b). And we will never be given information in a DS question stem that's not necessary!
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by GMATGuruNY » Mon Jan 01, 2018 9:48 am
VJesus12 wrote:If a+b=200 and a<b, is a+b>c+d?

(1) c+d<200
(2) b+c+d=300
Substituting a+b = 200 into a+b > c+d?, we get:
200 > c+d?
c+d < 200?

Statement 1; c+d < 200
SUFFICIENT.

Statement 2: b+c+d = 300
Test the THRESHOLD value for c+d.
In other words, test whether it's possible that c+d =200.
Substituting c+d = 200 into b+c+d = 300, we get:
b+200 = 300
b=100, with the result that a=100, since a+b = 200.
Doesn't work, since the prompt indicates that b>a.
Implication:
To satisfy the constraint that b>a, b must be GREATER THAN 100, with the result that c+d < 200, since b+c+d = 300.
SUFFICIENT.

The correct answer is D.
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