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Is a + b > c + d?

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by M7MBA » Thu Mar 22, 2018 3:55 am
Is a + b > c + d ?

(1) a > c

(2) d < b

The OA is C.

How can I use both statements together to get an answer? The inequality in the second statement is opposite. <i class="em em-disappointed"></i>
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Source: — Data Sufficiency |
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by GMATGuruNY » Thu Mar 22, 2018 4:13 am
M7MBA wrote:How can I use both statements together to get an answer? The inequality in the second statement is opposite. <i class="em em-disappointed"></i>
Inequalities can be ADDED together as long as the <> in each inequality faces the same direction.
Here, d < b can be rephrased as b>d, allowing us to add together a>c and b>d:
a+b > c+d.
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by Brent@GMATPrepNow » Thu Mar 22, 2018 6:31 am
M7MBA wrote:Is a + b > c + d ?

(1) a > c
(2) d < b
Target question: Is a + b > c + d ?

Statement 1: a > c
Since we have no information about b or d, we cannot determine whether a + b > c + d
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: d < b
Since we have no information about a or c, we cannot determine whether a + b > c + d
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that a > c
Statement 2 tells us that b > d (NOTE: I rewrote the inequality so that the inequality symbol is facing the other direction)
Since the two inequality symbols are facing in the SAME DIRECTION, we can ADD THEM to get: a + b > c + d
PERFECT.
We can now say, with certainty that the answer to the target question is YES, a + b IS greater than c + d
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

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by Jeff@TargetTestPrep » Fri Mar 23, 2018 11:56 am
M7MBA wrote:Is a + b > c + d ?

(1) a > c

(2) d < b
Statement One Alone:

a > c

Since we do not know anything about the relationship between d and b, statement one alone is not sufficient to answer the question.

Statement Two Alone:

d < b

Since we do not know anything about the relationship between a and c, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using our statements together, we see that since a is greater than c and b is greater than d, the sum of a and b must be greater than the sum of c and d.

Answer: C

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