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Inequalities

by gmattesttaker2 » Sun Feb 10, 2013 4:35 pm
Hello,

This is from MGMAT Guide 2. P. 101:

If d > a and L < a, which of the following cannot be true?

A) d + L = 14 B) d - L = 7 C) d - L = 1 D) a - d = 9 E) a + d = 9

Answer: D

I was stuck between C and D. Can you please assist?

Thanks,
Sri
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by Brent@GMATPrepNow » Sun Feb 10, 2013 4:48 pm
gmattesttaker2 wrote:Hello,

This is from MGMAT Guide 2. P. 101:

If d > a and L < a, which of the following cannot be true?

A) d + L = 14 B) d - L = 7 C) d - L = 1 D) a - d = 9 E) a + d = 9
Let's first rewrite the inequalities as: L < a and a < d, which means L < a < d

Now check the answer choices and see which answer choice is impossible.
A) d + L = 14 (possible with L=6, a=7, d=8, so eliminate A)
B) d - L = 7 (possible with L=1, a=7, d=8, so eliminate B)
C) d - L = 1 (possible with L=7, a=7.5, d=8, so eliminate C)
D) a - d = 9 IMPOSSIBLE
E) a + d = 9 (possible with L=1, a=4, d=5, so eliminate E)

By the process of elimination, we can see that D must be correct.


Alternatively, we can conclude that, if a < d, then a - d must be negative.
Proof:
Start with: a < d
Subtract d from both sides to get: a - d < 0

Since a - d must be negative, it cannot be true that a - d = 9

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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