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

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

by sachin_yadav » Thu May 22, 2014 7:14 am
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

OA is D

I am not able to eliminate C as i am not getting values in my mind. This is what i did d>a>L because of which i eliminate A,B, and E.

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by GMATGuruNY » Thu May 22, 2014 7:30 am
sachin_yadav wrote: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

OA is D
Since a<d, a-d < 0.
Thus, it is not possible that a-d = 9.

The correct answer is D.
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by sachin_yadav » Thu May 22, 2014 7:51 am
Thank you :D . I just didn't realize that step.
GMATGuruNY wrote:

Since a<d, a-d < 0.
Thus, it is not possible that a-d = 9.

The correct answer is D.
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by Brent@GMATPrepNow » Thu May 22, 2014 8:13 am
sachin_yadav wrote: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
SLOW APPROACH
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.

FAST APPROACH
If a < d, then we can conclude that 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
Answer: D

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by Jeff@TargetTestPrep » Mon Jan 29, 2018 10:17 am
sachin_yadav wrote: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
Since d is greater than a, it is not possible for a - d to equal a positive number. For example, if d = 11 and a = 5, then a - d = -6. No matter what values are chosen for a and d, the difference a - d will always be positive.

Answer:D

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