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Math Expert V
Joined: 02 Sep 2009
Posts: 58398
If d>a and L<a, which of the following cannot be true?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 70% (01:34) correct 30% (01:30) wrong based on 246 sessions

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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

Kudos for a correct solution.

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Re: If d>a and L<a, which of the following cannot be true?  [#permalink]

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2
Is the answer D?

If d>a, then d-a>0 (always positive). The converse would be a-d<0 (always negative). Option D states that a-d=9, which can never be true.
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Re: If d>a and L<a, which of the following cannot be true?  [#permalink]

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

Since d>a
a-d, cannot be positive.

Lets take some examples
d=5, a<5 :: 4.99-5 = -0.01 :: 4-5 = -1 :: -4-5 = -9
d=-4, a>-4 :: -4.01 -(-4) = -0.01 :: -9 -(-4) = -5

Ans:D
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Re: If d>a and L<a, which of the following cannot be true?  [#permalink]

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1
Rearranging the above equation we get
d-a>0 ---1
a-l>0 -----2
adding above equation we get,
d-l>0 ; hence, answer choice b and c can be possible
Equation 1 can be written as a-d<0 so option D ca not be possible.

[ This can also be solved by taking example where we have d>a>l , and cross verify ]

Hence answer is D
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Re: If d>a and L<a, which of the following cannot be true?  [#permalink]

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Bunuel 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

Kudos for a correct solution.

d > a
adding -d to both sides of inequality
0 > a-d

Hence a-d is negative. Hence Option D cannot be correct
Math Expert V
Joined: 02 Sep 2009
Posts: 58398
Re: If d>a and L<a, which of the following cannot be true?  [#permalink]

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1
Bunuel 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

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

Simplify the inequalities, so that all the inequality symbols point in the same direction. Then, line up the inequalities as shown. Finally, combine the inequalities.
L < a
a < d
Thus, L < a < d

Since d is a larger number than a, a — d cannot be positive.

Therefore, (D) cannot be true.
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Re: If d>a and L<a, which of the following cannot be true?  [#permalink]

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Hi,

If d>a, but if both the numbers are negative eg: d=-3, a=-12. Here d>a, but d-a=9
Considering previous posts, d-a is positive. Hence value of d-a is positive.

How can we say d-a can never be positive ?

This is true only if d>0 and a>0, but there is no such condition given here.
So what will be current answer for this ?
Math Expert V
Joined: 02 Sep 2009
Posts: 58398
Re: If d>a and L<a, which of the following cannot be true?  [#permalink]

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Saahiljeet wrote:
Hi,

If d>a, but if both the numbers are negative eg: d=-3, a=-12. Here d>a, but d-a=9
Considering previous posts, d-a is positive. Hence value of d-a is positive.

How can we say d-a can never be positive ?

This is true only if d>0 and a>0, but there is no such condition given here.
So what will be current answer for this ?

The solution says a — d cannot be positive, not d - a.
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Re: If d>a and L<a, which of the following cannot be true?  [#permalink]

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Bunuel 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

Kudos for a correct solution.

the question translated to L<a<d
Even if -ve value are considered a-d will always be -ve.
Ans D)
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Re: If d>a and L<a, which of the following cannot be true?  [#permalink]

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I got confused by assuming that a,d and L are integers.
If they would have been integers, then even option C was correct.
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Re: If d>a and L<a, which of the following cannot be true?  [#permalink]

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Bunuel 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.

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Re: If d>a and L<a, which of the following cannot be true?  [#permalink]

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