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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? [#permalink]

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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.
[Reveal] Spoiler: OA

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

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New post 24 Jun 2015, 01:11
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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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New post 24 Jun 2015, 01:11
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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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New post 24 Jun 2015, 09:00
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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
Thanks,
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Re: If d>a and L<a, which of the following cannot be true? [#permalink]

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New post 26 Jun 2015, 07:07
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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
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Re: If d>a and L<a, which of the following cannot be true? [#permalink]

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New post 29 Jun 2015, 05:15
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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.


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

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New post 15 Jul 2016, 05:54
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 ?
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Re: If d>a and L<a, which of the following cannot be true? [#permalink]

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New post 15 Jul 2016, 06:29
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 15 Jul 2016, 06:58
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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New post 20 Jul 2016, 13:06
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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New post 29 Jan 2018, 09:55
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.

Answer: D
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Re: If d>a and L<a, which of the following cannot be true?   [#permalink] 29 Jan 2018, 09:55
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