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# Is d ≠ e ? (1) d > e + 1 (2) d < e + 2

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Math Expert
Joined: 02 Sep 2009
Posts: 62353
Is d ≠ e ? (1) d > e + 1 (2) d < e + 2  [#permalink]

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27 Feb 2017, 03:32
1
8
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Difficulty:

55% (hard)

Question Stats:

54% (01:22) correct 46% (01:27) wrong based on 169 sessions

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Is d ≠ e ?

(1) d > e + 1
(2) d < e + 2

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Joined: 11 Sep 2015
Posts: 4551
GMAT 1: 770 Q49 V46
Re: Is d ≠ e ? (1) d > e + 1 (2) d < e + 2  [#permalink]

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27 Feb 2017, 08:16
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Top Contributor
3
Bunuel wrote:
Is d ≠ e ?

(1) d > e + 1
(2) d < e + 2

Target question: Is d ≠ e ?
This is a good candidate for rephrasing the target question.
If d = e, then we can say that d - e = 0
Likewise, if d ≠ e then we can say that d - e ≠ 0

REPHRASED target question: Is d - e ≠ 0 ?

Statement 1: d > e + 1
Subtract e from both sides to get: d - e > 1
If d - e is GREATER THAN 1, we can be certain that d - e will NEVER EQUAL ZERO.
In other words, d - e ≠ 0
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: d < e + 2
Subtract e from both sides to get: d - e < 2
If d - e is LESS THAN 2, it's POSSIBLE that d - e = 0, and it's POSSIBLE that d - e ≠ 0
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

ASIDE: If you're not convinced that statement 2 is not sufficient, consider these two cases that yield contradictory answers to the target question:
Case a: d = 3 and e = 2. In this case, d - e ≠ 0
Case b: d = 3 and e = 3. In this case, d - e = 0

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Re: Is d ≠ e ? (1) d > e + 1 (2) d < e + 2  [#permalink]

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27 Feb 2017, 07:35
Bunuel wrote:
Is d ≠ e ?

(1) d > e + 1
(2) d < e + 2

Question: Is d ≠ e ?

Statement 1: d > e + 1
i.e. d > 1
SUFFICIENT

Statement 2: d < e + 2
i.e. d and e may be equal and may be different too
NOT SUFFICIENT

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Re: Is d ≠ e ? (1) d > e + 1 (2) d < e + 2  [#permalink]

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28 Feb 2017, 04:01
GMATinsight wrote:

Question: Is d ≠ e ?

Statement 1: d > e + 1
i.e. d > 1
SUFFICIENT

Dear GMATInsight,

Why did you conclude that d>1.

If d=-2 & e=-4.............then....-2>-3
If d=-100 & e=-200 then ......-100>-199

So here d is not greater than 1.
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Re: Is d ≠ e ? (1) d > e + 1 (2) d < e + 2  [#permalink]

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07 Oct 2018, 23:46
d>e+1
take any value d will never be equal to e
hence suff
statement 2
d<e+2
suppose e = 0
d<2
d can be 0
hence insuff
Re: Is d ≠ e ? (1) d > e + 1 (2) d < e + 2   [#permalink] 07 Oct 2018, 23:46
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