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# What is N when N is an integer and x < N < y?

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Math Expert
Joined: 02 Sep 2009
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What is N when N is an integer and x < N < y?  [#permalink]

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19 Apr 2017, 00:42
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5% (low)

Question Stats:

92% (01:03) correct 8% (00:55) wrong based on 132 sessions

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What is N when N is an integer and x < N < y?

(1) y − x = 7
(2) x and y are integers.

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Re: What is N when N is an integer and x < N < y?  [#permalink]

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19 Apr 2017, 00:49
1
statement 1:
as y-x = 7, N can be anything from x+1 to x+6. --insufficient
statement 2:
if x and y are integers, N can or cannot be an integer. so we aren't sure about the value of N.---insufficient

If we combine both the answers, then also we are not sure about N

hence E.
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Re: What is N when N is an integer and x < N < y?  [#permalink]

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19 Apr 2017, 06:58
2
Top Contributor
Bunuel wrote:
What is N when N is an integer and x < N < y?

(1) y − x = 7
(2) x and y are integers.

Target question: What is the value of N?

Given: N is an integer and x < N < y

Statement 1: y − x = 7
Let's TEST some values.
There are several values of x, y and N that satisfy statement 1 and the given information. Here are two possible cases:
Case a: x = 1, y = 8, and N = 4. In this case, N = 4
Case b: x = 1, y = 8, and N = 5. In this case, N = 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x and y are integers
NOTE: I see that I can re-use the two cases I used above to show that statement 1 is not sufficient.
Case a: x = 1, y = 8, and N = 4. In this case, N = 4
Case b: x = 1, y = 8, and N = 5. In this case, N = 5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Since we were able to use the SAME two cases for statement 1 and statement 2 alone, we can also use them when we COMBINE the statements.
Case a: x = 1, y = 8, and N = 4. In this case, N = 4
Case b: x = 1, y = 8, and N = 5. In this case, N = 5
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent
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Re: What is N when N is an integer and x < N < y?  [#permalink]

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08 Sep 2018, 22:44
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Re: What is N when N is an integer and x < N < y?   [#permalink] 08 Sep 2018, 22:44
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