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For how many integer values of m is x < m < y ?

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For how many integer values of m is x < m < y ? [#permalink]

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New post Updated on: 11 Apr 2014, 03:39
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A
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C
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  55% (hard)

Question Stats:

57% (00:52) correct 43% (01:00) wrong based on 93 sessions

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For how many integer values of m is x < m < y ?

(1) x and y are positive integers
(2) y – x = 6

Spoiler: ::
Work:
1. Statement 1 tells me only that x and y are positive integers, which means that the range between them could be literally anything, insufficient
BCE
2. Statement 2 tells me the distance between y and x is simply 6 (eg y=7, x=1, so M could be 2,3,4,5, or 6). Statement 2 does not give me any positive or negative indications, fractions, but that shouldn't matter as the number of integer's should be the same.

So answer should be...B right?
Spoiler: OA

Originally posted by SwordfishII on 10 Apr 2014, 19:37.
Last edited by Bunuel on 11 Apr 2014, 03:39, edited 1 time in total.
Renamed the topic and edited the question.
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Re: (Work check) For how many integer values of m is x < m < y ? [#permalink]

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New post 10 Apr 2014, 20:05
IMO the answer should be C.
Given x<m<y,
Consider two cases:
A) x=0.5 then y=6.5, then the number of integer values of m will be 6 ie, {1,2,3,4,5,6}; and
B) x=1 then y=7, then the number of integer values of m will be 5 ie, {2,3,4,5,6}
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Re: (Work check) For how many integer values of m is x < m < y ? [#permalink]

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New post 10 Apr 2014, 20:21
rishiroadster wrote:
IMO the answer should be C.
Given x<m<y,
Consider two cases:
A) x=0.5 then y=6.5, then the number of integer values of m will be 6 ie, {1,2,3,4,5,6}; and
B) x=1 then y=7, then the number of integer values of m will be 5 ie, {2,3,4,5,6}


hm interesting, thank you for the response
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Re: For how many integer values of m is x < m < y ? [#permalink]

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New post 11 Apr 2014, 03:41
SwordfishII wrote:
For how many integer values of m is x < m < y ?

(1) x and y are positive integers
(2) y – x = 6

Spoiler: ::
Work:
1. Statement 1 tells me only that x and y are positive integers, which means that the range between them could be literally anything, insufficient
BCE
2. Statement 2 tells me the distance between y and x is simply 6 (eg y=7, x=1, so M could be 2,3,4,5, or 6). Statement 2 does not give me any positive or negative indications, fractions, but that shouldn't matter as the number of integer's should be the same.

So answer should be...B right?


This is a copy of OG13 following question:
Quote:

How many integers n are there such that r < n < s ?

(1) s - r = 5
(2) r and s are not integers.


Discussed here: how-many-integers-n-are-there-such-that-r-n-s-166396.html

Similar questions to practice:
how-many-integers-are-there-between-c-and-d-1-neither-c-115561.html
how-many-integers-are-there-such-that-v-n-w-129065.html

P.S. Please provide the OA's when posting. Thank you.
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Re: For how many integer values of m is x < m < y ? [#permalink]

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New post 08 Mar 2018, 11:33
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SwordfishII wrote:
For how many integer values of m is x < m < y ?

(1) x and y are positive integers
(2) y – x = 6


Target question: For how many integer values of m is x < m < y ?

Statement 1: x and y are positive integers
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 1 and y = 3. In this case, only ONE value of m (m = 2) satisfies the inequality x < m < y
Case b: x = 1 and y = 4. In this case, TWO values of m (m = 2 and m = 3) satisfy the inequality x < m < y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y – x = 6
It would SEEM that this statement provides sufficient information. HOWEVER, the answer to the target question varies, depending on whether x and y have INTEGER values or whether they have NON-INTEGER values. Here's what I mean:
Case a: x = 1.1 and y = 7.1. (notice that y - x = 7.1 - 1.1 = 6). In this case, there are 6 values of m (m = 2, 3, 4, 5, 6, and 7) that satisfy the inequality x < m < y
Case b: x = 1 and y = 7. (notice that y - x = 7 - 1 = 6). In this case, there are 5 values of m (m = 2, 3, 4, 5 and 6) that satisfy the inequality x < m < y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When we combine BOTH statements, there is ONLY ONE answer to the target question
If x and y are both integers, AND it is the case that y - x = 6, then there are 5 values of m that satisfy the inequality x < m < y
To be more specific, if y - x = 6, then y = x + 6
So, the FIVE values of m that satisfy the inequality x < m < y will be: m = x + 1, m = x + 2, m = x + 3, m = x + 4, and m = x + 5
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
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Re: For how many integer values of m is x < m < y ?   [#permalink] 08 Mar 2018, 11:33
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