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Intern  Joined: 10 Apr 2014
Posts: 2
For how many integer values of m is x < m < y ?  [#permalink]

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2 00:00

Difficulty:   55% (hard)

Question Stats: 57% (01:15) correct 43% (01:19) wrong based on 96 sessions

### HideShow timer Statistics For how many integer values of m is x < m < y ?

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

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.

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.
Intern  Joined: 19 Feb 2013
Posts: 23
Re: (Work check) For how many integer values of m is x < m < y ?  [#permalink]

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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}
Intern  Joined: 10 Apr 2014
Posts: 2
Re: (Work check) For how many integer values of m is x < m < y ?  [#permalink]

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 56244
Re: For how many integer values of m is x < m < y ?  [#permalink]

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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

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.

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.
_________________
CEO  V
Joined: 12 Sep 2015
Posts: 3847
Re: For how many integer values of m is x < m < y ?  [#permalink]

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Top Contributor
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

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