For how many integer values of m is x

Question

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.

So answer should be...B right?

rishiroadster · Answer

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}

SwordfishII · Answer

hm interesting, thank you for the response

Bunuel · Answer

This is a copy of OG13 following question: 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.

BrentGMATPrepNow · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards