Is the range of the 6 integers greater than 20?

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Mon Mar 31, 2014 9:13 pm

Hello,

Can you please tell me where I am going wrong here in my solution for Statement 2:

If r is the range of the 6 integers in set S, is r greater than 20?

(1) When ordered from least to greatest, the difference between any two
consecutive integers in S is less than 4.

(2) When ordered from least to greatest, the difference between any two
consecutive integers in S is less than 5.

Let the 6 integers be a, b, c, d, e, f
Range = f - a

Is f - a > 20?

1) b - a < 4
c - b < 4
d - c < 4
e - d < 4
f - e < 4

On adding the above we get f - a < 20. Hence, sufficient

2) b - a < 5
c - b < 5
d - c < 5
e - d < 5
f - e < 5

=> f - e < 25. Hence in-suff.

However, the OA is given as D. Can you please assist? Thanks a lot.

Best Regards,
Sri

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Source: Beat The GMAT — Data Sufficiency | Mon Mar 31, 2014 9:13 pm

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Mon Mar 31, 2014 11:11 pm

Hi Sri,

Your organization for this question is good, but you forgot about some of the details in the question.

Since the 6 numbers are all INTEGERS, this provides an interesting limitation in Fact 2:

Fact 2: When ordered from least to greatest, the difference between any two consecutive integers is the set is less than 5.

Since the values are all INTEGERS, This means that difference is 0, 1, 2, 3 or 4

You correctly noted that there are 5 "differences", but it's not enough to say each is < 5. You have to note that each is < 5 AND an integer (since subtracting an integer FROM an integer = an integer).

With 5 "differences" that are integers AND are 0, 1, 2, 3 or 4, the maximum range would be 20. Since the question asks if the range is GREATER than 20, the answer to this question will ALWAYS be NO. Fact 2 is SUFFICIENT.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Apr 12, 2014 11:17 am

[email protected] wrote:Hi Sri,

Your organization for this question is good, but you forgot about some of the details in the question.

Since the 6 numbers are all INTEGERS, this provides an interesting limitation in Fact 2:

Fact 2: When ordered from least to greatest, the difference between any two consecutive integers is the set is less than 5.

Since the values are all INTEGERS, This means that difference is 0, 1, 2, 3 or 4

You correctly noted that there are 5 "differences", but it's not enough to say each is < 5. You have to note that each is < 5 AND an integer (since subtracting an integer FROM an integer = an integer).

With 5 "differences" that are integers AND are 0, 1, 2, 3 or 4, the maximum range would be 20. Since the question asks if the range is GREATER than 20, the answer to this question will ALWAYS be NO. Fact 2 is SUFFICIENT.

GMAT assassins aren't born, they're made,
Rich

Hello Rich,

Thanks for the excellent and detailed explanation.

Best Regards,
Sri

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Sat Apr 12, 2014 1:50 pm

Rich is absolutely right. I always tell my students that if there is an integer constraint, and the statement says "x is less than 5," you should really translate that as "x is less than or equal to 4."

If you set up your statement 2 this way, you would have gotten f - a </= 20, which would have been sufficient.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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