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Is 10m > 5n - k?

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lucas211: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Mon Aug 04, 2014 5:39 pmFollowed by: 2 members; Thanked: 1 times

by lucas211 » Mon Apr 25, 2016 9:05 am

Hello BTG

Would appreciate a little help with the following DS-problem - especially statement (2):

Is 10m > 5n - k?

1. n = 2m
2. IkI = -k

Thanks in advance

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Source: Beat The GMAT — Data Sufficiency | Mon Apr 25, 2016 9:05 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Mon Apr 25, 2016 9:09 am

lucas211 wrote:Hello BTG

Would appreciate a little help with the following DS-problem - especially statement (2):

Is 10m > 5n - k?

1. n = 2m
2. IkI = -k

Thanks in advance

Statement 2 is simply telling us that k is negative. (You can see this by plugging in values. If k = 2, then plugging into the equation we'd get |2| = -2. This isn't true. But if k = -2, we'd get |-2| = -(-2), or 2 = 2. This is true.) Now give this one another shot...

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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 Apr 25, 2016 9:28 am

Hi lucas211,

This question can be solved by TESTing VALUES, Number Properties and/or a bit of logic.

We're asked if 10M > (5N - K). This is a YES/NO question. To answer it, we'll need to have some specific information about all 3 variables.

1) N = 2M

With this Fact, the question now becomes....

is 10M > 5(2M) - K?
is 10M > 10M - K?

This tells us nothing about the value of K, so the answer to the question will not be consistent.
Fact 1 is INSUFFICIENT

2) |K| = -K

This Fact tells us that K is either 0 or negative, but it doesn't tell us anything about the values of M or N , so the answer to the question will not be consistent.
Fact 2 is INSUFFICIENT

Combined, we know...
N = 2M
|K| = -K

Using the work we did in Fact 1, we know that the question now asks...

is 10M > 10M - K?

Since K will either be 0 or a negative, the 'left side' of the inequality will NEVER be greater than the 'right side'; thus the answer to the question is ALWAYS NO.
Combined, SUFFICIENT

Final Answer: C

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Rich

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