Equations DS question

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DevB: Senior | Next Rank: 100 Posts; Posts: 43; Joined: Sun Apr 06, 2014 10:50 amFollowed by: 1 member; Thanked: 1 times

by DevB » Tue Jul 22, 2014 5:08 am

This question is from GMAT Prep so anyone planning to give the practice exam may avoid to see it here.

For others, Please help me in answering the below question:

Is m + z > 0 ?

1. m - 3z > 0
2. 4z - m > 0

Thanks in advance!

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Source: Beat The GMAT — Data Sufficiency | Tue Jul 22, 2014 5:08 am

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Tue Jul 22, 2014 5:46 am

DevB wrote:This question is from GMAT Prep so anyone planning to give the practice exam may avoid to see it here.

For others, Please help me in answering the below question:

Is m + z > 0 ?

1. m - 3z > 0
2. 4z - m > 0

Thanks in advance!

Question : Is m + z > 0 ?
Answer must be in the form of "YES" or "NO"

Statement 1) m - 3z > 0
Case 1: m = 10, z = 1 The answer to the question is YES
Case 2: m = -5, z = -3 The answer to the question is NO
INSUFFICIENT

Statement 2) 4z-m > 0

i.e. 4z > m
Case 1: m = 10, z = 1 The answer to the question is YES
Case 2: m = -5, z = -1 The answer to the question is NO
INSUFFICIENT

Combining the two statements
4z-m > 0 and m - 3z > 0
4z > m and m > 3z
Also

Adding the two equation
(4z-m)+(m-3z) > 0
i.e Z > 0

i.e. 4z>m>3z

Therefore both m and z are positive. therefore m+z>0

SUFFICIENT

Answer: Option C

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Jul 22, 2014 5:56 am

Is m + z > 0?

(1) m - 3z > 0
(2) 4z - m > 0

Target question: Is m + z > 0?

Statement 1: m - 3z > 0
There are several sets of numbers that meet this condition. Here are two:
Case a: m = 4 and z = 1, in which case m + z is greater than 0
Case a: m = 4 and z = -10, in which case m + z is not greater than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 4z - m > 0
There are several sets of numbers that meet this condition. Here are two:
Case a: m = 1 and z = 4, in which case m + z is greater than 0
Case a: m = -10 and z = 1, in which case m + z is not greater than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
Rearrange statement 1 to get: -3z + m > 0
Statement 2: 4z - m > 0

Multiply both sides of -3z + m > 0 by 5 to get: -15z + 5m > 0
Multiply both sides of 4z - m > 0 by 4 to get: 16z - 4m > 0

Since both inequality signs are facing the same direction, we can ADD the two green inequalities to get: z + m > 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jul 22, 2014 6:03 am

Is m+z > 0?

(1) m-3z > 0
(2) 4z-m > 0

Statement 1: m > 3z.
m and z could both be positive, m and z could both be negative.
Insufficient.

Statement 2: m < 4z
m and z could both be positive, m and z could both be negative.
Insufficient.

Statements 1 and 2 combined:
Linking the inequalities, we get:
3z < m < 4z
3z < 4z.
0 < z.
Since z is positive, we know that m -- which is between 3z and 4z -- also is positive.
Thus, m+z > 0.
Sufficient.

The correct answer is C.

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