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!
Equations DS question
This topic has expert replies
- GMATinsight
- Legendary Member
- Posts: 1100
- Joined: Sat May 10, 2014 11:34 pm
- Location: New Delhi, India
- Thanked: 205 times
- Followed by:24 members
Question : Is m + z > 0 ?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!
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
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Target question: Is m + z > 0?Is m + z > 0?
(1) m - 3z > 0
(2) 4z - m > 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
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Statement 1: m > 3z.Is m+z > 0?
(1) m-3z > 0
(2) 4z-m > 0
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3