If wz < 2, is z < 1?
(1) w > 2
(2) z < 2
Ans should be A?
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
GMAT Set 12
This topic has expert replies
-
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: w > 2Abhijit K wrote:If wz < 2, is z < 1?
(1) w > 2
(2) z < 2
Linking together wz < 2 and 2 < w, we get:
wz < 2 < w
wz < w.
Since w > 2, we can safely divide each side by w, as follows:
wz/w < w/w
z < 1.
SUFFICIENT.
Statement 2: z < 2
Case 1: z=1 and w=1, satisfying the constraints that z < 2 and wz < 2.
In this case, z=1, so the answer to the question stem is NO.
Case 1: z=1/2 and w=1, satisfying the constraints that z < 2 and wz < 2.
In this case, z<1, so the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.
The correct answer is A.
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
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi Abhijit K,
This DS question can be solved by TESTing VALUES and considering how the inequalities impact the "limits" of what Z and W can be...
We're told that (W)(Z) < 2. We're asked if Z is less than 1. This is a YES/NO question.
Fact 1: W > 2
IF we make W big, then Z would have to be really small (or even negative).
IF....
W = 10
(10)(Z) < 2
Z < 2/10
Z < 1/5 so the answer to the question is YES.
But we also need to consider what happens when W gets really close to 2...
IF....
W = 2.001
(2.001)(Z) < 2
Z < 2/2.001
Since the denominator of this fraction is GREATER than the numerator, the fraction is LESS than 1. Thus Z is less than 1 and the answer to the question is still YES.
Fact 1 is SUFFICIENT.
Fact 2: Z < 2
We don't even have to consider the value of W here.
IF...
Z = 1.5 then the answer to the question is NO
Z = 0 then the answer to the question is YES
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
This DS question can be solved by TESTing VALUES and considering how the inequalities impact the "limits" of what Z and W can be...
We're told that (W)(Z) < 2. We're asked if Z is less than 1. This is a YES/NO question.
Fact 1: W > 2
IF we make W big, then Z would have to be really small (or even negative).
IF....
W = 10
(10)(Z) < 2
Z < 2/10
Z < 1/5 so the answer to the question is YES.
But we also need to consider what happens when W gets really close to 2...
IF....
W = 2.001
(2.001)(Z) < 2
Z < 2/2.001
Since the denominator of this fraction is GREATER than the numerator, the fraction is LESS than 1. Thus Z is less than 1 and the answer to the question is still YES.
Fact 1 is SUFFICIENT.
Fact 2: Z < 2
We don't even have to consider the value of W here.
IF...
Z = 1.5 then the answer to the question is NO
Z = 0 then the answer to the question is YES
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
