BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

If x ≠ 0, is x^2 / |x| < 1?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 124
Joined: Wed May 19, 2010 10:20 pm
Thanked: 3 times
GMAT Score:1100

If x ≠ 0, is x^2 / |x| < 1?

by mitzwillrockgmat » Sat May 22, 2010 8:19 am
If x ≠ 0, is x^2 / |x| < 1?

(1) x < 1
(2) x > −1

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Please explain!! thanks :)
Top
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 758
Joined: Sat Aug 29, 2009 9:32 pm
Location: Bangalore,India
Thanked: 67 times
Followed by:2 members

by sumanr84 » Sat May 22, 2010 8:45 am
IMO : A

A. Since x is NOT = 0, for all values of x, x^2 / |x| < 1

B . If we check with values x = 2 , we get , x^2 / |x| > 1
for x = 1/2 , we get , x^2 / |x| < 1
I am on a break !!
Top
User avatar
Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Sun May 02, 2010 11:10 am
Thanked: 1 times

by nwalker001 » Sat May 22, 2010 11:34 am
If x ≠ 0, is (x^2) / |x| < 1?

(1) x < 1
(2) x > -1

Evaluate Statement 1 (x < 1)

To solve Yes or No question plug in some values for x:

x = -1; ((-1)^2) / |-1| = 1 / 1 = 1, Answer: No
x = 1/2; ((1/2)^2) / |1/2| = (1/4) / (1/2) = 1/2, Answer: Yes

Statement 1 is insufficient, so eliminate choices A and D

Evaluate Statement 2 (x > -1)

Again, plug in some values for x and answer Yes or No

x = 1; ((1)^2) / |1| = 1 / 1 = 1, Answer: No
x = 1/2; ((1/2)^2) / |1/2| = (1/4) / (1/2) = 1/2, Answer: Yes

Statement 2 is insufficient, so eliminate choice B

Evaluate Statements 1 & 2 Together (x < 1) and (x > -1)

Combine statements: -1 < x < 1, but x ≠ 0

To solve Yes or No question plug in some values for x:

x = 1/2; ((1/2)^2) / |1/2| = (1/4) / (1/2) = 1/2, Answer: Yes
x = -1/2; ((-1/2)^2) / |-1/2| = (1/4) / (1/2) = 1/2, Answer: Yes
x = 1/4; ((1/4)^2) / |1/4| = (1/16) / (1/4) = 1/4, Answer: Yes
x = -1/4; ((-1/4)^2) / |-1/4| = (1/16) / (1/4) = 1/4, Answer: Yes
etc.

Answer C
Top
Legendary Member
Posts: 759
Joined: Mon Apr 26, 2010 10:15 am
Thanked: 85 times
Followed by:3 members

by clock60 » Sat May 22, 2010 2:15 pm
mitzwillrockgmat wrote:If x ≠ 0, is x^2 / |x| < 1?

(1) x < 1
(2) x > −1

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Please explain!! thanks :)
also got C, my thinking
as x^2 and |x| are both +ve
we can square them to get rid off module
and left with
x^4/x^2=x^2
so the prolem asks is x^2<1
the given will be true for
(x-1)(x+1)<0
x<1 and x>-1
so to our statements
(1)x<1 not sufficient
(2) x>-1 alone not sufficient
together
-1<x<1 sifficient
so C
Top
Post new topic Post Reply
• Page 1 of 1