Is xy > x^2y^2? (1) 14x^2 = 3 (2) y^2 = 1

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mitzwillrockgmat: Master | Next Rank: 500 Posts; Posts: 124; Joined: Wed May 19, 2010 10:20 pm; Thanked: 3 times; GMAT Score:1100

by mitzwillrockgmat » Sat May 22, 2010 7:39 am

Is xy > x^2y^2?

(1) 14x^2 = 3

(2) y^2 = 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 give a detailed explaination. thanks!

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Source: Beat The GMAT — Data Sufficiency | Sat May 22, 2010 7:39 am

sumanr84: Legendary Member; Posts: 758; Joined: Sat Aug 29, 2009 9:32 pmFollowed by: 2 members; Location: Bangalore,India; Thanked: 67 times

by sumanr84 » Sat May 22, 2010 9:02 am

mitzwillrockgmat wrote:Is xy > x^2y^2?

(1) 14x^2 = 3

(2) y^2 = 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 give a detailed explaination. thanks!

IMO : E
Clearly, A and B alone cannot let us to arrive at any conclusion.
Now, from 1, x = + sqrt ( 3/14) or x = - sqrt (3/14)
From 2, y = +1 or -1

if we draw a table keeping in mind these values of x and y, we will arrive at E
x=+sqrt(3/14) y = 1
x=+sqrt(3/14) y = -1

x=-sqrt(3/14 y=1
x=-sqrt(3/14 y=-1

Is there a short-cut way ?

I am on a break !!

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clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Sat May 22, 2010 2:54 pm

mitzwillrockgmat wrote:Is xy > x^2y^2?

(1) 14x^2 = 3

(2) y^2 = 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 give a detailed explaination. thanks!

also E for me
is xy-x^2y^2>0
xy(1-xy)>0 this can be true if xy>0 and xy<1, or
xy<0 and xy>1
as per st clearly insufficient
both
insufficient as x can be -ve, or +ve
the same is true about y (-ve or +ve)
if x=-(3/14)^1/2 and y=-1 true , the product is +ve and less than 1, but for
x=(3/14)^1/2 and y=-1 th product is -ve and less than 1
so E

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