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# If x and y are positive, is 4x > 3y? (1) x > y - x (2)

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If x and y are positive, is 4x > 3y? (1) x > y - x (2) [#permalink]

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22 Mar 2009, 22:22
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If x and y are positive, is 4x > 3y?
(1) x > y - x
(2) x/y < 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.
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23 Mar 2009, 00:39
E.
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23 Mar 2009, 07:45
Economist wrote:
If x and y are positive, is 4x > 3y?
(1) x > y - x
(2) x/y < 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.

those who find it difficult to use the graphical method, here is an alternative :

Fact 1: x > y -x

=> x = y -x +k where k is a positive number

2x = k+y
4x = 2k + 2y

depending upon k, 4x may or may not be greater than 3y

Fact 2: x < y

=> x+h = y

4x = 4y -4h

depending upon h, 4x may or may not b greater than 3y

combining both Fact 1 and Fact 2 together :

2k + 2y = 4y - 4h
y = k + 2h
=> 3y = 3k + 6h and 4x = 4k + 4h

again we are not sure whether 4x > 3y because we don't know the values of h and k.

Hence E.
Re: DS: Inequality   [#permalink] 23 Mar 2009, 07:45
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# If x and y are positive, is 4x > 3y? (1) x > y - x (2)

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