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# Given that x ≠ 0, y ≠ 0, and (x + y) ≠ 0, is y/x > y/(x + y) ?

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Math Expert
Joined: 02 Sep 2009
Posts: 58297
Given that x ≠ 0, y ≠ 0, and (x + y) ≠ 0, is y/x > y/(x + y) ?  [#permalink]

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13 Aug 2018, 03:20
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35% (medium)

Question Stats:

79% (02:14) correct 21% (02:19) wrong based on 40 sessions

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Given that x ≠ 0, y ≠ 0, and (x + y) ≠ 0, is y/x > y/(x + y) ?

(1) x > -1

(2) y > -1

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Joined: 09 Oct 2015
Posts: 226
Given that x ≠ 0, y ≠ 0, and (x + y) ≠ 0, is y/x > y/(x + y) ?  [#permalink]

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Updated on: 13 Aug 2018, 04:15
question boils down to :

is y^2/ x^2+xy >0

that is, is xy>0

for this we would need to know whether both x and y are of the same sign.
a and b is required for this, hence c is the ans if it were given that a and b are integers.

but we arent given this, hence a and b can be negative decimals.
so E

Originally posted by rahulkashyap on 13 Aug 2018, 03:43.
Last edited by rahulkashyap on 13 Aug 2018, 04:15, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 7952
Given that x ≠ 0, y ≠ 0, and (x + y) ≠ 0, is y/x > y/(x + y) ?  [#permalink]

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13 Aug 2018, 03:56
1
Given that x ≠ 0, y ≠ 0, and (x + y) ≠ 0, is y/x > y/(x + y) ?

Clearly we require both values so individually both are insufficient

Combined
x > -1 and y > -1
Say x=-1/2 and y=2, $$\frac{2*2}{-1}>2/(2-1/2)$$.......-4>4/3..............NO

Say x=4 and y=2, $$\frac{2}{4}>\frac{2}{4+2}$$.......1/2>1/3................YES

Insufficient

E
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Given that x ≠ 0, y ≠ 0, and (x + y) ≠ 0, is y/x > y/(x + y) ?   [#permalink] 13 Aug 2018, 03:56
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