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Is x > y? (1) x/2 = y - 3 (2) y > 6

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Is x > y? (1) x/2 = y - 3 (2) y > 6  [#permalink]

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18 Sep 2019, 21:42
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Difficulty:

45% (medium)

Question Stats:

67% (01:28) correct 33% (01:25) wrong based on 51 sessions

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Is $$x > y$$?

(1) $$\frac{x}{2} = y-3$$

(2) $$y > 6$$

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Re: Is x > y? (1) x/2 = y - 3 (2) y > 6  [#permalink]

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Updated on: 18 Sep 2019, 23:23
1
Is x>y?

(1) $$\frac{x}{2}$$=y−3
x=2y-6
x and y can be any number(positive or negative) or fraction.
If y=1, x=-4, is x>y? NO

If y=-2, x=-10, is x>y? NO

If y=8, x=10, is x>y? YES

(2) y>6
If y>6, then x could be anything. Different answers possible. INSUFFICIENT!

(1) + (2)
x=2y-6 and y>6

If y=8, x=10, is x>y? YES

If y=$$\frac{21}{2}$$, x=15, is x>y? YES

If y=100, x=194, is x>y? YES

Twice the y less 6 would make x ALWAYS greater.
SUFFICIENT!

If y>6(any positive number or fraction greater than 6), x would always be greater and positive. Therefore answer is option C.

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Originally posted by EncounterGMAT on 18 Sep 2019, 21:53.
Last edited by EncounterGMAT on 18 Sep 2019, 23:23, edited 1 time in total.
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Re: Is x > y? (1) x/2 = y - 3 (2) y > 6  [#permalink]

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18 Sep 2019, 22:19
1
1
A alone says nothing. For example for Y=4, X is 2(less than y) and for Y=8, X is 10(greater than y).

B alone says nothing as well.

Together they represent a set of points for which x>y

Hence c

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Re: Is x > y? (1) x/2 = y - 3 (2) y > 6  [#permalink]

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18 Sep 2019, 22:54
1
statement 1: x/2 = y-3 meaning x=2y-6. This is insufficient because y can take infinite values some which will be less than x while other possible values of y can be greater than x.

Statement 2: y>6. Clearly insufficient because no information is provided to enable us determine x.

1+2: sufficient because combining both statements means that all possible values of x will be greater than 6, hence we can conclusively stay that x>y.

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Re: Is x > y? (1) x/2 = y - 3 (2) y > 6  [#permalink]

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18 Sep 2019, 23:47
1
Is x > y ?

STATEMENT (1) - $$\frac{x}{2}$$ = y-3

y = $$\frac{x+6}{2}$$
if x = 8 then y = 7---is x>y?---YES
if x = 5 then y = 5.5---is x>y?---NO

STATEMENT (2) - y>6
no information is given about x
so, INSUFFICIENT

combining both statements

x = 2y-6 and y>6

if y = 6.1 then x = 6.2 ---x>y
any value of y > 6 will yield value of x that will be > y

hence, Is x>y -- the answer is YES
SUFFICIENT

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Re: Is x > y? (1) x/2 = y - 3 (2) y > 6  [#permalink]

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19 Sep 2019, 00:20
Is x > y?

(1) $$\frac{x}{2} = y − 3$$
x = 0 → y = 3, x > y NO
x = 10 → y = 8, x > y YES
INSUFFICIENT.

(2) y > 6
INSUFFICIENT.

Together 1) and 2)
y = 6.1 → x = 6.2, x > y YES
y = 10 → x = 14, x > y YES

SUFFICIENT.

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Re: Is x > y? (1) x/2 = y - 3 (2) y > 6  [#permalink]

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19 Sep 2019, 04:32
1
Quote:
Is x>y?

(1) x/2=y−3
(2) y>6

(1) x/2=y-3…x-2y=-6…x=-6+2y; substitute, $$x>y…-6+2y>y…y>6$$? insufic.
(2) y>6: no info about $$x$$, insufic.
(1&2) y>6, true, sufic.

Re: Is x > y? (1) x/2 = y - 3 (2) y > 6   [#permalink] 19 Sep 2019, 04:32
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