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# M01 #13

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Manager
Joined: 11 Jul 2010
Posts: 222

Kudos [?]: 109 [0], given: 20

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19 Sep 2010, 09:33
If the product of two integers X and Y is negative, what is the value of X-Y?
1. X+Y = 2
2. -3<X<Y

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

I don't agree with OA
[Reveal] Spoiler:
OA = E

x, y carry opposite signs

If x is -ve and y +ve: x-y = -(x+y)
If x is +ve and y is -ve: x-y = x+y

(1) Gives x+y=2; insufficient as answer could be 2 or -2
(2) Tells us 2 things -> x is the one which is -ve and y is +ve. x and y also cannot have the same value.

(1) and (2) together ---> since we know x is -ve and y is +ve then x-y = -(x+y)

=> x-y = -2 (as we know from (1) that x+y =2)

How can it be E? It has to be C.

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Math Expert
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135256 [0], given: 12679

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19 Sep 2010, 09:48
gmat1011 wrote:
If the product of two integers X and Y is negative, what is the value of X-Y?
1. X+Y = 2
2. -3<X<Y

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

I don't agree with OA
[Reveal] Spoiler:
OA = E

x, y carry opposite signs

If x is -ve and y +ve: x-y = -(x+y)
If x is +ve and y is -ve: x-y = x+y

(1) Gives x+y=2; insufficient as answer could be 2 or -2
(2) Tells us 2 things -> x is the one which is -ve and y is +ve. x and y also cannot have the same value.

(1) and (2) together ---> since we know x is -ve and y is +ve then x-y = -(x+y)

=> x-y = -2 (as we know from (1) that x+y =2)

How can it be E? It has to be C.

The red part under the spoiler is not correct.

If the product of two integers X and Y is negative, what is the value of X-Y?

Just see the examples below.

(1) X+Y = 2 --> if $$x=-1$$ and $$y=3$$ then $$x-y=-4$$ but if $$x=-2$$ and $$y=4$$ then $$x-y=-6$$. Not sufficient.

(2) -3<X<Y --> means that x equals to either -1 or -2, so the same example works here as well: if $$x=-1$$ and $$y=3$$ then $$x-y=-4$$ but if $$x=-2$$ and $$y=4$$ then $$x-y=-6$$. Not sufficient.

(1)+(2) Again the same example (as it satisfies both statements): if $$x=-1$$ and $$y=3$$ then $$x-y=-4$$ but if $$x=-2$$ and $$y=4$$ then $$x-y=-6$$. Not sufficient.

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Manager
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19 Sep 2010, 10:05
Thanks Bunuel

There was an example given in the model solution as well... The example does make it E - thanks, but do you know why doesn't the part you colored red work here based on what we know of the signs of x and y?

If x is -ve and y +ve: x-y = -(x+y)
If x is +ve and y is -ve: x-y = x+y

Just want to figure it out so I don't repeat this error in the future.. Thx.

Kudos [?]: 109 [0], given: 20

Math Expert
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135256 [0], given: 12679

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19 Sep 2010, 10:24
gmat1011 wrote:
Thanks Bunuel

There was an example given in the model solution as well... The example does make it E - thanks, but do you know why doesn't the part you colored red work here based on what we know of the signs of x and y?

If x is -ve and y +ve: x-y = -(x+y)
If x is +ve and y is -ve: x-y = x+y

Just want to figure it out so I don't repeat this error in the future.. Thx.

Examples matched because only these values of x and y are possible when we combine statements.

As for your approach. What makes you think that "if x is -ve and y +ve: x-y = -(x+y)"? How did you derive this? It's just not right. For example: x=-1 and y=2 then x-y=-3 and -(x+y)=-1.
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19 Sep 2010, 10:41
If x is -ve and y is +ve, this is what I thought may work ---

x-y can be written as:

-x - (+y) = - x -y = -(x+y)

If you take specific examples then it doesn't seem to hold...

Kudos [?]: 109 [0], given: 20

Math Expert
Joined: 02 Sep 2009
Posts: 42544

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19 Sep 2010, 10:46
1
KUDOS
Expert's post
gmat1011 wrote:
If x is -ve and y is +ve, this is what I thought may work ---

x-y can be written as:

-x - (+y) = - x -y = -(x+y)

If you take specific examples then it doesn't seem to hold...

I see. It would be true if we had absolute values: if $$x<0$$ and $$y>0$$ then $$|x|-|y|=-x-y=-(x+y)$$. But when we have just $$x-y$$ (without modulus) then it doesn't hold true.
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Manager
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20 Sep 2010, 10:20
Thanks Bunuel... as always, much appreciated...

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Re: M01 #13   [#permalink] 20 Sep 2010, 10:20
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# M01 #13

Moderator: Bunuel

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