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Is x < y ? (1) The ratio of x to y is 7/9. (2) xy > 0

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Naina1605
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Is x < y ? (1) The ratio of x to y is 7/9. (2) xy > 0 [#permalink] New post   12 Feb 2012, 12:18
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Is x < y ?

(1) The ratio of x to y is 7/9.
(2) xy>0

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OA is E.

My question is, if x and y are both negative then wont the minus signs cancel out? If this holds true then, the ratio will always be positive and statement (1) will be sufficient.

Anyone?? Thanks in advance.
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E
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Bunuel
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Re: Is x < y ? (1) The ratio of x to y is 7/9. (2) xy > 0 [#permalink] New post   12 Feb 2012, 12:41
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Is x < y ?

(1) The ratio of x to y is 7/9 --> if x=7 and y=9 then x<y and the answer to the question is YES, but if x=-7 and y=-9 then x>y and the answer to the question is NO. Not sufficient.

Notice that in both cases x/y=7/9, but in first case x<y and in second case x>y.

(2) xy>0 --> x and y have the same sign. Not sufficient to answer whether x<y.

(1)+(2) Example from (1) is still valid. Not sufficient.

Answer: E.

Hope it's clear.
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Re: Is x < y ? (1) The ratio of x to y is 7/9. (2) xy > 0 [#permalink] New post   15 Feb 2012, 10:47
Thank you Bunuel for your reply. I have understood your explanation.

But I am still confused about 1 thing. If the ratio of x and y = say -1/-2 then, will u not cancel out the negative signs to make the ratio positive before determining the values of x and y? In other words can the ratio of x and y remain -1/-2 and not 1/2 (by cancelling out the negative signs)...

hope you have understood my query. Any comments will be helpful. Thanks in advance.
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Re: Is x < y ? (1) The ratio of x to y is 7/9. (2) xy > 0 [#permalink] New post   15 Feb 2012, 11:00
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Naina1605 wrote:
Thank you Bunuel for your reply. I have understood your explanation.

But I am still confused about 1 thing. If the ratio of x and y = say -1/-2 then, will u not cancel out the negative signs to make the ratio positive before determining the values of x and y? In other words can the ratio of x and y remain -1/-2 and not 1/2 (by cancelling out the negative signs)...

hope you have understood my query. Any comments will be helpful. Thanks in advance.


I'm not sure I understand your question.

If you are asking whether (-1)/(-2) equals to 1/2, then the answer is yes: (-1)/(-2)=1/2. Consider this: we are told that the ratio of x to y is 1/2 (or which is the same (-1)/(-2)) then x and y can be: 1 and 2, -1 and -2, 2 and 4, -2 and -4, ... basically any two numbers which when divided result 1/2.

For more on Number Theory check this: math-number-theory-88376.html

Hope it helps.
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Re: Is x < y ? (1) The ratio of x to y is 7/9. (2) xy > 0 [#permalink] New post   17 Oct 2013, 01:58
Naina1605 wrote:
Thank you Bunuel for your reply. I have understood your explanation.

But I am still confused about 1 thing. If the ratio of x and y = say -1/-2 then, will u not cancel out the negative signs to make the ratio positive before determining the values of x and y? In other words can the ratio of x and y remain -1/-2 and not 1/2 (by cancelling out the negative signs)...

hope you have understood my query. Any comments will be helpful. Thanks in advance.



We are asked about x and y (x < y) not the fraction itself. So, the fraction 1/2 might equal -1/-2, but x and y don't equal to -x and -y.
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Re: Is x < y ? (1) The ratio of x to y is 7/9. (2) xy > 0 [#permalink] New post   08 Jan 2014, 13:51
Naina1605 wrote:
Is x < y ?

(1) The ratio of x to y is 7/9.
(2) xy>0

Show Spoiler
OA is E.

My question is, if x and y are both negative then wont the minus signs cancel out? If this holds true then, the ratio will always be positive and statement (1) will be sufficient.

Anyone?? Thanks in advance.


Question: Is y>x?

(1) x/y = 7/9

9x = 7y

Now question can be translated to 9y>9x
Is 9y>7y? Is y>0?

Insuff, we don't know the sign of y

2) xy>0

We only know that signs are the same but it could be either y>x or x>y

(1) and (2) together

Signs are the same, but we still don't know whether x,y>0 or x,y<0

E

Hope it helps

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Re: Is x < y ? (1) The ratio of x to y is 7/9. (2) xy > 0 [#permalink] New post   18 Apr 2017, 13:16
i got 2 examples.
x=-1
y=-9/7
x>y

and
x=7
y=9
x<y

each statement alone works with both of the examples.
together - same.

answer is E.
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Re: Is x < y ? (1) The ratio of x to y is 7/9. (2) xy > 0 [#permalink]
18 Apr 2017, 13:16
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