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Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0

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Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0  [#permalink]

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New post 24 Jun 2018, 10:13
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Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0  [#permalink]

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New post Updated on: 24 Jun 2018, 10:59
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Bunuel wrote:
Is \(\frac{x + 1}{y + 1} > \frac{x}{y}\)?


(1) \(0 < x < y\)

(2) \(xy > 0\)


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We'll simplify the inequalities so we understand what we need to do.
This is a Precise approach.

(1) Multiplying both sides by y(y+1) (note that both are positive), gives yx+y > yx+x and cancelling out yx gives y > x.
This is exactly what we're told in our statement!
Sufficient.

(2) If y(y+1) is positive we can repeat the same process as above to get y > x, but since all we know is that both x,y are positive or both are negative but do not know which is larger we cannot answer.
If y(y+1) is negative we'll get the expression y < x, but, for the same reason as above, we still cannot answer.
Insufficient

(A) is our answer.
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Originally posted by DavidTutorexamPAL on 24 Jun 2018, 10:50.
Last edited by DavidTutorexamPAL on 24 Jun 2018, 10:59, edited 2 times in total.
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Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0  [#permalink]

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New post 24 Jun 2018, 10:51
Bunuel wrote:
Is \(\frac{x + 1}{y + 1} > \frac{x}{y}\)?


This can be re-written as \(\frac{x + 1}{y + 1} - \frac{x}{y}\) > 0

Simplifying this further, we get

\(\frac{(x + 1)y - x(y - 1)}{y(y + 1)} > 0\) -> \(\frac{xy + y - xy + x}{y(y+1)} > 0\) -> \(\frac{x+y}{y(y+1)} > 0\)

The rephrased question now reads \(\frac{x+y}{y(y+1)} > 0\)

(1) \(0 < x < y\)
Since x and y are both positive, the expression will always be positive. (Sufficient)

(2) \(xy > 0\)
Here, both x and y can be positive or negative. If x and y are negative,
the expression is NOT positive. We don't get a unique answer. (Insufficient) (Option A)
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Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0  [#permalink]

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New post 24 Jun 2018, 14:33
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Bunuel wrote:
Is \(\frac{x + 1}{y + 1} > \frac{x}{y}\)?


(1) \(0 < x < y\)

(2) \(xy > 0\)



Target question: Is (x+1)/(y+1) > x/y ?

Statement 1: 0 < x < y
This tells us that y is POSITIVE, which means y+1 is also POSITIVE.
This means we can safely take the inequality (x+1)/(y+1) > x/y and safely multiply both sides by y
When we do so, we get: (y)(x+1)/(y+1) > x
We can also multiply both sides by y+1 to get: (y)(x+1) > (x)(y+1)
Expand to get: xy + y > xy + x
Subtract xy from both sides to get: y > x
So, with the help of statement 1, our original target question Is (x+1)/(y+1) > x/y ? becomes Is y > x ?
Since statement 1 tells us that y > x, the answer to the target question is a definitive YES
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: xy > 0
Let's TEST some values
There are several values of x and y that satisfy statement 2 (xy > 0). Here are two:
Case a: x = 1 and y = 1. In this case, (x+1)/(y+1) = (1+1)/(1+1) = 2/2 = 1, and x/y = 1/1 = 1. So, the answer to the target question is NO, (x+1)/(y+1) is NOT greater than x/y ?
Case b: x = -3 and y = -2. In this case, (x+1)/(y+1) = (-3 +1)/(-2 +1) = -2/-1 = 2, and x/y = -3/-2 = 3/2. So, the answer to the target question is YES, (x+1)/(y+1) IS greater than x/y ?
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

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Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0  [#permalink]

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New post 25 Oct 2018, 03:38
Dear Bunuel DavidTutorexamPAL GMATPrepNow pushpitkc

How can we cross multiply in this question, when we are not aware of the signs of x and y?

Warm Regards,
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Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0  [#permalink]

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New post 25 Oct 2018, 04:15
FANewJersey wrote:
Dear Bunuel DavidTutorexamPAL GMATPrepNow pushpitkc

How can we cross multiply in this question, when we are not aware of the signs of x and y?

Warm Regards,
FANJ
Hey FANewJersey, good question! In 1) we do know the sign: we are told that 0 < x < y - this means they are both bigger than 0 - they are positive!
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Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0  [#permalink]

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New post 25 Oct 2018, 04:23
Hi DavidTutorexamPAL,
So basically you are reading ahead to get an idea and then applying something from the statements to firm up your stem question (is x less than y). Correct?
Warmly,
FANJ

DavidTutorexamPAL wrote:
FANewJersey wrote:
Dear Bunuel DavidTutorexamPAL GMATPrepNow pushpitkc

How can we cross multiply in this question, when we are not aware of the signs of x and y?

Warm Regards,
FANJ
Hey FANewJersey, good question! In 1) we do know the sign: we are told that 0 < x < y - this means they are both bigger than 0 - they are positive!
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Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0  [#permalink]

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New post 25 Oct 2018, 05:06
FANewJersey wrote:
Hi DavidTutorexamPAL,
So basically you are reading ahead to get an idea and then applying something from the statements to firm up your stem question (is x less than y). Correct?
Warmly,
FANJ

DavidTutorexamPAL wrote:
FANewJersey wrote:
Dear Bunuel DavidTutorexamPAL GMATPrepNow pushpitkc

How can we cross multiply in this question, when we are not aware of the signs of x and y?

Warm Regards,
FANJ
Hey FANewJersey, good question! In 1) we do know the sign: we are told that 0 < x < y - this means they are both bigger than 0 - they are positive!


You could say that, I suppose... I don't think of it as "reading ahead" since solving with statement (1) is the first thing we are supposed to try and do anyway. The question stem on its own isn't going to give us the answer....
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Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0  [#permalink]

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New post 27 Oct 2018, 14:44
Thanks DavidTutorexamPAL, But we will have to nail down a goal, which we drive from the stem question (value vs. Yes/No, what is being asked etc. etc.). But I believe I got the idea here. Thanks
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Re: Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 &nbs [#permalink] 27 Oct 2018, 14:44
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