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Sub 505 Level|   Inequalities|                  
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avigutman
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Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 11 Feb 2022, 17:16
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pumarox95
I solved this a different way. Can someone let me know if this approach is correct? Thanks!

From statement 1: Since we know X and Y are positive, we know X+1/Y+1 tends to 1 while X/Y would be closer to 0.
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Hi pumarox95, your inference above is not correct. You made the assumption that x﹤y (that x/y is a proper fraction, less than 1).
See my video solution for further analysis.
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Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 11 Feb 2022, 18:37
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avigutman

Hi pumarox95, your inference above is not correct. You made the assumption that x﹤y (that x/y is a proper fraction, less than 1).
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I don't think pumarox assumed x < y, because they were using Statement 1, which tells us that x < y. If so, their inference is correct -- as long as everything is positive (and x and y are different), (x+1)/(y + 1) is always closer to 1 than x/y is. So since Statement 1 tells us x/y < 1, it's instantly sufficient.
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Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 11 Feb 2022, 20:20
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IanStewart

I don't think pumarox assumed x < y, because they were using Statement 1, which tells us that x < y. If so, their inference is correct -- as long as everything is positive (and x and y are different), (x+1)/(y + 1) is always closer to 1 than x/y is. So since Statement 1 tells us x/y < 1, it's instantly sufficient.
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Right, IanStewart, if pumarox95 relied on the given relationship of x<y, it's all good.
I was responding directly to this inference:
pumarox95
Since we know X and Y are positive, we know X+1/Y+1 tends to 1 while X/Y would be closer to 0.
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Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 14 Jan 2024, 21:17
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Bunuel
Is \(\frac{x + 1}{y + 1} > \frac{x}{y}\)?


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

(2) \(xy > 0\)


(DS09315)
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All, I know this is an easy question. The only thing that I want to know is -
Since we do not know the sings of x and y, is it advisable to rephrase the expression in the question?

xy + y > xy +x, that is - Is y>x?

KarishmaB MartyMurray chetan2u Thanks in advance!
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Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 14 Jan 2024, 21:38
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Bunuel
Is \(\frac{x + 1}{y + 1} > \frac{x}{y}\)?


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

(2) \(xy > 0\)


(DS09315)


All, I know this is an easy question. The only thing that I want to know is -
Since we do not know the sings of x and y, is it advisable to rephrase the expression in the question?

xy + y > xy +x, that is - Is y>x?

KarishmaB MartyMurray chetan2u Thanks in advance!
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Without using data from any statement, this manipulation will be incorrect.
Using statement 1, you can manipulate the inequality as given since now you know that y is positive and hence so is y+1.
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Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 14 Jan 2024, 21:44
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Bunuel
Is \(\frac{x + 1}{y + 1} > \frac{x}{y}\)?


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

(2) \(xy > 0\)


(DS09315)
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The question can be solved without putting pen to paper in 30 secs using number properties.

Is \(\frac{x + 1}{y + 1} > \frac{x}{y}\)?

Recall that when we add the same positive number to both the numerator and denominator of a positive fraction, it moves towards 1.

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

x and y both are positive so x/y is positive and less than 1. When we add 1 to both x and y, the fraction obtained (x+1)/(y+1) will be closer to 1 and hence will be greater than x/y. Imagine them on the number line:

-------------------- 0 ----------- x/y------x+1/y+1-------------1-----------

Hence, (x+1)/(y+1) is greater than x/y and we can answer the question with a 'Yes'. Sufficient alone.

(2) \(xy > 0\)

We don't know whether x and y are positive or negative. Also we don't know whether x/y is less than 1 or greater than 1 even if they are both positive.
Not sufficient.

Answer (A)
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Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 14 Jan 2024, 22:22
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Engineer1
Bunuel
Is \(\frac{x + 1}{y + 1} > \frac{x}{y}\)?


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

(2) \(xy > 0\)


(DS09315)


All, I know this is an easy question. The only thing that I want to know is -
Since we do not know the sings of x and y, is it advisable to rephrase the expression in the question?

xy + y > xy +x, that is - Is y>x?

KarishmaB MartyMurray chetan2u Thanks in advance!
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KarishmaB has already touched upon the query, so just adding a link that may help to do such questions faster.
https://gmatclub.com/forum/effects-of-a ... 69413.html

As far as the query is concerned, you cannot modify the initial statement unless you know the signs of x and y.
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Is (x + 1)/(y + 1) > x/y? (1) 0 < x < y (2) xy > 0 20 Mar 2025, 19:11
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