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If x and y are positive numbers, is (x + 1)/(y + 1) > x/y
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Updated on: 02 Jan 2019, 15:24

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Bunuel wrote:

If x and y are positive numbers, is \(\frac{x + 1}{y + 1} > \frac{x}{y}\)?

(1) x > 1 (2) x < y

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

Given: x and y are positive numbers

This is a great candidate for rephrasing the target question.

We have the inequality: (x + 1)/(y + 1) > x/y Since y is positive, we can multiply both sides of the inequality by y Likewise, since y is positive, we know that y+1 is positive, which means we can multiply both sides of the inequality by (y+1) When perform both of these multiplications we get: (x + 1)(y) > (x)(y + 1) Expand to get: xy + y > xy + x Subtract xy from both sides to get: y > x So, we can now ask... REPHRASED target question:Is y > x ?

Statement 1: x > 1 There's no information about y, so there's no way to determine whether or not y > x Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x < y Perfect!!! Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Re: If x and y are positive numbers, is (x + 1)/(y + 1) > x/y
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26 Jun 2017, 02:57

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If x and y are positive numbers, is \(\frac{x + 1}{y + 1} > \frac{x}{y}\)?

x & y are POSITIVE numbers

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

Lets simplify the equation, as we are given that x & y are positive integers we can multiply the R.H.S. with the L.H.S. as there will not be any impact on the inequality SIGN of the equation.

\((x + 1) * (y) > (y + 1) * (x)\)

\(xy + y > xy + x\)

Cancelling \(xy\) from both the sides.

\(y > x\)

So we want to answer, Is \(y > x\) ?

(1) \(x > 1\)

This does not tell us anything about y. Hence, Eq. (1) =====> NOT SUFFICIENT (2) \(x < y\)

We can write it as y > x, this is what we have to prove. Hence, Eq. (2) =====> SUFFICIENT

Hence, Answer is B

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If x and y are positive numbers, is (x + 1)/(y + 1) > x/y
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26 Jun 2017, 09:30

x and y are positive numbers \(x,y>0 ; (x+1)y>(y+1)x ; y>x\)

(1) x > 1 X can be a proper fraction or improper fraction and y can be proper or improper fraction NS (2) x < y Rephrased expression Suff

Option B
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Re: If x and y are positive numbers, is (x + 1)/(y + 1) > x/y
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22 Jan 2019, 05:58

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(1) x <1 -- Insufficient (2) x< y let's understand:

Effects of addition if the ratio is less than 1: After adding some positive number to the numerator and denominator, the resulting ration increases eg 2/3 adding 10 to numerator and denominator 2+10 / 3+10 =12/13 > 2/3

if the ratio is greater than 1: After adding some positive number to the numerator and denominator, the resulting ration decreases eg. 7/5 7+20 /5 +20 = 27/25 <75

If x and y are positive numbers, is (x + 1)/(y + 1) > x/y
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27 Mar 2019, 03:28

Bunuel wrote:

If x and y are positive numbers, is \(\frac{x + 1}{y + 1} > \frac{x}{y}\)?

(1) x > 1 (2) x < y

Here, x and y are positive numbers (i.e., \(x>0\) and \(y>0\)) If this is the case then \(\frac{x}{y}\) must be positive. If \(\frac{x}{y}\) is positive, then \(\frac{x + 1}{y + 1}\) must be positive too.. So, the question is: \(\frac{x + 1}{y + 1} > \frac{x}{y}\)? I can answer this question if I know value of x and y (whatever the value it is!).

In statement 2: Here is given that \(x < y\). I don't care what about the specific value of x and y here. I know from this statement that y is greater than x. If the statement even says that x is greater than y, i still don't care because statement NEVER lies!. Without any calculation in statement 2, I can surely say that it gives a definite YES or a definite NO, but NOT the simultaneous YES and NO. So, sufficient.

In statement 1: There is no value of y. So, insufficient. Is my understanding wrong Bunuel, IanStewart? Thanks__
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Re: If x and y are positive numbers, is (x + 1)/(y + 1) > x/y
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16 Nov 2019, 14:04

It might be a silly question, but before ruling Statement 1 out, can't we use the fee values of Y (as the question stem says Y is a positive number) ? Use few positive values of Y and plug in the question to see if we get all Yes or all No?

gmatclubot

Re: If x and y are positive numbers, is (x + 1)/(y + 1) > x/y
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16 Nov 2019, 14:04