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Re: If x and y are positive numbers, is (x + 1)/(y + 1) > x/y [#permalink]

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26 Jun 2017, 02:57

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2

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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Re: If x and y are positive numbers, is (x + 1)/(y + 1) > x/y [#permalink]

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26 Jun 2017, 08:10

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Top Contributor

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

If x and y are positive numbers, is (x + 1)/(y + 1) > x/y [#permalink]

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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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