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If x and y are positive numbers, is (x + 1)/(y + 1) > x/y

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

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New post 26 Jun 2017, 02:33
2
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

74% (01:23) correct 26% (01:51) wrong based on 500 sessions

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

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New post 26 Jun 2017, 08:10
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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

Answer:

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

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

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New post 26 Jun 2017, 02:40
1
x+1/y+1>x/y
cross multiply
xy +y > xy + x
subtract xy from both sides
y > x or x<y?

Ans B.

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New post 26 Jun 2017, 09:04
Might as well share that I picked C due to not Reading that x and y - positive. This would not allow crossmultiplication.:)

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

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New post 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  [#permalink]

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New post 15 Nov 2017, 17:27
Bunuel wrote:
If x and y are positive numbers, is \(\frac{x + 1}{y + 1} > \frac{x}{y}\)?

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


We are given that x and y are positive numbers and need to determine whether (x + 1)/(y + 1) > x/y. Simplifying the question, we have:

Is y(x + 1) > x(y + 1)? (Note that we multiplied each side by y(y + 1), which is allowed because y > 0.)

Is yx + y > xy + x?

Is y > x?

Statement One Alone:

x > 1

Since we do not know anything about y, statement one alone is not sufficient to answer the question.

Statement Two Alone:

x < y

We see that statement two has answered the question; y is greater than x.

Answer: B
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Re: If x and y are positive numbers, is (x + 1)/(y + 1) > x/y &nbs [#permalink] 15 Nov 2017, 17:27
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