Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Re: If x and y are positive numbers, is (x + 1)/(y + 1) > x/y
[#permalink]
Show Tags
26 Jun 2017, 08:10
5
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
Re: If x and y are positive numbers, is (x + 1)/(y + 1) > x/y
[#permalink]
Show Tags
26 Jun 2017, 02:57
17
3
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
You liked the solution, 1 Kudos Please! _________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."
Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
If x and y are positive numbers, is (x + 1)/(y + 1) > x/y
[#permalink]
Show Tags
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
_________________
Never stop fighting until you arrive at your destined place - that is, the unique you. Have an aim in life, continuously acquire knowledge, work hard, and have the perseverance to realise the great life.A. P. J. Abdul Kalam
close
74% (01:23) correct 
