BTGModeratorVI wrote: ↑

Fri Jul 03, 2020 7:03 am

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

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

Answer: B
Source: Official guide

Note the following for positive numbers x and y.

• If x/y < 1 (or x < y), then we have (x + a)/(y + a) > x/y, where a is a positive number

This is because proportionately a greater quantity (a/x*100%) is added to the numerator than to the denominator (a/x*100% > a/y*100%).

• If x/y > 1 (or x < y), then we have (x + a)/(y + a) < x/y, where a is a positive number

This is because proportionately a smaller quantity (a/x*100%) is added to the numerator than to the denominator (a/x*100% < a/y*100%).

Correct answer: B

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Fri Jul 03, 2020 7:03 am

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

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

Answer: B
Source: Official guide

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: B