BTGModeratorVI wrote: ↑Mon Sep 07, 2020 7:00 am
If x and y are positive integers, is x/y < (x+5)/(y+5)?
(1) y = 5
(2) x > y
Answer:
B
Source: Magoosh
Target question: Is x/y < (x+5)/(y+5)?
This is a great candidate for REPHRASING the target question.
Aside: We have a free video with tips on rephrasing the target question (below)
If y is a positive integer, then we can be certain that y and (y+5) are both POSITIVE. This allows us to safely multiply both sides of our inequality by y and (y+5).
Take
x/y < (x+5)/(y+5) and multiply both sides by y to get:
Is x < (y)(x+5)/(y+5)?
Then take
x < (y)(x+5)/(y+5) and multiply both sides by (y+5) to get:
Is x(y+5) < (y)(x+5)?
Expand to get:
Is xy + 5x < xy + 5y?
Subtract xy from both sides to get:
Is 5x < 5y?
Divide both sides by 5 to get:
Is x < y?
We now have a very simple, REPHRASED target question.....
REPHRASED target question:
Is x < y?
Now onto the statements!
Statement 1: y = 5
Since we have no information about x, there's no way to tell whether or not
x < y.
Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x > y
Perfect!
If
x > y then we can answer our
REPHRASED target question with certainty:
NO, x is definitely not less than y.
So, statement 2 is SUFFICIENT
Answer = B
