Data Sufficiency

BTGModeratorVI wrote: ↑

Tue Feb 16, 2021 8:23 am

Is x + 5 greater than y - 5 ?

(1) y < -3
(2) x > -13

Answer: C
Source: official guide

Target question: Is x + 5 > y - 5 ?

Statement 1: y < -3
No information about x.
Statement 1 is NOT SUFFICIENT

Statement 2: x > -13
No information about y.
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that y < -3
Statement 2 tells us that x > -13

Important: There's a nice property of inequalities that says "If two inequalities have their inequality symbols facing the same direction, we can ADD the two inequalities"
At the moment, the inequality symbols are not facing the same direction.
We can quickly fix this by taking the bottom inequality and multiplying both sides by -1 to get: -x < 13 [aside: Since we multiplied both sides of the inequality by a NEGATIVE number, we must reverse the direction of the inequality symbol]
We now have the following inequalities:
y < -3
-x < 13

When we add the inequalities we get: y - x < 10

It's hard to say whether this provides enough information to answer the target question: Is x + 5 > y - 5 ?
Let's manipulate the inequality in the target question.
Take: Is x + 5 > y - 5 ?
Add 5 to both sides to get: Is x + 10 > y?
Subtract x from both sides to get: Is 10 > y - x?

Perfect! Since we now know that y - x < 10, the answer to the rephrased target question is YES, 10 is definitely greater than y-x
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent