BTGModeratorVI wrote: ↑Fri Apr 03, 2020 9:35 am
Is x < 1/y?
1) y > 0
2) xy < 1
Answer:
C
Source: Math Revolution
Target question: Is x < 1/y?
Statement 1: y > 0
No information about x, so statement 1 is NOT SUFFICIENT
Statement 2: xy < 1
IMPORTANT: some students will want to divide both sides by y to get x < 1/y, HOWEVER doing so is incorrect, because we don't know whether y is POSITIVE or NEGATIVE.
If y is POSITIVE, then dividing both sides by y gives us
x < 1/y
If y is NEGATIVE, then dividing both sides by y gives us
x > 1/y [when we divide both sides by a negative value, we must REVERSE the direction of the inequality]
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that y is POSITIVE
Statement 2 tells us that xy < 1
Since we know that y is POSITIVE, we can safely divide both sides by y to get the inequality
x < 1/y.
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
