Fraction Question

[topspin20]

Is (a/b)>(3/5)?

1) (a+1/b)>(3/5)

2) (a/b+1)>(3/5)

Answer: B

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Hi topspin20,

This DS question has a great built-in "comparison" shortcut.

The question asks " Is A/B > 3/5?" This is a Yes/No question, so we have to keep track of if the answer is ALWAYS yes, ALWAYS no or Inconsistent.

Let's cross-multiply to make this question easier: "Is 5A > 3B?"

Fact 1 - let's cross-multiply this inequality:

5A + 5 > 3B

We know for sure that 5A + 5 is greater than 3B

MAYBE 5A is greater than 3B, but we have no way to know for sure. By comparison, MAYBE the answer is YES, MAYBE it's NO.
Inconsistent = INSUFFICIENT.

Fact 2 - let's cross-multiply this too:

5A > 3B + 3

Here we know that 5A is greater than 3B + 3, which by definition is greater than 3B. Visually:
5A > 3B + 3 > 3B
So, the comparison proves it - we know that 5A is greater than 3B.
Fact 2 is SUFFICIENT.

Final answer: B

GMAT assassins aren't born, they're made,
Rich

[kevincanspain]

Let's cross-multiply to make this question easier: "Is 5A > 3B?"

Doing so can cause trouble if variables are negative!

[GMATGuruNY]

Is (a/b)>(3/5)?

1) (a+1/b)>(3/5)

2) (a/b+1)>(3/5)

Answer: B

Given a/b > 3/5, we can rephrase the question stem as 5a > 3b ONLY IF THE PROBLEM IS RESTRICTED TO POSITIVE VALUES.
Here, it's possible that b<0, in which case statement 2 is NOT sufficient.

Statement 2: a/(b+1) > 3/5
Case 1: a=4 and b=3
The constraint that a/(b+1) > 3/5 is satisfied:
a/(b+1) = 4/(3+1) = 4/4 = 1.
In this case, a/b = 4/3, so a/b > 3/5.

Case 2: a=0.5 and b=-0.5
The constraint that a/(b+1) > 3/5 is satisfied:
a/(b+1) = 0.5/(-0.5+1) = 0.5/0.5 = 1.
In this case, a/b = 0.5/-0.5 = -1, so a/b < 3/5.
INSUFFICIENT.

Note the following:
In Case 2, a/b < 3/5, but 5a > 3b.
This illustrates why -- if the signs of a and b are unknown -- it's best not to rephrase a/b > 3/5 as 5a > 3b.

If the problem has been posted correctly, the OA should not be B.
What is the source?

[topspin20]

Thank you all for the responses. Mitch, B would be the correct answer if we specify that a and b are positive, correct?

I made the question up to help me to review this concept. I certainly appreciate the correction-which allowed me to learn even more.

[[email protected]]

Hey All,

Both Kevin and Mitch are right on; I goofed that one. Both A and B COULD be negative (or even fractions/decimals). There's a lesson in there about not answering questions too late at night and not after having a couple of drinks. But the point is important and worth noting: when you have no information about a variable in a DS question, then that variable could be ANYTHING.

-Rich