If a, b, c, and d are positive integers is (a - b)/(c - d)

Question

If a, b, c, and d are positive integers is  \frac{(a-b)}{(c-d)} < -1 ?

(1) |a - b| > |c - d|
(2) c > b > d > a

GMATCoachBen · Answer

This is a good question to learn from.

First, what's our "Rephrase"?  What is necessary to get a "Yes" answer?

Both of these 2 conditions:
A) The absolute value of the numerator must be greater than the absolute value of the denominator.
B) To get a negative number, the numerator and denominator must have opposite signs.

An example that would give a "Yes" answer is  \frac{-2}{1}

Statement (1):  This fulfills condition A, but we don't know about condition B. Insufficient alone.

Statement (2):  If c > d and b > a, then the denominator is positive and the numerator is negative. This fulfills condition B, but we don't know about condition A. Insufficient alone.

Together:  Both conditions for a "Yes" answer are met.   Sufficient together: answer is C.

Hoozan · Answer

But what if

c = 4
b = 3
d = 2 
a = 1

In that case our Numerator will be a -2 and our Denominator a +2. This means, our fractional value will be -1 and not < -1

What am I missing?

Posted from my mobile device

EducationAisle · Answer

Hi Hoozan, this combination is not possible because (1) says that |a - b| > |c - d|.

For the values you have mentioned, |a - b| = |c - d|. So, your assumed values violate statement (1) of the question.

Hoozan · Answer

Oops! Thanks for spotting that one for me

bumpbot · Answer

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If a, b, c, and d are positive integers is (a - b)/(c - d) < -1 ?

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