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

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Hoozan
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If a, b, c, and d are positive integers is (a - b)/(c - d) < -1 ? [#permalink] New post   26 Nov 2021, 03:43
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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
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Re: If a, b, c, and d are positive integers is (a - b)/(c - d) < -1 ? [#permalink] New post   26 Nov 2021, 22:21
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Hoozan wrote:
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
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.
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If a, b, c, and d are positive integers is (a - b)/(c - d) < -1 ? [#permalink] New post   02 Dec 2021, 08:13
GMATCoachBen wrote:
Hoozan wrote:
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
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.



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?

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Re: If a, b, c, and d are positive integers is (a - b)/(c - d) < -1 ? [#permalink] New post   02 Dec 2021, 10:06
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Hoozan wrote:
But what if

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

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.
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Re: If a, b, c, and d are positive integers is (a - b)/(c - d) < -1 ? [#permalink] New post   02 Dec 2021, 10:36
EducationAisle wrote:
Hoozan wrote:
But what if

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

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.


Oops! Thanks for spotting that one for me
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Re: If a, b, c, and d are positive integers is (a - b)/(c - d) < -1 ? [#permalink] New post   30 May 2023, 10:06
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Re: If a, b, c, and d are positive integers is (a - b)/(c - d) < -1 ? [#permalink]
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