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

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Joined: 21 Nov 2018
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Location: India
GMAT 1: 680 Q48 V35
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If a, b, c, and d are positive integers (a − b)/(c − d) < −1 ?  [#permalink]

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21 Jan 2020, 04:36
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Difficulty:

65% (hard)

Question Stats:

54% (02:00) correct 46% (02:33) wrong based on 37 sessions

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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 (a − b)/(c − d) < −1 ?  [#permalink]

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21 Jan 2020, 05:31
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

Question: $$\frac{a − b}{c − d} <−1$$ ?

Statement 1: |a – b| > |c – d|

i.e. Absolute value of a-b is greater than absolute value of c-d

i.e. for the fraction $$\frac{a − b}{c − d}$$ the absolute value of numerator is greater than absolute value of denominator

BUT the value of $$\frac{a − b}{c − d}$$ may be Less than -1 or Greater than +1 hence

NOT SUFFICIENT

Statement 2: c > b > d > a

i,.e. we can deduce that $$\frac{a − b}{c − d}$$ will be negative cause a-b is negative and c-d is positive

Still we can't compare absolute values of a-b and c-d hence result may be between 0 and -1 or less than -1 hence

NOT SUFFICIENT

Combining the two statements

We can now deduce that $$\frac{a − b}{c − d}$$ MUST be Less than -1 as it's negative as explained in statement 2

SUFFICIENT

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Re: If a, b, c, and d are positive integers (a − b)/(c − d) < −1 ?   [#permalink] 21 Jan 2020, 05:31
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