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

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

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New post 21 Jan 2020, 04:36
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A
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Difficulty:

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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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New post 21 Jan 2020, 05:31
DiyaDutta 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



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

ANswer: Option C
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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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