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Is (a + b) < (c + d)? (1) c and d are negative integers such that

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Is (a + b) < (c + d)? (1) c and d are negative integers such that [#permalink]

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Is (a + b) < (c + d)?


(1) c and d are negative integers such that \((a + b)^3-(c + d)^3 = 0\).

(2) a and b are positive integers such that \((a + b)^2-(c + d)^2 = 0\).


source: Time4education
[Reveal] Spoiler: OA

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Originally posted by Nixondutta on 08 Apr 2018, 23:45.
Last edited by amanvermagmat on 09 Apr 2018, 04:40, edited 2 times in total.
Edited the question.
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Re: Is (a + b) < (c + d)? (1) c and d are negative integers such that [#permalink]

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Nixondutta wrote:
Is (a + b) < (c + d)?
source: Time4education

(1) c and d are negative integers such that \((a + b)^3\) - \((c + d)^3\) = 0.
(2) a and b are positive integers such that \((a + b)^2\) - \((c + d)^2\) = 0.



From 1: a+b=c+d

sufficient

From 2: a+b=c+d

sufficient

hence D
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Re: Is (a + b) < (c + d)? (1) c and d are negative integers such that [#permalink]

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New post 09 Apr 2018, 03:49
Statement (1) - (a+b)^3 = (c+d)^3
Thus, (a+b) = (c+d).

Sufficient.

Statement (2) - (a+b)^2 = (c+d)^2
+/- (a+b) = +/- (c+d)

Thus, one may be positive and other may be negative and vice versa, at the same time. Otherwise both may be positive and equal.
Thus, insufficient.

Hence option A.

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Re: Is (a + b) < (c + d)? (1) c and d are negative integers such that [#permalink]

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SonalSinha803 wrote:
Statement (1) - (a+b)^3 = (c+d)^3
Thus, (a+b) = (c+d).

Sufficient.

Statement (2) - (a+b)^2 = (c+d)^2
+/- (a+b) = +/- (c+d)

Thus, one may be positive and other may be negative and vice versa, at the same time. Otherwise both may be positive and equal.
Thus, insufficient.

Hence option A.

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From option b it is given that a+b>0. so,

either a+b>c+d or a+b=c+d

a+b<c+d is not possible. hence sufficient
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Re: Is (a + b) < (c + d)? (1) c and d are negative integers such that [#permalink]

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New post 09 Apr 2018, 05:39
Nixondutta wrote:
Is (a + b) < (c + d)?


(1) c and d are negative integers such that \((a + b)^3-(c + d)^3 = 0\).

(2) a and b are positive integers such that \((a + b)^2-(c + d)^2 = 0\).


source: Time4education


we don't know the individual values of a,b,c,d. we are to find out the greater one between a+b and c+d

statement 1: we are given that (a+b)^3 - (c+d)^3=0

(a+b)^3=(c+d)^3
remove the exponents as both are same. we get a+c = c+d. sufficient as c+d is not greater than a+b.

statement 2 is the same as statement 1.

thus both statement are individually sufficient. Answer will be D.
Re: Is (a + b) < (c + d)? (1) c and d are negative integers such that   [#permalink] 09 Apr 2018, 05:39
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