Is (a + b)

Question

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

kunalcvrce · Answer

From 1: a+b=c+d

sufficient

From 2: a+b=c+d

sufficient

hence D

SonalSinha803 · Answer

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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kunalcvrce · Answer

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

KSBGC · Answer

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.

puneetb · Answer

Why are we not using the formula   here? Am I missing something? Also it does not say anything like a, b needs to be integers.

Dushyant20 · Answer

Wrong OA.

In 2. a+b = +- (c+d).

Posted from my mobile device

ShukhratJon · Answer

Hi Dushyant20,

The OA is correct, both statements are sufficient.

The question is  (a + b) < (c + d)  ?
Or in other words  (a + b) - (c + d) < 0  ?

The answer is NO, if left side is  equal  to zero or  greater  than 0
The answer is YES, if left side is  less  than 0

Statement 2 :  a  and  b  are positive integers such that  (a+b)^2−(c+d)^2=0

So  (a+b)^2−(c+d)^2=0  and  (a+b) > 0  while  (c+d)  can be both  positive  and  negative

First let  (c+d)  be postive and , for example, equal to  5 . For the equality in Statement 2 to be true  (a+b)  should also be equal to  5 
Now answer the question whether  (a+b) - (c+d)<0  ? Or is  5 - 5  less than  0 ? The answer is NO because  0  is not less than  0 .

Second let  (c+d)  be negative and equal to  -5 . Now  (a+b)  is still positive according to Statement 2 and thus equal to  5 .
Again answer the question whether  (a+b) - (c+d)<0  ? Or is  5 - (-5)  less than  0 ? The answer is again NO because 10 is not less than 0.

Thus, Statement 2 is  Sufficient .

ShukhratJon · Answer

However, pay attention to an important fact that the question itself is  wrong  because Statement 1 and Statement 2 contradict each other.

Statement 1 :  c  and  d  are negative integers such that  (a+b)^3−(c+d)^3=0

If  c  and  d  are  negative  integers, then  (c+d)  is also  negative . In this case  (a+b)  also  has to be   negative  so that  (a+b)^3−(c+d)^3  be equal to  0 . For example,  -5 - (-5) = 0

But  Statement 2  says that  a  and  b  are positive integers. Hence  (a+b)  also is  positive . How can  (a+b)  be simultaneously  positive  and  negative ? That's how  Statement 1  and  Statement 2  contradict each other.

The question is  wrong .

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

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