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Q.)The question is followed by two statements. As the answer

Mark(a) If the question can be answered with the help of any one statement independently

Mark(b) If the question can be answered with the help of any one statement independently

Mark(c) If the question can be answered with the help of both statements independently

Mark(d) If the question can not be answered with the help of both statements together

What is the value of ${ a }^{ 3 }+{ b }^{ 3 }$ ? [CAT 1997 Question,CAT Question,Number System]

I. ${ a }^{ 2 }+{ b }^{ 2 }$ = 22

II . ab = 3

Solution : From statement I : ${ a }^{ 2 }+{ b }^{ 2 }$ = 22

Nothing can be said about ${ a }^{ 3 }+{ b }^{ 3 }$.

So, Statement I alone is not sufficient to answer.

From Statement II: ab = 3

Nothing can be said about the values of a and b . It can be both positive or both negative.

So, Statement II alone is not sufficient to answer.

Using both statements together :

${ a }^{ 2 }+{ b }^{ 2 }$ = 22

and ab = 3

${(a+b)}^{2}$ = ${ a }^{ 2 }+{ b }^{ 2 }$ + 2ab = 22+2*3 = 28

Hence , a+b = $\pm \sqrt { 28 } $

As , the value of (a+b) is not unique , hence nothing can be said about the value of ${ a }^{ 3 }+{ b }^{ 3 }$ .

Hence, even by using both statements , It cannot be answered.

Hence, OPTION(d)