Directions: Below question is followed by two statements labelled I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below: Given, a and b are integers. What is the value of a

Directions: Below question is followed by two statements labelled I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:

Given, a and b are integers. What is the value of a – b?

I. a² + b² = 40

II. a × b = 12

A Statement I alone is sufficient to answer the question.

B Statement II alone is sufficient to answer the question.

C Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.

D Either Statement I or Statement I alone is sufficient to answer the question.

E Neither Statement I nor Statement II is sufficient to answer the question.

Solution

Correct Answer: Option E

From statement I:

a² + b² = 40

No values of a or b or that of the question can be arrived at using this statement.

Hence, statement I is insufficient to answer this question.

From statement II:

a × b = 12

No values of a or b or that of the question can be arrived at using this statement.

Hence, statement II is insufficient to answer this question.

Combining both,

a² + b² = 40

a × b = 12

(a - b)² = a² + b² - 2ab

⇒ (a - b)² = 40 – 2 × 12 = 40 – 24 = 16

⇒ a – b = ± 4

Since it is not known if a > b or b > a, determining the value of a – b is not possible.

Hence, both the statements combined also cannot give us the answer.

Solution

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