Question

Consider the following question and decide which statement is sufficient to answer the question.

Question:

Find the value of X.

Statement:

I. The sum of squares of two consecutive positive even numbers is 52.

II. The difference of numbers is 2.

1. Only statement I is sufficient, while statement II alone is not sufficient.
2. Only statement II is sufficient, whereas statement I alone is not sufficient.
3. Neither statement I nor II is sufficient.
4. Statements I and II are both sufficient.

Answer 1

Correct Answer - Option 1 : Only statement I is sufficient, while statement II alone is not sufficient.

Calculation:

From statement I,

Let the numbers be x and (x + 2)

According to question,

x² + (x + 2)² = 52

⇒ x² + x² + 4 + 4x = 52

⇒ 2x² + 4x – 48 = 0

⇒ x² + 2x – 24 = 0

⇒ x² + 6x – 4x – 24 = 0

⇒ x(x + 6) – 4(x + 6) = 0

⇒ (x + 6) (x –  4) = 0

⇒ x = 4 or -6

We can get the numbers by statement I

From statement II,

We can't get the number by statement II

∴ Only statement I is sufficient, while statement II alone is not sufficient.