Question

Choose or find odd number pair$\left( {11 - 15} \right)$,$\left( {10 - 90} \right)$,$\left( {9 - 72} \right)$, $\left( {8 - 56} \right)$
A) $\left( {11 - 15} \right)$
B) $\left( {10 - 90} \right)$
C) $\left( {9 - 72} \right)$
D) $\left( {8 - 56} \right)$

Answer 1

Hint: Here, we are given some pairs of numbers. We are asked to find the odd number pair among the other number pairs. We may think that it is difficult to find the odd pair. We need to analyze the given number pairs. Some relations occur in each pair except the one. For example, the number pair may contain the relation that the first number is nine times the second number. Similarly, we need to find a relationship. Also, all the number pairs except the one contain the same relation only.

Complete step by step answer:
 Our given number pairs are$\left( {11 - 15} \right)$,$\left( {10 - 90} \right)$, $\left( {9 - 72} \right)$, $\left( {8 - 56} \right)$.
We are asked to find the odd number pair among the other number pairs. We need to analyze the given number pairs to find the relation.
    Let us analyze the second number pair $\left( {10 - 90} \right)$.
When we add the first and the second numbers, we get$10 + 90 = 100$ . Here $100$ is a perfect square of $10$ .
    Now, let us analyze the third number pair $\left( {9 - 72} \right)$.
When we add the first and the second numbers, we get$9 + 72 = 81$ . Here $81$ is a perfect square of $9$ .
     Now, let us analyze the fourth number pair $\left( {8 - 56} \right)$.
When we add the first and the second numbers, we get$8 + 56 = 64$ . Here $64$ is a perfect square of $8$ .
     Now, let us analyze the first number pair$\left( {11 - 15} \right)$.
When we add the first and the second numbers, we get $11 + 15 = 26$ . But, we know that $26$ is not a perfect square number.

Here we found that the first number pair is odd because others contain the same relation that the sum of the number results in a perfect square.

So, the correct answer is “Option A”.

Note: We note that in the second, third, and fourth pairs, the sum of the numbers is a perfect square. Since the first pair does not satisfy the relation, it is considered as the odd number pair. Hence, $\left( {11 - 15} \right)$is the odd number pair.