The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54. Consider the following statements: 1. The sum of the two digits of the number can be determined only if the product of the two digits is known. 2. The difference between the two digits of the number can be determined. Which of the above statements is/are correct?

QUESTION

CSAT

Easy

Maths

Prelims 2021

The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54.

Consider the following statements:

The sum of the two digits of the number can be determined only if the product of the two digits is known.
The difference between the two digits of the number can be determined.

Which of the above statements is/are correct?

Select an option to attempt

Explanation

Let the number be $xy$ , i.e. $10x + y$

The number obtained on interchanging the positions of the digits will be $yx$ , i.e. $10y + x$

Difference between these two numbers = $(10x + y) – (10y + x) = 9x – 9y = 9 (x - y) = 54$

So, $9 (x - y) = 54$

Or $x - y = 6$

So, statement 2 is correct.

The possible pair of such two-digit numbers are: $(17, 71)$ , $(28, 82)$ , $(39, 93)$

Respective product of their digits are: $1 \times 7 = 7$ ; $2 \times 8 = 16$ ; $3 \times 9 = 27$

So, we can determine the exact number-pair and hence the sum of their digits, if we know the product of their digits.

So, statement 1 is also correct.

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