Question

THREE STUDENTS A,B AND C, WALKING ON THE STREET WITNESSED A CAR VIOLATING A TRAFFIC REGULATION.NO ONE REMEMBERED THE LICENCE NUMBER,BUT EACH GOT SOME PERTICULAR ASPECT OF IT.A REMEMBERED THAT THE FIRST TWO DIGITS ARE EQUAL, B NOTED THAT THE LAST TWO DIGITS ARE ALSO EQUAL,AND C SAID THAT IT IS A FOUR-DIGIT NUMBER AND IS A PERFECT SQUARE.WHAT IS THE LICENCE NUMBER OF THE CAR?

Answer 1

Given:

A REMEMBERED THAT THE FIRST TWO DIGITS ARE EQUAL,

B NOTED THAT THE LAST TWO DIGITS ARE ALSO EQUAL,AND

C SAID THAT IT IS A FOUR-DIGIT NUMBER AND IS A PERFECT SQUARE.

To find:

WHAT IS THE LICENCE NUMBER OF THE CAR?

Solution:

From given we can note that,

The first two and last two digits are same.

Licence number of the car is a 4 digit number.

Therefore, we have,

7744 = 88 × 88

7744 has first two and last two digits are same and is even a perfect square of 88.

⇒ 88² = 7744

Therefore, 7744 is the license number of the car.