Q3 REPRESENTATIONS

(BE)²= MPB, where B, E, M and P are distinct integers. Then M =

a. 2

b. 3

c. 9

d. None of these

A digit number when squared produces a 3 digit number. This means that the number ranges from [10, 31].

First digit of BE² should be unit digit of E^2.

But unit digit of E is B.

Look at the numbers and the unit digit of their square.

0-0, 1-1, 2-4, 3-9, 4-6, 5-5, 6-6, 7-9, 8-4, 9-1.

Only 2-4, 3-9, 4-6, 7-9, 8-4 and 9-1 are kind of pairs we are looking after.

But all the pairs except 9-1 produce a number greater than 31.

Now, the number we can form from 9-1 is 19 whose square is 361 which satisfies all the condition we are looking for.

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