Question

A two digit non zero number x is equal to the sum of a number y and its square. If sum of the digits of x is equal to y and tens digit of x is half of its unit digit, then product of x and y will be

Answer 1

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A two digit number has 3 in its unit digit. The sum of its digits is one seventh of the number itself. What is the number?

Every two-digit number can be decomposed by multiplying the digit from the left by 10 and adding the result to the digit from the right.

For instance:

46 = 4 • 10 + 6 = 40 + 6

97 = 9 • 10 + 7 = 90 + 7

So it is correct to say that every two-digit number has this structure:

10x + y, being “x” the digit from the left; and being “y” the digit from the right.

So a two digit number that has 3 as its unit digit can be represented as: 10x + 3.

And its digits’ sum can be represented as: x + 3

Therefore our final equation is:

x + 3 = 1/7 • (10x + 3)

Solving it, we get:

x + 3 = (10x + 3)/7

7(x +3) = 10x + 3

7x + 21 = 10x + 3

7x - 10x = 3 - 21

-3x = - 18

(-1)•(-3x) = (-1)•(-18)

3x = 18

x = 18/3

x = 6

Knowing that 6 is the digit from the left and that 3 is the digit from the right, we can easily conclude that the number is 63.