Question

34. Lora is thinking of a number. It is less than 50 It is a 2-digit number. 3 is a factor of this number. The sum of its digits is one third of the number What number is Lora thinking of? 8 A. 33 B. 27 C. 12 D. 36​

Answer 1

B

Explanation:

The number is between 10 and 49

The number is divisible by 3

Let the 10s digit = x

Let the units digit = y

1/3 * (10x + y) = x + y multiply both sides by 3

10x + y = 3(x +y) remove the brackets.

10x +y = 3x + 3y Subtract 3x from both sides

10x - 3x + y = 3y Combine\

7x + y = 3y Subtract y from both sides.

7x = 3y - y Combine

7x = 2y

x can't be very big. Even taking 1/3 will get out of range is you use 6.

Also x should be an even number. The units digit cannot have a fraction in it.

Try making x = 2

7*2 = 2*y

14 = 2y Divide by 2

14/2 = y

y = 7

So the number is possibly 27. Let's check it out.

• The number is between and includes 10 and 49. 27 is between these two endpoints.
• 27 is divisible by 3
• 1/3(27) = sum of digits
• 9 = (2 + 7)

All of the conditions are met. It's B