Question

If a thirteen - digit number 507x13219256y is divisible by 72, then the maximum value of $\sqrt{5x+3y}$ will be.

• A. 6
• B. 8
• C. $$\sqrt{46}$$
• D. 7

Answer 1

Answer:

D. 7

Solution:

Given:

507x13219256y

Concept used:

Divisibility rule of 9 = Sum of all digits is divisible by 9

Divisibility rule of 8 = If the last three digits of a number are divisible by 8, then the number is completely divisible by 8

.

Calculation:

507x13219256y

56y

⇒ y = 0 or y = 8     -----(by divisibility rule of 8)

⇒ 560 or 568 is divisible by 8

So y = 0 or 8

507x13219256y

If, y = 0

⇒ 5 + 0 + 7 + x + 1 + 3 + 2 + 1 + 9 + 2 + 5 + 6 + 0

⇒ 41 + x

⇒ 41 + 4 = 45 is divisible by 9

So x = 4

or y = 8

⇒ 5 + 0 + 7 + x + 1 + 3 + 2 + 1 + 9 + 2 + 5 + 6 + 8

⇒ 49 + x 

⇒ 49 + 5 = 54 is divisible by 9

According to the question maximum value of x and y is 5 and 8

√{5x+3y}

⇒ √(5 × 5 + 3 × 8) 

⇒ √49

⇒ 7

⇒ 7

∴ Required answer is 7.