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If a nine-digit number 985x3678y is divisible by 72, then the value of (4x – 3y) is : यदि नौ अंको की संख्या 985x3678y, संख्या 72 से विभाज्य है, तो (4x – 3y) का मान होगा:

SSC CGL Tier-1 (2018)

(a) 5

(b) 4

(c) 3

(d) 6

Answer – (b) 4

Solution for 985x3678y Divisibility by 72

Step 1: Divisibility by 8

To check if the number is divisible by 8, the last three digits must be divisible by 8.

The last three digits are 78y.

We need to find a digit y such that 78y is divisible by 8:

  • y = 0: 780 ÷ 8 = 97.5 (not divisible)
  • y = 1: 781 ÷ 8 = 97.625 (not divisible)
  • y = 2: 782 ÷ 8 = 97.75 (not divisible)
  • y = 3: 783 ÷ 8 = 97.875 (not divisible)
  • y = 4: 784 ÷ 8 = 98 (divisible)

Therefore, y = 4 satisfies the divisibility rule for 8.

Step 2: Divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9.

Let’s calculate the sum of the digits for 985×36784 (considering y = 4):

Sum of the digits: 9 + 8 + 5 + x + 3 + 6 + 7 + 8 + 4 = 50 + x

We need 50 + x to be divisible by 9. Let’s test different values of x:

  • x = 0: 50 + 0 = 50 (not divisible)
  • x = 1: 50 + 1 = 51 (not divisible)
  • x = 2: 50 + 2 = 52 (not divisible)
  • x = 3: 50 + 3 = 53 (not divisible)
  • x = 4: 50 + 4 = 54 (divisible)

Therefore, x = 4 satisfies the divisibility rule for 9.

Step 3: Calculate 4x – 3y

Given x = 4 and y = 4:

4x – 3y = 4(4) – 3(4) = 16 – 12 = 4

Final Answer

The value of 4x – 3y is 4.

sudhirracer Changed status to publish June 5, 2024
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