### 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