If 37y4 is exactly divisible by 9, then the least value of y is

Options

A. 2
B. 3
C. 1
D. 4

Answer

To solve the problem of finding the least value of \( y \) such that the number \( 37y4 \) is exactly divisible by 9, we can follow these steps:

### Step 1: Understand the divisibility rule for 9
A number is divisible by 9 if the sum of its digits is divisible by 9.

### Step 2: Identify the digits of the number
The number given is \( 37y4 \). The digits are:
- 3
- 7
- \( y \)
- 4

### Step 3: Calculate the sum of the known digits
Now, we will add the known digits:
\[ 3 + 7 + 4 = 14 \]
So, the sum of the digits becomes:
\[ 14 + y \]

### Step 4: Set up the equation for divisibility by 9
For \( 37y4 \) to be divisible by 9, the sum \( 14 + y \) must be divisible by 9.

### Step 5: Find the smallest \( y \)
We will check the smallest values of \( y \) (which can be from 0 to 9) to find the least value that makes \( 14 + y \) divisible by 9.

- If \( y = 0 \): \( 14 + 0 = 14 \) (not divisible by 9)
- If \( y = 1 \): \( 14 + 1 = 15 \) (not divisible by 9)
- If \( y = 2 \): \( 14 + 2 = 16 \) (not divisible by 9)
- If \( y = 3 \): \( 14 + 3 = 17 \) (not divisible by 9)
- If \( y = 4 \): \( 14 + 4 = 18 \) (divisible by 9)

### Conclusion
The least value of \( y \) that makes \( 37y4 \) divisible by 9 is \( 4 \).

Thus, the answer is:
\[ \boxed{4} \]

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