A number when divided by 296 leaves 75 as remainder. If the same number is divided by 37, thé remainder obtained is

Options

A. 2
B. 1
C. 11
D. 8

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the number
Let the number be \( x \).

### Step 2: Set up the equation based on the given information
According to the problem, when \( x \) is divided by 296, it leaves a remainder of 75. This can be expressed mathematically as:
\[ x = 296Q + 75 \]
where \( Q \) is the quotient when \( x \) is divided by 296.

### Step 3: Rewrite the equation in terms of 37
Next, we want to express \( x \) in a way that allows us to find the remainder when \( x \) is divided by 37. To do this, we can break down 296 and 75 in terms of 37:
\[ 296 = 37 \times 8 \]
\[ 75 = 37 \times 2 + 1 \]
This means we can rewrite \( x \) as:
\[ x = 37 \times 8Q + (37 \times 2 + 1) \]

### Step 4: Combine the terms
Now, we can combine the terms:
\[ x = 37 \times 8Q + 37 \times 2 + 1 \]
\[ x = 37(8Q + 2) + 1 \]

### Step 5: Identify the remainder
From the expression \( x = 37(8Q + 2) + 1 \), we can see that when \( x \) is divided by 37, the remainder is 1.

### Final Answer
Thus, when the number \( x \) is divided by 37, the remainder obtained is:
\[ \text{Remainder} = 1 \]

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