Question

Find a number that leaves remainder 3 when divided by 7, and 2 when divided by 5.

• A. 22
• B. 38
• C. 17
• D. 24

Hint:

For remainder-based questions with options, the fastest approach is always to test each option against the given conditions.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We are looking for a number 'N' that satisfies two conditions simultaneously:
1. When N is divided by 7, the remainder is 3. This can be written as N = 7k + 3 for some integer k.
2. When N is divided by 5, the remainder is 2. This can be written as N = 5m + 2 for some integer m.
Step 2: Detailed Explanation:
The quickest method for multiple-choice questions is to check each option against the given conditions.

(A) 22:
Dividing 22 by 7 gives a quotient of 3 and a remainder of 1. (22 = 7 \(\times\) 3 + 1). This does not satisfy the first condition.

(B) 38:
Dividing 38 by 7 gives a quotient of 5 and a remainder of 3. (38 = 7 \(\times\) 5 + 3). This satisfies the first condition.
Dividing 38 by 5 gives a quotient of 7 and a remainder of 3. (38 = 5 \(\times\) 7 + 3). This does not satisfy the second condition.

(C) 17:
Dividing 17 by 7 gives a quotient of 2 and a remainder of 3. (17 = 7 \(\times\) 2 + 3). This satisfies the first condition.
Dividing 17 by 5 gives a quotient of 3 and a remainder of 2. (17 = 5 \(\times\) 3 + 2). This satisfies the second condition.
Since both conditions are met, this is the correct answer.

(D) 24:
Dividing 24 by 7 gives a quotient of 3 and a remainder of 3. (24 = 7 \(\times\) 3 + 3). This satisfies the first condition.
Dividing 24 by 5 gives a quotient of 4 and a remainder of 4. (24 = 5 \(\times\) 4 + 4). This does not satisfy the second condition.
Step 3: Final Answer:
The number 17 is the only option that satisfies both conditions.