Question

When a certain single digit number multiples with 1,234, the units digit and the thousand’s digit will be the same in the product. What is the number formed by the other two digits in the same order?

• A. 17
• B. 36
• C. 45
• D. 63
• E. 81

Answer 1

The Correct Option is D

The correct answer is option (D):

63

Let the single-digit number be x. We are given that when x is multiplied by 1234, the units digit and the thousands digit of the product are the same. We can write this as:
x * 1234 = Product.

Let's test each possible value of x from 1 to 9.
If x = 1: 1 * 1234 = 1234. Units digit is 4, thousands digit is 1. Not the same.
If x = 2: 2 * 1234 = 2468. Units digit is 8, thousands digit is 2. Not the same.
If x = 3: 3 * 1234 = 3702. Units digit is 2, thousands digit is 3. Not the same.
If x = 4: 4 * 1234 = 4936. Units digit is 6, thousands digit is 4. Not the same.
If x = 5: 5 * 1234 = 6170. Units digit is 0, thousands digit is 6. Not the same.
If x = 6: 6 * 1234 = 7404. Units digit is 4, thousands digit is 7. Not the same.
If x = 7: 7 * 1234 = 8638. Units digit is 8, thousands digit is 8. This is correct.

Therefore, x = 7. The product is 8638. The units digit is 8 and the thousands digit is 8, which are the same. The number formed by the other two digits in order is 63.

Thus, the answer is 63.