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

To solve the problem, first identify the requirements: A single digit number multiplies with 1,234, and the product's unit digit and thousand's digit must be the same.

Let's denote this single-digit number as \(x\). When 1,234 is multiplied by \(x\), the product can be represented as:

\(P = 1234 \times x\)

We need the unit digit and the thousand's digit in the product \(P\) to be identical. 

Step 1: Explore possible values of \(x\).

Consider the digits 1 to 9 for \(x\) since it represents a single-digit number.

Step 2: Calculate and check the product for each possible digit:

• If \(x = 1\), \(P = 1234 \times 1 = 1234\). The unit digit is 4, and the thousand digit is 1 (not the same).
• If \(x = 2\), \(P = 1234 \times 2 = 2468\). The unit digit is 8, and the thousand digit is 2 (not the same).
• If \(x = 3\), \(P = 1234 \times 3 = 3702\). The unit digit is 2, and the thousand digit is 3 (not the same).
• If \(x = 4\), \(P = 1234 \times 4 = 4936\). The unit digit is 6, and the thousand digit is 4 (not the same).
• If \(x = 5\), \(P = 1234 \times 5 = 6170\). The unit digit is 0, and the thousand digit is 6 (not the same).
• If \(x = 6\), \(P = 1234 \times 6 = 7404\). The unit digit is 4, and the thousand digit is 7 (not the same).
• If \(x = 7\), \(P = 1234 \times 7 = 8638\). The unit digit is 8, and the thousand digit is 8 (they are the same).

Step 3: Check the number formed by the other two digits in the product `8638`.

Ignoring the identical thousand and unit digits (8), the other two digits in the given sequence are 63.

Thus, the number formed by these digits in order is 63, matching with one of the provided options.

Therefore, the correct answer is:

63