The number 1621 was subtracted from 6244 in base x. If the result was 4323, find x.

Let me work through it carefully.

Analyze the question: 6244 − 1621 = 4323, all in base x. Equivalently, 1621 + 4323 = 6244 in base x.

Column-by-column check (units first):

Units: 1 + 3 = 4. No carry, which works in any base above 4.

Tens: 2 + 2 = 4. No carry.

Hundreds: 6 + 3 = 9. The digit in the answer is 2, so 9 = x + 2, which gives x = 7, with a carry of 1.

Thousands: 1 + 4 + carry 1 = 6. This matches the 6 in 6244.

So x = 7.

Verification with base-10 conversion (base 7):

• 6244₇ = 6(343) + 2(49) + 4(7) + 4 = 2058 + 98 + 28 + 4 = 2188
• 1621₇ = 343 + 6(49) + 2(7) + 1 = 343 + 294 + 14 + 1 = 652
• 4323₇ = 4(343) + 3(49) + 2(7) + 3 = 1372 + 147 + 14 + 3 = 1536

2188 − 652 = 1536 ✓

Also, the digit 6 appears, so the base must be greater than 6, and 7 fits.

Answer: A. Seven

Tip: In base questions like this, convert subtraction to addition (check the result + subtrahend = minuend). Then look for the column where a carry happens: the sum minus the digit written equals the base.