Problem 9 · Reasoning with digit place values · 4 points
Made by AI and not reviewed by a real person.
I made an odd four-digit number using 1, 2, 3, and 4 once each. Swapping its thousands and tens digits makes it 1,980 larger; swapping its hundreds and ones digits makes it 198 smaller. What number did I make?
- 4321
- 1432
- 2143
- 1243
- 2341
Show a hint
- Think about what each digit is worth before and after a swap. The other two digits do not change.
- Swapping the thousands and tens places changes the number by 990 times the difference between those digits. For the hundreds and ones places, the multiplier is 99.
Show the answer and solution
Answer: E — 2341
The first swap shows that the tens digit is 1,980 ÷ 990 = 2 greater than the thousands digit. The second shows that the hundreds digit is 198 ÷ 99 = 2 greater than the ones digit. Using 1, 2, 3, and 4 once each gives two possibilities: 1432 and 2341. Although 1432 satisfies both swaps, it is even. The odd number is 2341.