Largest four-digit multiple of 88 — Aptitude Question
Largest four-digit multiple of 88: What is the largest four-digit number exactly divisible by 88? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
What is the largest four-digit number exactly divisible by 88?
Options
- 9944
- 9954
- 9968
- 9988
Show the answer and the worked solution
Correct answer: A. 9944
Worked solution
- 9999 ÷ 88 = 113 remainder 55.
- So the largest multiple is 9999 − 55 = 9944.
- Check: 88 × 113 = 9944. ✓
Answer: 9944.
The idea
For the largest n-digit multiple, divide the largest n-digit number by the divisor and subtract the remainder. For the smallest, divide the smallest n-digit number and add whatever is needed to reach the next multiple.
Shortcut. Test the options from the top with 88 = 8 × 11: 9988 fails 8 (988 ÷ 8 is not whole), 9968 fails 11 (9 − 9 + 6 − 8 = −2) and 9954 fails 8, while 9944 passes both (944 = 8 × 118, alternating sum 0).
Common trap. 9988 — it passes the test for 11 and its last two digits are divisible by 4, so checking 4 in place of 8 accepts it; 988 ÷ 8 = 123.5, so it is a multiple of 44 but not of 88.