Multiple choice

Find the largest 5-digit number which when divided by 4, 9, and 11 leaves the same but largest remainder for all the three numbers?

  1. 99785

  2. 99945

  3. 99965

  4. 99795
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

LCM(4, 9, 11) = 396. To leave the same largest remainder, we look for numbers near 99999. 99999 / 396 leaves a remainder of 171. The number is 99999 - (171 - r). For the largest remainder, r should be 395. Number = 99999 - 171 + 395 = 100223 (not 5-digit). Adjusting, 99999 - 396*k. The logic leads to 99795.

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