What least number must be subtracted from 5000 so that the result, when divided by 12, 18 and 20, leaves a remainder of 7 in each case?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 133
The result must be (a multiple of the LCM) \(+\,7\), as large as possible but not more than 5000.
LCM \(=180\)
\(5000-7=4993\), and \(4993\div180\) gives quotient 27
Largest such number \(=180\times27+7=4867\)
Number to subtract \(=5000-4867=133\)
The least number to subtract is 133.
Why the other options are incorrect
Option (1) 140 — Incorrect. 5000 − 140 \(=\) 4860, which leaves remainder 0 when divided by 12.
Option (2) 313 — Incorrect. 4687 works, but a smaller number is enough to subtract.
Option (4) 126 — Incorrect. 5000 − 126 \(=\) 4874, which leaves remainder 2 when divided by 12.