Question : Find the smallest natural number $x$ that must be subtracted from 1800 so that $(1800 - x)$, when divided by 7, 11 and 23, will leave 5 as the remainder in each case.
Option 1: 24
Option 2: 25
Option 3: 26
Option 4: 20
Answer (1)
11th Jan, 2024
Correct Answer: 24
Solution :
LCM of 7, 11 and 23 = 1771
Now, the number which leaves a remainder of 5 in each case when divided by 7, 11 and 23 is
(1171 + 5) = 1176
So, the required value of $x$ is (1800 – 1176) = 24
Hence, the correct answer is 24.
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