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
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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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Question : Find the second smallest number which, when divided by 81 or 63, leaves a remainder of 7 in each case.
Option 1: 1246
Option 2: 1141
Option 3: 1362
Option 4: 1137
Question : What is the smallest three-digit number when divided by 2, 3, and 4 leaving the remainder 1 in each case?
Option 1: 111
Option 2: 105
Option 3: 101
Option 4: 109
Question : What is the smallest three-digit number which, when divided by 8 or 6, leaves a remainder of 1 in each case?
Option 1: 121
Option 2: 119
Option 3: 123
Option 4: 125
Question : If A : B = 5 : 4, B: C = 6 : 5, C: D = 7 : 10, then what is the value of A : D?
Option 1: 21 : 25
Option 2: 7 : 3
Option 3: 21 : 20
Option 4: 25 : 24
Question : What is the least number which when divided by 18, 24, and 36 leaves 3 as a remainder in each case?
Option 1: 75
Option 2: 93
Option 3: 111
Option 4: 99
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