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21 Jul 2020, 03:43
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Difficulty:
5%
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Question Stats:
85% (01:20) correct
15%
(01:48)
wrong
based on 140
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What is the least positive three-digit integer that is divisible by both 3 and 14 and leaves a remainder of 1 when divided by 5?
A. 112
B. 126
C. 141
D. 156
E. 336
A. 112
B. 126
C. 141
D. 156
E. 336
21 Jul 2020, 03:50
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Bunuel
What is the least positive three-digit integer that is divisible by both 3 and 14 and leaves a remainder of 1 when divided by 5?
A. 112
B. 126
C. 141
D. 156
E. 336
A. 112
B. 126
C. 141
D. 156
E. 336
i.e Number, n = Multiple of LCM(3 & 14) = Multiple of 42
Three-digit Multiples of 42 = {126} which leaves remainder 1 when divided by 5
So all conditions satisfied hence
Answer: Option B
P.S. I would have done this problem using options in test-like situation
Rini10
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21 Jul 2020, 03:55
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Bunuel
What is the least positive three-digit integer that is divisible by both 3 and 14 and leaves a remainder of 1 when divided by 5?
A. 112
B. 126
C. 141
D. 156
E. 336
A. 112
B. 126
C. 141
D. 156
E. 336
Since 3 and 14 have no common factors, the number that is divisible by both must also be divisible by 3*14 i.e. 42.
Now, the least 3 digit number that is divisible by 42 is 42*3 i.e. 126.
126 also satisfies the other condition (leaves reminder of 1 when divided by 5) given in the question prompt.
Hence, ans is 126.
