A natural number N < 1000 when divided by 3, 5 and 6 successively leaves remainder 1, 3 and 2. Find the possible numbers of valves N can take.
A natural number N < 1000 when divided by 3, 5 and 6 successively leaves remainder 1, 3 and 2. Find the possible numbers of valves N can take.
Option 1 -
23
Option 2 -
19
Option 3 -
35
Option 4 -
11
Asked by Shiksha User
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1 Answer
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Correct Option - 4
Detailed Solution:Let the quotient obtained when the numbers is divided by 3, 5 and 6 be x1, x2 and x3
Respectively
N = 3 x1 + 1
x1 = 5 x2 + 3
x2 = 6 x3 + 2
N = 3 [5 (6 x3 + 2) + 3] + 1
=90 x3 + 40 < 1000
x3 can take 11 values
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