What is the least number which, when divided by 5, 6, 7 and 8 gives the remainder 3 but is divisible by 9? [SSC (CGL) 2001, (CPO) 2009] |
A) 1463
B) 1573
C) 1683
D) 1793
Correct Answer: C
Solution :
LCM of \[5,\]\[6,\]\[7,\]\[8=35\times 24=840\] |
\[\therefore \]Required number \[840x+3,\]such that it is exactly divisible by 9. |
By Hit and Trial, |
For \[x=2,\] it is divisible by 9. |
\[\therefore \]Required number \[=840x+3\] |
\[=840\times 2+3=1683\] |
(these types of questions can be solved with the help of given options) |
So, out of all the given options, only 1683 is divisible by 9. |
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