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27 Aug 2019, 10:25
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
57% (01:50) correct
43%
(02:06)
wrong
based on 201
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A number when successively divided by 3 and 5, leaves remainders of 2 and 1 respectively. What is the remainder when the same number is divided by 15?
(A) 1
(B) 2
(C) 5
(D) 7
(E) 9
(A) 1
(B) 2
(C) 5
(D) 7
(E) 9
27 Aug 2019, 10:54
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Generally, we calculate remainders of each number (n) when divided by 3 and 5 respectively and then calculate the remainder by taking a common n that we would divide by 15. However, in this question, a number when successively divided by 3 and 5, leaves remainders of 2 and 1 respectively.
Firstly, the number when divided by 3 gives remainder 2. Algebraically, n=3q+2, where q is quotient from the first division..........eq(1)
Now as the division is done successively , we divide the quotient from the first step by 5 to get the remainder of 1 => q=5k+1, where k is quotient from the second division..eq(2)
Substitute the value of eq(2) in eq(1)
n=3q+2
n=3(5k+1)+2
n=15k+5
Now if you notice, when n is divided by 15, we get a remainder of 5.
IMO Option (C)
Firstly, the number when divided by 3 gives remainder 2. Algebraically, n=3q+2, where q is quotient from the first division..........eq(1)
Now as the division is done successively , we divide the quotient from the first step by 5 to get the remainder of 1 => q=5k+1, where k is quotient from the second division..eq(2)
Substitute the value of eq(2) in eq(1)
n=3q+2
n=3(5k+1)+2
n=15k+5
Now if you notice, when n is divided by 15, we get a remainder of 5.
IMO Option (C)
General Discussion
