ChandlerBong wrote:
When a positive integer N is divided by 11, the remainder is 5. What is the remainder when N is divided by 10?
(A) If N is divided by 6, the remainder is 5.
(B) If N is divided by 5, the remainder is 0.
Given:
N = 11q + 5
q ⇒ quotient, when N is divided by 11.
Question:
Remainder(\(\frac{\text{N}}{10}\)) = ?
Statement 1(A) If N is divided by 6, the remainder is 5.Basis the information provided in this statement N can also be represented as
\(N = 6q_2 + 5\)
\(q_2\) ⇒ quotient, when N is divided by 6.
Using the information of the premise and statement 1, N can be expressed as
\(N = 66y + 5\)
Case 1: y = 0
N = 5
Remainder(\(\frac{\text{5}}{10}\)) = 5
Case 2: y = 2
N = 137
Remainder(\(\frac{\text{137}}{10}\)) = 7
As we are getting two conflicting results, the statement alone is not sufficient. We can eliminate A and D.
Statement 2(B) If N is divided by 5, the remainder is 0.Therefore N can have its unit digit as either 0 or 5.
If the unit digit of N = 0, Remainder(\(\frac{\text{N}}{10}\)) = 0
If the unit digit of N = 5, Remainder(\(\frac{\text{N}}{10}\)) = 5
As we are getting two conflicting results, the statement alone is not sufficient. We can eliminate B.
Combined\(N = 66y + 5\)
As N is divisible by 5, '66y' must be divisible by 5. Hence, 'y' should be divisible by 5.
If y = even multiple of 5, the unit digit of N will be 5
If y = odd multiple of 5, the unit digit of N will be 5
Hence, Remainder(\(\frac{\text{N}}{10}\)) = 5
The statements combined are sufficient.
Option C