swerve wrote:If t is a positive integer and r is the remainder when t^2 + 5t + 6 is divided by 7, what is the value of r?
(1) When t is divided by 7, the remainder is 6.
(2) When t^2 is divided by 7, the remainder is 1.
The OA is A.
Please, can anyone explain this DS question? I don't understand why A is the correct answer. I need help. Thanks.
Given: t is a positive integer and r is the remainder when t^2 + 5t + 6 is divided by 7
So, we have to find out the remainder of (t^2 + 5t + 6)/7 = the remainder of (t^2/7 + t/7 + 6/7)
Let's take each statement one by one.
(1) When t is divided by 7, the remainder is 6.
=> the remainder when t^2 is divided by 7 = the remainder when 6^2 is divided by 7 = the remainder when 36 is divided by 7 = 1
Thus, the remainder of t^2/7 + t/7 + 6/7 = the remainder of (1 +6 + 6)/7 = the remainder of (13)/7 = 6. Sufficient.
(2) When t^2 is divided by 7, the remainder is 1.
Case 1: Say t = 6, then the remainder when t^2 = 6^2 = 36 is divided by 7 is 1; and the remainder when t = 6 is divided by 7 is 6.
Thus, the remainder of t^2/7 + t/7 + 6/7 = the remainder of (1 +6 + 6)/7 = the remainder of (13)/7 = 6.
Case 2: Say t = 8, then the remainder when t^2 = 8^2 = 64 is divided by 7 is 1; and the remainder when t = 8 is divided by 7 is 1.
Thus, the remainder of t^2/7 + t/7 + 6/7 = the remainder of (1 +1 + 6)/7 = the remainder of (8)/7 = 1.
No unique answer. Insufficient.
The correct answer:
A
Hope this helps!
-Jay
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