M
jainrahul1985 wrote:If t is a positive integer and r is the remainder when t2 + 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 t2 is divided by 7, the remainder is 1
OA A
When positive integer x is divided by the divisor D, the remainder is R.
Given the information above:
-- Make a list of possible values for x.
-- The smallest possible value of x = the remainder R.
-- To determine the other possible values of x, just keep adding multiples of the divisor D.
The question at hand rephrased: What is the remainder when (t+2)(t+3) is divided by 7?
Statement 1: When t is divided by 7, the remainder is 6.
Smallest value = R = 6.
Now add multiples of the divisor 7:
t = 6, 13, 20, 27...
If t=6, then (t+2)(t+3) = 8*9 = 72.
72/7 = 10 R2.
If t=13, then (t+2)(t+3) = 15*16 = 240.
240/7 = 34 R2.
Just to be safe:
If t=27, then (t+2)(t+3) = 29*30 = 870.
870/7 = 124 R2.
Since in each case R=2, sufficient.
Statement 2: When t² is divided by 7, the remainder is 1.
Smallest value = R = 1.
Now add multiples of the divisor 7:
t² = 1, 8, 15, 22, 29, 36...
The list above includes two perfect squares: 1 and 36.
Thus, integer values for t = 1, 6...
If t=1, then (t+2)(t+3) = 3*4 = 12.
12/7 = 1 R5.
If t=6, then (t+2)(t+3) = 8*9 = 72.
72/7 = 10 R2.
Since R can be different values, insufficient.
The correct answer is
A.
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