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22 Apr 2016, 06:38
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If n is a positive integer, what is the remainder when n^2 is divided by 4?
(1) When n is divided by 4, the remainder is 1.
(2) n is odd.
(1) When n is divided by 4, the remainder is 1.
(2) n is odd.
raarun
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22 Apr 2016, 07:53
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Stmnt 1> so n can be 1 ,4 ,9, 13 ,17 ,21 etc so n^2/4 will always leave a remainder of 1
Sufficient
Stmnt 2 > n= 1,3,5,7,9 etc so n^2/4 will always leave a remainder of 1
Sufficient
Ans D
Sufficient
Stmnt 2 > n= 1,3,5,7,9 etc so n^2/4 will always leave a remainder of 1
Sufficient
Ans D
22 Apr 2016, 17:46
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Statement 1: When n is divided by 4, the remainder is 1.
so the Number is (4x + 1)
On squaring this number and checking divisibility with 4 , we get
R[(4x + 1)^2 / 4] = R[(16x^2 + 8x +1) /4] = 1
The remainder of the above equation is 1 regardless of value of x
Sufficient
Statement 2: n is odd.
Here the number can be (4x + 1) or (4x - 1)
As we saw above, the remainder will be 1 in the end
Sufficient
Correct option: D
so the Number is (4x + 1)
On squaring this number and checking divisibility with 4 , we get
R[(4x + 1)^2 / 4] = R[(16x^2 + 8x +1) /4] = 1
The remainder of the above equation is 1 regardless of value of x
Sufficient
Statement 2: n is odd.
Here the number can be (4x + 1) or (4x - 1)
As we saw above, the remainder will be 1 in the end
Sufficient
Correct option: D
