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27 Jul 2023, 08:00
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If n is a positive integer, what is the value of (x - 3)^n + (3 - x)^n ?
(1) n divided by 6 gives the remainder of 1.
(2) 21 divided by n gives the same remainder as 20 divided by n.
(1) n divided by 6 gives the remainder of 1.
(2) 21 divided by n gives the same remainder as 20 divided by n.
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27 Jul 2023, 08:17
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Bunuel
If n is a positive integer, what is the value of (x - 3)^n + (3 - x)^n ?
(1) n divided by 6 gives the remainder of 1.
(2) 21 divided by n gives the same remainder as 20 divided by n.
(1) n divided by 6 gives the remainder of 1.
(2) 21 divided by n gives the same remainder as 20 divided by n.
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(1) n divided by 6 gives the remainder of 1.
Therefore n is in the form 6k+1, which is an odd number.
So value of (x - 3)^n + (3 - x)^n is 0.
Hence sufficient
(2) 21 divided by n gives the same remainder as 20 divided by n.
This means n must be a factor of 1, because the difference between 21 and 20 is 1. Therefore, n can only be 1.
if n is 1, it is odd and the value of (x - 3)^n + (3 - x)^n is 0.
Hence sufficient
Hence D
27 Jul 2023, 08:36
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answer is D.
STATEMENT 1 : n divided by 6 gives the remainder of 1.
so n is odd. (3-x)^n = ((-1)*(x-3))^n = (-1)^n * (x-3)^n = -((x-3)^n) ------ since n is odd
therefore the required value is 0. this statment is sufficient
STATEMENT 2 : 21 divided by n gives the same remainder as 20 divided by n.
21 and 20 are co prime. and n is positive. thus n is 1. placing 1 in the equation, we can determine the value to be 0. this statment is sufficient
EACH ALONE IS SUFFICIENT. SO ANSWER IS D
STATEMENT 1 : n divided by 6 gives the remainder of 1.
so n is odd. (3-x)^n = ((-1)*(x-3))^n = (-1)^n * (x-3)^n = -((x-3)^n) ------ since n is odd
therefore the required value is 0. this statment is sufficient
STATEMENT 2 : 21 divided by n gives the same remainder as 20 divided by n.
21 and 20 are co prime. and n is positive. thus n is 1. placing 1 in the equation, we can determine the value to be 0. this statment is sufficient
EACH ALONE IS SUFFICIENT. SO ANSWER IS D
