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24 Jun 2016, 03:21
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M is a positive integer, is M odd?
(1) 2M^3 + 2M is divisible by 8.
(2) M + 10 is divisible by 10.
(1) 2M^3 + 2M is divisible by 8.
(2) M + 10 is divisible by 10.
Statement 1: 2M^3 + 2M mod 8 = 0 -----> 2M(M^2+1) mod 8 =0 -----> M(M^2+1) mod 4 = 0
We know that square of even is even and square of odd is odd. So, if M is even, (M^2+1) will be odd and if M is off (M^2+1) will be even.
For M(M^2+1) mod 4 = 0 to be true we want one of M or (M^2+1) to be divisible by 4.
For even M, such as M=4, we can have M(M^2+1) mod 4 = 0
For any odd M... (M^2+1) mod 2 will be = 0 but (M^2+1) mod 4 will never be = 0
For ex. M=3 ---> M^2+1=10, M=5 ---> M^2+1=26, M=7 ---> M^2+1=50, M=9 ----> M^2+1=82
Hence, we can conclude that M has to be even in order to have M(M^2+1) mod 4 = 0
Statement 1 Sufficient.
Statement 2: M+10 mod 10 = 0
So, M has to be a multiple of 10 for above to be true and all multiple of 10 are even.
Statement 2 satisfies.
Answer D.
-------------------------------------
P.S. Don't forget to give Kudos.
We know that square of even is even and square of odd is odd. So, if M is even, (M^2+1) will be odd and if M is off (M^2+1) will be even.
For M(M^2+1) mod 4 = 0 to be true we want one of M or (M^2+1) to be divisible by 4.
For even M, such as M=4, we can have M(M^2+1) mod 4 = 0
For any odd M... (M^2+1) mod 2 will be = 0 but (M^2+1) mod 4 will never be = 0
For ex. M=3 ---> M^2+1=10, M=5 ---> M^2+1=26, M=7 ---> M^2+1=50, M=9 ----> M^2+1=82
Hence, we can conclude that M has to be even in order to have M(M^2+1) mod 4 = 0
Statement 1 Sufficient.
Statement 2: M+10 mod 10 = 0
So, M has to be a multiple of 10 for above to be true and all multiple of 10 are even.
Statement 2 satisfies.
Answer D.
-------------------------------------
P.S. Don't forget to give Kudos.
Nightfury14
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24 Jun 2016, 11:20
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M is a positive integer, is M odd?
(1) 2M^3 + 2M is divisible by 8.
(2) M + 10 is divisible by 10.
(1) 2M^3 + 2M is divisible by 8.
(2) M + 10 is divisible by 10.
Statement 1)
Case 1 :: M=1 => 2x\(1^3\)+2x1 = 4 .. Not divisible by 8
Case 2 :: M=4 => 2x\(4^3\)+2x4 = 136 .. Divisible by 8 .. Not sufficient
Statement 2) M is multiple of 10 .. M is even .. Sufficient
Anser Choice B)
Good luck
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