topper97 wrote:
N is the sum of two positive integers p and q. Is N divisible by 8?
1) Neither p nor q is divisible by 8.
2) Both p and q are individually divisible by 4.
This is a Yes/ No question, and requires extra attention to detail.
(1) Nieither p nor q is divisible by 8. This means p does not equal 0 and q does not equal 0. This will be important for later. p and q can equal anything not divisible by 8
let p =4, q = 4 N = 8 ---The answer is yes
Let p = 1 q = 1 N = 2 -- The answer is No. Since we get a yes and a no NS
(2) both p and q individually divisible by 4. Both p and q can each individually be any of 0,4,8,12,16....
Let p =0 q=0 N= 0 Yes
Let p =8, q=20 N = 28 --- No Since we get a yes and a no NS
(1) and (2) p and q are divisible by 4 but not b 8. P and q can each be any of 4,12,20,28... Let p =4 q =4--> N=8 -- > Yes Let p=4, q =12 N = 16 --> Yes Let p=4 q = 20
N = 24 ---> Yes. NO matter which appropriate value we pick for p or q we get a sum divisible by 4 Suff. Answer is C