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# N is the sum of two positive integers p and q. Is N divisible by 8? 1.

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Manager
Joined: 10 Oct 2018
Posts: 182
GPA: 4
N is the sum of two positive integers p and q. Is N divisible by 8? 1.  [#permalink]

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05 Jan 2019, 10:55
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65% (hard)

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41% (01:39) correct 59% (01:17) wrong based on 38 sessions

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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.

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Manager
Joined: 01 May 2017
Posts: 82
Location: India
N is the sum of two positive integers p and q. Is N divisible by 8? 1.  [#permalink]

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05 Jan 2019, 18:27
N is the sum of two positive integers p and q. Is N divisible by 8?
N = p+q
Is N = 8x? where x, any positive integer

1) Neither p nor q is divisible by 8.
Case (1) Either p, q can both be odd, resulting in an even number which is only divisible by 2
Case(2) p,q one of them resulting in odd values, which is not a multiple of 8
Case (3) p,q one of them even and other is odd multiple of 4, resulting in a number not divisible by 8 (4+8 = 12)
Case(4) p,q can be both even or odd multiples of 4 resulting in number divisible by 8
(4+12 = 16) ---- both odd multiples of 4
16 + 8 = 24 ----- both even multiples of 4
But we don't know anything about p,q except they are not divisible by 8
Insufficient

2) Both p and q are individually divisible by 4.
Case (1) p,q one of them even and other is odd multiple of 4, resulting in a number not divisible by 4 (4+8 = 12)
Case(2) p,q can be both even or odd multiples of 4 resulting in number divisible by 8
(4+12 = 16) ---- both odd multiples of 4
16 + 8 = 48 ----- both even multiples of 4
But we don't know anything about p,q except they are individually divisible by 4
Insufficient

(1) and (2) together, sufficient
As p,q are not multiples of 8, and multiples of 4 which implies they are odd multiples of 4
4+12 = 16
Clearly we can say, resultant is divisible by 8
sufficient

Option C is correct
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Re: N is the sum of two positive integers p and q. Is N divisible by 8? 1.  [#permalink]

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05 Jan 2019, 21:21
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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
Re: N is the sum of two positive integers p and q. Is N divisible by 8? 1.   [#permalink] 05 Jan 2019, 21:21
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