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If j and k are positive integers, j - 2 is divisible by 4 [#permalink]
 17 Apr 2011, 11:43
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Question Stats:
62% (02:35) correct
37% (02:23) wrong based on 6 sessions
If j and k are positive integers, j - 2 is divisible by 4 and k - 5 is divisible by 4, all of the following could be the value of j - k EXCEPT: A. 43 B. 33 C. 21 D. 13 E. 5 j -2 = 4a => j = 4a + 2
k - 5 = 4b => k = 4b + 5
j - k = 4(a - b) - 3
This means j - k is 3 less than the multiple of 4. That means add 3 to make it the multiple of 4.
43 + 3 = 46 Not the multiple of 4 ---> Answer
33 + 3 = 36. Multiple of 4
21 + 3 = 24 Multiple of 4
13 + 3 = 16 Multiple of 4
5 + 3 = 8 Multiple of 4
Since there is a reversal in thinking - our answer is A.
Last edited by Bunuel on 28 Aug 2012, 06:08, edited 1 time in total.
Edited the question.
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j-2 = 4k => j = 4k + 2 = 2,6,8,14,18,22,26,30,34,38, 42, 46,50 k-5 = 4j => k = 4j + 5 = 5,9,13,17,21,25,29,33 5 = 22 - 17 13 = 30 - 17 21 = 42 - 21 33 = 50 - 17 So by POE, we can see that all the answer choices are posible here except A We can stop as soon as we see that all other options are possible, by proceeding from lowest value to higher ones. Answer - A
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j = 2 +4 (p)
k = 5 + 4(q)
=> j-k = -3+4(...)
A is the only choice that doesnt have this pattern. (i.e multiple of 4 - 3)/
Answer is A.
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if j -2 is divisible by 4, we can say that j is 4x +2
if k-5 is divisible by 4, it means so will be k-1. and therefore k can be expressed as 4y +1
j - k will be 4x +2- (4y+1) = 4x-4y +2-1 = 4(x-y) +1
The number will have to be a multiple of 4 added to 1.
42 cant be expressed like that . Rest all options can be - (4*8+1, 4*5+1, 4*3+1, 4*1+1)
Hence A.
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if j-2 is divisible by 4 and k-5 is divisible by 4 then j-2 - (k-5) is divisible by 4
--> j-k+1 is divisible by 4.
now substitute each of the answer choices in (j-k) + 1 --> 43-1 = 42 --> NOT divisible by 4
Ans A.
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dreambeliever wrote: if j-2 is divisible by 4 and k-5 is divisible by 4 then j-2 - (k-5) is divisible by 4
--> j-k+1 is divisible by 4.
now substitute each of the answer choices in (j-k) + 1 --> 43-1 = 42 --> NOT divisible by 4
Ans A. I may be missing something, how did you get j-k+1? Should it be j - k + 3 instead? Ans remains the same. 43+3 is not divisible by 4.
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Yeah I typed that wrong. It should be j-k+3. Posted from my mobile device 
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j-k = (4a-4b) - 3. 4(a-b) !=46. Hence A.
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Logical way to solve the problem j-2 = 4a ==> j=4a+2 k-5 = 4b ==> k=4b+5 j-k = 4(a-b) - 3 As the remainder can not be negative we must add divisor to the remainder to make remainder positive j-k = 4(a-b) + (4-3) j-k = 4(a-b) +1 i.e. when (j-k) is divided by 4, it will a remainder of 1 All except option "43" leave remainder 1 Solution A
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Re: If j and k are positive integers, j - 2 is divisible by 4 [#permalink]
03 Dec 2012, 02:24
1. If j - 2 is divisible by 4 it can be represented as 4j+2
k - 5 is divisible by 4 and is equal to 4k+5
Thus, j - k is equal to 4j+2-(4k+5)=4(j+k) -3
Which means that the difference of j and k will be a multiple of 4 minus 3.
From there all we need is just to which numbers are multiples of 4.
43+3=46 and it's not divisible by 4
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Re: If j and k are positive integers, j - 2 is divisible by 4
[#permalink]
03 Dec 2012, 02:24
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