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If j and k are positive integers, j - 2 is divisible by 4

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If j and k are positive integers, j - 2 is divisible by 4 [#permalink]

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New post 17 Apr 2011, 11:43
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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


[Reveal] Spoiler:
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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Aug 2012, 06:08, edited 1 time in total.
Edited the question.

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Re: Difficult [#permalink]

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New post 17 Apr 2011, 20:45
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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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Re: Difficult [#permalink]

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New post 28 Aug 2012, 06:04
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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: Difficult [#permalink]

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New post 17 Apr 2011, 19:37
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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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Re: Difficult [#permalink]

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New post 17 Apr 2011, 19:59
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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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Re: Difficult [#permalink]

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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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Re: If j and k are positive integers, j - 2 is divisible by 4 [#permalink]

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Re: Difficult [#permalink]

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New post 18 Apr 2011, 23:04
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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Re: Difficult [#permalink]

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New post 19 Apr 2011, 10:28
Yeah I typed that wrong. It should be j-k+3.

Posted from my mobile device

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Re: Difficult [#permalink]

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New post 30 Apr 2011, 22:10
j-k = (4a-4b) - 3.
4(a-b) !=46.

Hence A.
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Re: If j and k are positive integers, j - 2 is divisible by 4 [#permalink]

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New post 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]

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New post 11 Mar 2014, 01:02
gmat1220 wrote:
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


[Reveal] Spoiler:
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.



j-2 is divisible by 4 & k-5 is divisible by 4, means

j-2 - (k-5) is also divisibly by 4

(j - k + 3) is also divisible by 4

Just putting in the values, 43 is the exception

Answer = A
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Re: If j and k are positive integers, j - 2 is divisible by 4 [#permalink]

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New post 23 Jun 2015, 16:08
Hello from the GMAT Club BumpBot!

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If j and k are positive integers, j - 2 is divisible by 4 [#permalink]

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New post 27 Jun 2015, 09:49
\(j = 4q + 2\)
\(k = 4q + 5\)

\(j - k = 4q + 2 - (4q + 5) = 2 - 5 = -3\)
Add 4 to -3 to arrive at the remainder value, and therefore R1.

Subtract one from answer choice to calculate whether it's divisible by 4. If not divisible by 4, it meets the criteria.
Answer A. 43

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Re: If j and k are positive integers, j - 2 is divisible by 4 [#permalink]

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New post 21 Jul 2016, 06:52
Hello from the GMAT Club BumpBot!

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Re: If j and k are positive integers, j - 2 is divisible by 4   [#permalink] 21 Jul 2016, 06:52
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