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If j and k are positive integers, j  2 is divisible by 4 [#permalink]
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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 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.
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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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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 k5 is divisible by 4, it means so will be k1. and therefore k can be expressed as 4y +1
j  k will be 4x +2 (4y+1) = 4x4y +21 = 4(xy) +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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28 Aug 2012, 06:04
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Logical way to solve the problem j2 = 4a ==> j=4a+2 k5 = 4b ==> k=4b+5 jk = 4(ab)  3 As the remainder can not be negative we must add divisor to the remainder to make remainder positive jk = 4(ab) + (43) jk = 4(ab) +1 i.e. when (jk) 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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17 Apr 2011, 19:37
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j2 = 4k => j = 4k + 2 = 2,6,8,14,18,22,26,30,34,38, 42, 46,50 k5 = 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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17 Apr 2011, 19:59
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j = 2 +4 (p)
k = 5 + 4(q)
=> jk = 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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17 Apr 2011, 21:30
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if j2 is divisible by 4 and k5 is divisible by 4 then j2  (k5) is divisible by 4 > jk+1 is divisible by 4.
now substitute each of the answer choices in (jk) + 1 > 431 = 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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18 Apr 2011, 23:04
dreambeliever wrote: if j2 is divisible by 4 and k5 is divisible by 4 then j2  (k5) is divisible by 4 > jk+1 is divisible by 4.
now substitute each of the answer choices in (jk) + 1 > 431 = 42 > NOT divisible by 4
Ans A. I may be missing something, how did you get jk+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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19 Apr 2011, 10:28
Yeah I typed that wrong. It should be jk+3.
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Re: Difficult [#permalink]
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30 Apr 2011, 22:10
jk = (4a4b)  3. 4(ab) !=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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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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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 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. j2 is divisible by 4 & k5 is divisible by 4, means j2  (k5) 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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23 Jun 2015, 16:08
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If j and k are positive integers, j  2 is divisible by 4 [#permalink]
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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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