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Updated on: 08 Jul 2019, 13:38
Originally posted by BrentGMATPrepNow on 08 Jul 2019, 11:17.
Last edited by BrentGMATPrepNow on 08 Jul 2019, 13:38, edited 1 time in total.
Last edited by BrentGMATPrepNow on 08 Jul 2019, 13:38, edited 1 time in total.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
36% (02:27) correct
64%
(02:41)
wrong
based on 103
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When 420 is divided by positive integers j and k, the remainders are x and y respectively. If x and y are both positive, what is the remainder when k + j is divided by 5?
1) j and k are both 1-digit integers
2) j – k = 1
1) j and k are both 1-digit integers
2) j – k = 1
08 Jul 2019, 12:59
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GMATPrepNow
First - let's analyze the number 420 and it's prime factors:
420/2 => 210
210/2 => 105
105/5 => 21
21/3 => 7
7/7 => 1
So we have these prime factors: 2, 2 (note that we would require both 2 for the future calc), 5, 3, 7.
Let's look at the Assumptions:
1. if J and K are both 1-digit integers (and we know that 420 divided by J or K should have decimal answer) then J and K:
cannot be 0 (you cannot divide by 0)
cannot be 1 (divisor of 420)
cannot be 2 (divisor of 420)
cannot be 3 (divisor of 420)
cannot be 4 (divisor of 420, 2*2=4)
cannot be 5 (divisor of 420)
cannot be 6 (divisor of 420, 2*3=6)
cannot be 7 (divisor of 420)
can be 8 (not a divisor of 420)
can be 9 (not a divisor of 420)
We have no idea if J and K are same of distinct, therefore the J&K pairs can be 8&8, 8&9, 9&8, 9&9.
You can easily see that there is no answer for the remainder of J+K/5...
Therefore 1 is clearly unsufficient.
Let's look at 2. as a standalone Assumption:
if J is bigger than K by 1, then it really doesn't give us anything...
J can be 47 and K can be 48. Or 31 and 32...
(47+48)/5 = 19 with no remainder
(31+32)/5 = 12 with remainder 3.
So - insufficient!
If we combine Assumption 1 and Assumption 2 - you will see that the pairs 8&9 and 9&8 give the same remainder of 2, when the sum is divided by 5!.
Sufficient. The answer is C.
Please give KUDOSSSS, if the explanation helped you.
General Discussion
Mo2men
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08 Jul 2019, 15:39
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GMATPrepNow
Hi Brent,
The phrasing of the question means that there is a possibility that j & k are equal. Does it make sense because we have same equation if both are equal?
