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26 Apr 2018, 13:34
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
69% (01:40) correct
31%
(01:47)
wrong
based on 245
sessions
History
Date
Time
Result
Not Attempted Yet
If K is a positive integer such that the remainder when 17 is divided by K is 2, what is the sum of all the possible values of K?
(A) 8
(B) 18
(C) 20
(D) 23
(E) 25
(A) 8
(B) 18
(C) 20
(D) 23
(E) 25
26 Apr 2018, 13:48
Kudos
Bookmarks
Bunuel
When 17 is divided by K = 15(3*5), the remainder is 2.
The remainder is also 2 when K takes the value 3 or 5.
Therefore, the sum of all possible values of K is \(3+5+15 =\) 23(Option D)
26 Apr 2018, 13:55
Kudos
Bookmarks
Bunuel
We'll show two approaches:
If it isn't immediately clear where to look for an abstract solution, we'll list our options.
This is an Alternative approach.
1*17=17 so remainder 0
2*8=16 --> remainder 1
3*5 = 15 --> remainder 2 so good!
4*4 = 16 --> no good
5*3 = 15 --> good!
6*2 = 12 --> no good
7*2 = 14 --> no good
8*2 = 16 --> no good.
9,10... these are too large as multiplying by 2 makes them larger than 17.
Only 15 works as 15*1 = 15
Then our sum is 3 + 5 +15 = 23.
(D) is our answer.
A shorter, more abstract solution:
Questions dealing with remainders can often be solved with number properties and very few calculations.
We'll look for such a solution, a Logical approach.
If 17 divided by k gives a remainder of 2, then k must divide 17 - 2 = 15.
That is, k is either 1,3,5 or 15. But k=1 can't work as 17 divided by 1 has remainder 0.
So the only options are 3,5,15 and our sum is 23.
