BTGmoderatorDC wrote: ↑Thu Feb 06, 2020 5:57 pm
When 900 is divided by positive integer d, the remainder is r. For some integer N > 5000, when N is divided by positive integer D, the remainder is R. Is R > d?
(1) r = 1
(2) D = 23
OA
C
Source: Magoosh
Let's take each statement one by one.
(1) r = 1
No information about R. Insufficient.
(2) D = 23
No information about d. Insufficient.
(1) and (2) together
From (1), we know that when 900 is divided by positive integer d, the remainder is r; thus, when 899 is divisible by positive integer d.
By hit and trial, we can factorize 899. We can write 899 as 900 – 1 = 30^2 – 1^2 = (30 + 1)(30 – 1) = 31*29.
Thus, d is either 29 or 31.
From (2), we know that D = 23. Since R must be less than 23, the maximum value R can have is 22. So, for either value of R, we have R < d. The answer is no. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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