Problem Solving (PS) | Re: The sum of the digits of a positive integer N is 23. The remainder whe

­The sum of the digits of a positive integer N is 23. The remainder when N is divided by 11 is 7. What is the remainder when N is divided by 33?

Here's a "lucky" way to solve this question because of the answer choices. 
We know,
N = 11a + 7
Also, N = 33b + r
Therefore we can say 11a + 7 = 33b + r => r = 11(a-3b) + 7
We know 11(a-3b) will be a multiple of 11 => 11(a-3b) = 11, 22, 33, 44, etc
Let's put 11(a-3b) = 11 => r = 11+ 7 = 18 (Not present in answer choices but this also eliminates A, B, C and D)
Putting 11(a-3b) = 22 => r = 22 + 7 = 29 (Option E)

I say "lucky" because the options really helped out here so I didn't need to use the information that the sum of the digits is 23. Ofc, this isn't a legitimate solution but for this specific problem and given the answer choices, it works. 

Statistics : Posted by siddhantvarma • on 14 Apr 2020, 05:18 • Replies 6 • Views 7230

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