alphonsa
PareshGmat
alphonsa
What is the least positive integer that when divided by 3,6,9 leaves remainders of 2 in each case but is perfectly divisible by 11?
A) 33
B) 77
C)110
D) 121
Besides plugging in, can you tell me if there is another method of solving this problem? I mean just for a conceptual understanding.
Source: 4gmat
All are divisibly by 11
33 is divisible by 3; so ruled out
77 is 5 far from 72 (divisible by 9); so ruled out
110 best fits in
Answer = C
Does this question came up with only 4 options??
This question came with no options

..
Now can you help me solving it, considering no options were given?

GMAT questions tend to have 5 options; else this question would be "open ended"
As far as your question goes to find out the appropriate numbers, please refer diagram below:
Wrote down table of 3, added 2 in next column, table of 6, added 2 in next column, table of 9, added 2 in next column
Highlighted the numbers which appear common in all +2 columns & checked divisibility by 11 which gives the result
What I discovered is, starting 110, just add 198 to get the next number
110 + 198 = 308
308 + 198 = 506
506 + 198 = 704
All the above 3 results fulfil the divisibility/ remainder requirement
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