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What is the least positive integer

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alphonsa
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What is the least positive integer [#permalink] New post  03 Aug 2014, 09:49
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Question Stats:

77% (01:40) correct 23% (01:47) wrong based on 191 sessions
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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.


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gigi66653
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Re: What is the least positive integer [#permalink] New post  03 Aug 2014, 15:34
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3=3*1, 6=3*2, 9=3*3,
so, Least Common Multiple [3,6,9] = 3*3*2=18
Let A=18X+2 = 11Y, when X =6, Y= 10, A=110
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vad3tha
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Re: What is the least positive integer [#permalink] New post  03 Aug 2014, 23:56
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alphonsa wrote:
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


I think the fastest way is try and error. I use the tips that try from E to A, instead of A to E, will save more time.
I got C
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PareshGmat
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Re: What is the least positive integer [#permalink] New post  07 Aug 2014, 01:52
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alphonsa wrote:
PareshGmat wrote:
alphonsa wrote:
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 :cry: :cry: ..

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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PareshGmat
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Re: What is the least positive integer [#permalink] New post  06 Aug 2014, 03:41
alphonsa wrote:
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??
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alphonsa
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GMAT 1: 670 Q48 V34
WE:Engineering (Energy and Utilities)
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Re: What is the least positive integer [#permalink] New post  06 Aug 2014, 23:26
PareshGmat wrote:
alphonsa wrote:
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 :cry: :cry: ..

Now can you help me solving it, considering no options were given? :( :( :(
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fra
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Re: What is the least positive integer [#permalink] New post  07 Aug 2014, 03:57
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Just check if (n-2) is divisible by 3,6 and 9. Plug in the options in place of 'n'
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Abhishek009
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Re: What is the least positive integer [#permalink] New post  16 Jan 2024, 10:34
alphonsa wrote:
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

(A) 33 - 2 = 31 , not divisible by 3, 6 & 9
(B) 77 - 2 = 75 , not divisible by 3, 6 & 9
(C) 110 - 2 = 108, Divisible by 3, 6 & 9 {Also note units digit is divisible by 2 , hence divisible by 6 and sum is divisible by3}
(D) 121 - 2 = 119 , not divisible by 3, 6 & 9

Answer must hence be (C)
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Re: What is the least positive integer [#permalink]
16 Jan 2024, 10:34
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