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Stange Question on LCM

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Stange Question on LCM

by gmattest001 » Wed Dec 19, 2012 9:47 am
I got this question on some site

It is known that no more than 7 children will be attending a party.what is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies.

A. 35
B. 105
C. 180
D. 210
E. 420

Please let me know what will be answer.
Thanks
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by puneetkhurana2000 » Wed Dec 19, 2012 11:28 am
Answer is 420, as any number of children <= 7 can be present.

So minimum cookies required are LCM of 1,2,3,4,5,6,7 i.e. 420.

Answer E.

Alternate Method:- Among options 420 is the only number divisible by all positive integers <=7.
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by GMATGuruNY » Wed Dec 19, 2012 2:04 pm
gmattest001 wrote:I got this question on some site

It is known that no more than 7 children will be attending a party.what is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies.

A. 35
B. 105
C. 180
D. 210
E. 420
Since it's possible that 4 children will attend, the correct answer must be a multiple of 4.
An integer is a multiple of 4 only if its LAST TWO DIGITS form a multiple of 4.
Eliminate A, B and D, since 35, 05, and 10 are not multiples of 4.

Since it's possible that 7 children will attend, the correct answer must be a multiple of 7.
Eliminate C, since 180 is not a multiple of 7.

The correct answer is E.
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by sharoonsaleem » Thu Dec 20, 2012 2:13 am
Got it Mitch!
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by shashank.ism » Thu Dec 20, 2012 3:47 am
From the question its clear that any no. of children from 1 to 7 can attend the party. And you have to bring smallest number cookies in such a way that each child receives the same number cookies.
It is clear from the question that you have to find smallest number which is divisble by 1, 2, 3, .....7 i.e. their LCM

LCM of 1 to 7 = 2x3x2x5x7 = 420 ANS.
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by shashank.ism » Thu Dec 20, 2012 3:51 am
Alternatively Mitch said very correctly that by checking out the provided options, we can easily figure out the correct answer.
Option A , Option B not divisible by 2
Option C not divisible by 7
Option D not divisible by 4
Option is divisible by 1, 2, 3, .... , 7
so by looking at the options you can directly pick the correct answer in few seconds. :)
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by gmattest001 » Thu Dec 20, 2012 6:22 am
GMATGuruNY wrote:
gmattest001 wrote:I got this question on some site

It is known that no more than 7 children will be attending a party.what is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies.

A. 35
B. 105
C. 180
D. 210
E. 420
Since it's possible that 4 children will attend, the correct answer must be a multiple of 4.
An integer is a multiple of 4 only if its LAST TWO DIGITS form a multiple of 4.
Eliminate A, B and D, since 35, 05, and 10 are not multiples of 4.

Since it's possible that 7 children will attend, the correct answer must be a multiple of 7.
Eliminate C, since 180 is not a multiple of 7.

The correct answer is E.
Thanks for the answer and you explain it nicely.
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