divisible ds questions

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ccassel: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 1:44 pmFollowed by: 2 members; Location: Canada; GMAT Score:530

by ccassel » Fri Mar 25, 2011 9:52 am

Hi,

Does anyone have a quick way of answering this question? I understand the divisibility rule but it took me quite some time to write out the 2nd part (N is divisible by 7). Any short hand solutions would be helpful to save time.

If K is a positive integer less than 10 and N=4321+K, what is the value of K?

(1) N is divisible by 3
(2) N is divisible by 7

The answer is B.

Thanks,

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Source: Beat The GMAT — Data Sufficiency | Fri Mar 25, 2011 9:52 am

vineeshp: Legendary Member; Posts: 965; Joined: Thu Jan 28, 2010 12:52 amFollowed by: 34 members; Thanked: 156 times; GMAT Score:720

by vineeshp » Fri Mar 25, 2011 10:12 am

Hi,

We just got to see if in either case K can have exactly one value that will get N to be perfectly divisible by 3 or 7.

With statement 1, K can be 2, 5 or 8 which will make N perfectly divisible by 3. Not sufficient.

With statement 2, K can be only 5 to make N perfectly divisible by 7 which makes B the correct answer.

The only way to solve such questions would be to see which is the closest number that can be clearly divided by the number. I mean, for statement 1

In a detailed way of explaining:
4320, 4323 are the nearest multiples of 3. Now the given number is 2 away from 4323 or 5 away from 4326 or 8 away from 4329.

Similarly.
for statement 2,
4319 is divisible by 7. Next number divisible by 7 is 4326 and this is 5 away from 4321.
4333 is 12 away from 4321, but K is less than 10 so 5 is our only choice.

Understanding the theory, the concept is the best way to save time in such questions.
If you try to apply short hand, you may miss subtle twists that the GMAT can include. You will be so into the method that you will get your answer wrong because you failed to account for the little twist.

Vineesh,
Just telling you what I know and think. I am not the expert.

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clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Fri Mar 25, 2011 10:20 am

one of the ways, perhaps not optimal for 2 st
(2) N=4321+K divisible by 7
4321=617*7+2. so we need to add 5=k to replenish the number
N=617*7+2+5=617*7+7*1-this number is divisible by 7 and k=5
the next k will equal 12, so as to be
N=617*7+2+12=617*7+2+12=617+2*7- also divisible by 7, but k=12>10 not complies with problem terms

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manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members; Thanked: 72 times

by manpsingh87 » Sat Mar 26, 2011 12:17 am

ccassel wrote:Hi,

Does anyone have a quick way of answering this question? I understand the divisibility rule but it took me quite some time to write out the 2nd part (N is divisible by 7). Any short hand solutions would be helpful to save time.

If K is a positive integer less than 10 and N=4321+K, what is the value of K?

(1) N is divisible by 3
(2) N is divisible by 7

The answer is B.

Thanks,

1) if N=4321+k is divisible by 3 than sum of the digits of N i.e. 4+3+2+1+k should also be divisible by 3, which is 10+k;

possible values of k for the expression to become divisible by 3 is 2,5,8.!! as we are not able to find the unique value of k by using statement 1; therefore 1 alone is not sufficient to answer the question.

2) for N=4321+k to become divisible by 7 then k must be 5 because for any other of k N won't be divisible by 7..!! as we are able to find the unique value of k by using statement 2 alone hence answer must be B

O Excellence... my search for you is on... you can be far.. but not beyond my reach!

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ccassel: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 1:44 pmFollowed by: 2 members; Location: Canada; GMAT Score:530

by ccassel » Sat Mar 26, 2011 9:48 am

Great explanations.

Thanks for your reply.

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