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Help with specific DS problems

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Help with specific DS problems

by ronm » Sun Dec 07, 2008 10:31 am
Hey all,

My exam is coming up soon and there are some specific questions that I am having trouble understanding.

I would really appreciate someone explaining the two questions below. Thank-you.

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Is the integer n a multiple of 15?

1) n is a multiple of 20

2) n+6 is a multiple of 3

ANS : Both 1) and 2) are required

I'm particularly interested in understanding the theory behind this type of question as I've seen this type of question and I don't understand the theory.

===============================================

If 11 consecutive integers are listed from least to greatest, what is the average of the 11 integers?

1) Average of 1st 9 integers is 7

2) Average of last 9 integers is 9

ANS : Each statement alone is sufficient.

I cannot for the life of me figure out how you could figure out the average of 11 integers while only knowing the average of 9 of them.

====================

Any help at all would be great appreciated. Thank you!
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Source: — Data Sufficiency |
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by Zipper » Sun Dec 07, 2008 11:25 am
Answer to the first question:

n/15=0 remainder?

1. n/20=0 remainder, so obviously YES and NO //insuff

2. (n+6)/3=remainder 0 <=> n/3 remainder 0 YES and NO //insuff

Both: n/20=remainder 0 and n/3=remainder 0

combining n/60=remainder 0

so n/15 will always be with remainder 0

hence, C
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by Zipper » Sun Dec 07, 2008 11:34 am
Answer to question 2:

1. The sum of the first nine integers is 9*7=63.

let x be the smallest integer so:

x+(x+1)+(x+2).....(x+8)=63

9x+36=63 (if not any earlier here you should already know this is going to solve)

x=3

In 11 consecutive integers the median will also be the mean (so the 6th will be the average)

x+5=6th so 8 is the median (not that someone is looking for it I just wanted to show you how it can be done)

2. The same as 1. You should know it will solve even before you start.

Hence, D
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