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Average of y numbers is x

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Average of y numbers is x

by Brent@GMATPrepNow » Wed Dec 31, 2008 2:24 pm
The average (arithmetic mean) of y numbers is x. If 30 is added to the numbers, then the average (arithmetic mean) will be x-5. What is the value of y in terms of x?

A) x/7 - 5
B) x/6 - 6
C) x/6 - 5
D) x/5 - 7
E) X/5 - 6
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by daisy » Wed Dec 31, 2008 2:47 pm
IMO (D)
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by cramya » Wed Dec 31, 2008 2:53 pm
Sum / y = x

Sum = xy

xy+30 / y+1 = x-5

xy+30 = xy+x-5y-5
35 = x-5y

y = x/5 - 7

Choose D)
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by Brent@GMATPrepNow » Wed Dec 31, 2008 3:10 pm
D it is.
Nice solution, cramya - short and sweet.
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by vivek.kapoor83 » Thu Jan 01, 2009 2:36 am
hi brent,
Thanks for the gr8 ques..
i was following the same approch as cramya but i couldnt get it
coz in as u said...30 is added to the sum, does it mean total y+1 element will be there...I mean, here we need to treat 30 as next no or something added to already existing y nos.

How we have to treat in exams.

and 1 more query wht is the value of 0^0 in gmac...coz diff explantions are given on diff links...like

https://www.faqs.org/faqs/sci-math-faq/s ... bers/0to0/
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by logitech » Thu Jan 01, 2009 11:17 am
This question makes me thinking...

How can we solve this problem in different ways ?

if adding 30 is actually decreasing the average by 5.

1) 30 is less than the average of the numbers

For Example we have only 1 number and it is 40

40/1 = 40 ( note that y=1 and x=40)

40+30 / 2 = 35 ( now y =2 and New X = Old X - 5 = 35 )

And also if we look at the correct answer:

X = 5 ( Y + 7 )

I am trying to find out where that 7 is coming into the equation. Since we are adding 30 and it is LESS than the average X > 30 ; so I can see why 7 is not not less than 5.

I am still trying to find out how we can look at this question and SPOT D as the answer by critical thinking.

This is what happens to you when you are an engineer :) :)
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by logitech » Thu Jan 01, 2009 11:31 am
Okay check this out

We can always check for y=1 and y=2 and to see if the X will be X-5 when y = 2

IF Y=1

A) x/7 - 5 --> X =42
B) x/6 - 6 --> X =42
C) x/6 - 5 --> X =36
D) x/5 - 7 --> X =40
E) X/5 - 6 --> X =35

Now we can simply add 30 and divide by 2 to see if we will have 5 as a difference

A) X =42 , 36
B) X =42 , 36
C) X =36 , 33
D) X =40 , 35
E) X =35 , 32,5


This calculation can be done within 90 seconds. I like it! :)
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by piyush_nitt » Thu Jan 01, 2009 11:58 am
Agree with Vivek.

I did the same mistake , added a 30 to each number and ended up by messing everything.

How someone gonna decide whether number has to be treated as a separate number?

Brant pls explain?

Thanks!
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by Brent@GMATPrepNow » Thu Jan 01, 2009 12:22 pm
piyush_nitt wrote:Agree with Vivek.

I did the same mistake , added a 30 to each number and ended up by messing everything.

How someone gonna decide whether number has to be treated as a separate number?

Brant pls explain?

Thanks!
Good point. To make this question less ambiguous, I should have written that "30 is added to the set of numbers." That would have been more clear.
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