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Averages-Min number

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by mallika hunsur » Sun Feb 15, 2015 7:30 am
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Hi all,

My doubt on the above question is that why has the worst case scenario been considered, i.e. 6 1's and not best case which is 6 7's.
If we pick 6 7's, we can add a number just above 14 to the list to exceed the average of 8.
Pls help!!
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by GMATinsight » Mon Feb 16, 2015 3:45 am
mallika hunsur wrote:Image

Hi all,

My doubt on the above question is that why has the worst case scenario been considered, i.e. 6 1's and not best case which is 6 7's.
If we pick 6 7's, we can add a number just above 14 to the list to exceed the average of 8.
Pls help!!
You have to pay attention to the word "GUARANTEE" mentioned in question stem

In order to guarantee we have to take the worst case scenario so that even in that scenario we can ensure that the new average is achieved.

In your pic the new average will be achieved but since you don't know whether the seat of values is the worst scenario or best scenario or in-between the two therefore your case will be proven wrong if the scenario is not best whereas we are supposed to GUARANTEE.

With the worst scenario, whatever scenario you take the new average or above will certainly be achieved.
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by mallika hunsur » Tue Feb 17, 2015 3:09 am
GMATinsight wrote:
mallika hunsur wrote:Image

Hi all,

My doubt on the above question is that why has the worst case scenario been considered, i.e. 6 1's and not best case which is 6 7's.
If we pick 6 7's, we can add a number just above 14 to the list to exceed the average of 8.
Pls help!!
You have to pay attention to the word "GUARANTEE" mentioned in question stem

In order to guarantee we have to take the worst case scenario so that even in that scenario we can ensure that the new average is achieved.

In your pic the new average will be achieved but since you don't know whether the seat of values is the worst scenario or best scenario or in-between the two therefore your case will be proven wrong if the scenario is not best whereas we are supposed to GUARANTEE.

With the worst scenario, whatever scenario you take the new average or above will certainly be achieved.
Many thanks GMATInsight!!I get why i need to consider worst case now..

Best,
Mallika
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by Brent@GMATPrepNow » Tue Feb 17, 2015 9:31 am
All numbers in a list of six positive integers are less than 8. What is the smallest integer that if added to the list would guarantee that the average becomes greater than 8?

(A) 14
(B) 35
(C) 42
(D) 50
(E) 51
Here's a full solution:

In order to guarantee that an average greater than 8, we must consider the scenario in which the original six integers are MINIMIZED.

Since the original numbers are "positive integers," their MINIMIZE values are: {1, 1, 1, 1, 1, 1}
From here, what is the smallest value we can add to this set so that the new average is greater than 8?

Let N = the number to be added to the set.
We get a new set of {1, 1, 1, 1, 1, 1, N}

If the average is greater than 8, we can write:
(1+1+1+1+1+1+N)/7 > 8
Simplify: (6+N)/7 > 8
Multiply both sides by 7 to get: 6 + N > 56
Subtract 6 from both sides to get N > 50

So, the number added must be greater than 50
Since we're told that the added number must be an INTEGER, the smallest possible value of N is 51


Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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