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Math Expert V
Joined: 02 Sep 2009
Posts: 58427
All numbers in a list of six positive integers are less than 8. What  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 39% (01:24) correct 61% (01:38) wrong based on 92 sessions

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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

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Re: All numbers in a list of six positive integers are less than 8. What  [#permalink]

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Let’s say all the six numbers are 7. Their sum is 42 and the average is 7. Now a new number is added to the list and the average has to be 8. Hence the sum has to be at least 7*8=56. Hence the new number is 56-42=14
Option A

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Re: All numbers in a list of six positive integers are less than 8. What  [#permalink]

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The question asks for the number to be added so that average becomes greater than 8. If we add 14 then average becomes equal to 8 not greater than 8, so the answer should be B (35)
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Re: All numbers in a list of six positive integers are less than 8. What  [#permalink]

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Bunuel wrote:
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

Answer should be greater than 14 so B has to be the choice.
Intern  Joined: 26 Jan 2018
Posts: 2
Re: All numbers in a list of six positive integers are less than 8. What  [#permalink]

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1
1
gurjitluvusa wrote:
Bunuel wrote:
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

Answer should be greater than 14 so B has to be the choice.

Answer is E. Since they have asked for an integer which guarantee that the average bcms greater than 8. So in case all the 6 integers are 1 and if we add 50 to these we get their average as 8. So 51 should be the choice.

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Math Expert V
Joined: 02 Aug 2009
Posts: 8008
All numbers in a list of six positive integers are less than 8. What  [#permalink]

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3
Bunuel wrote:
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

Hi...
A good question Bunuel..

Most above have gone wrong by not reading the info correctly..

so we are looking at " Smallest integer but integer that would GUARANTEE an average >8

for GUARANTEE, we will have to take the least possible value of 6 integers so SUM = 6*1 = 6
for exact average of 8 of 6+1 integer, SUM = 7*8=56..
But the average has to be >8, so SUM = 56+1=57

New integer = 57-6=51

E
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Re: All numbers in a list of six positive integers are less than 8. What  [#permalink]

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3
Bunuel wrote:
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

Let’s say each integer is equal to 1. Then, the sum of the six integers is 6(1) = 6. Let the unknown integer = x. Then we have:

(6 + x)/7 > 8

6 + x > 56

x > 50

So the minimum value of x is 51.

You might wonder why we chose the smallest possible value of 1 for each of the six integers. This was to fulfill the requirement that the added number would guarantee that the average of the 7 numbers would be greater than 8.

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Re: All numbers in a list of six positive integers are less than 8. What  [#permalink]

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Min value on the list is 1, so i have 1,1,1,1,1,1
Sum is 6
So I can set up the equation 6+x=7x8 that is x = 50
But 50 is the tricky answer choice as the stem states that I need an average that is >8!
The only answer that can match this condition is E (51)!
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Re: All numbers in a list of six positive integers are less than 8. What  [#permalink]

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Bunuel wrote:
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

Let the 6 numbers be - $${n1,n2,n3,n4,n5,n6} < 8$$.
Now, we have to find $$n7$$
$$n1 + n2 + n3 + n4 + n5 + n6 + n7 > 56$$
As the passage uses the word GUARANTEE, we have to keep $${n1,n2,n3,n4,n5,n6}$$ to be minimum i.e. each equal to 1.
Hence, $$n7 >50$$
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Intern  B
Joined: 10 May 2018
Posts: 48
Re: All numbers in a list of six positive integers are less than 8. What  [#permalink]

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I am not clear with why we have to take numbers as 1 ,Can anyone please help me in understanding this.
Thanks Re: All numbers in a list of six positive integers are less than 8. What   [#permalink] 08 Jul 2019, 11:26
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