All numbers in a list of six positive integers are less than 8. What

Question

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

JeffTargetTestPrep · Accepted Answer

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.

Answer: E

Sasindran · Answer

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

Sent from my iPhone using GMAT Club Forum

PraveenChahal · Answer

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)

gurjitluvusa · Answer

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

gurjitluvusa · Answer

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.

Sent from my SM-A510F using  GMAT Club Forum mobile app

chetan2u · Answer

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

MvArrow · Answer

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)!

rahul16singh28 · Answer

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

ManjariMishra · Answer

I am not clear with why we have to take numbers as 1 ,Can anyone please help me in understanding this.
Thanks

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

All numbers in a list of six positive integers are less than 8. What

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

All numbers in a list of six positive integers are less than 8. What

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards