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Director  Joined: 29 Nov 2012
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The average of five number is 16. Is the sum of the two larg  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 45% (02:11) correct 55% (01:57) wrong based on 121 sessions

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The average of five number is 16. Is the sum of the two largest numbers in the set greater than 34?

1) the largest number in the set is greater than 20.
2) The median of the set is 16.

Any better approaches for statement 1
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The average of five number is 16. Is the sum of the two largest numbers in the set greater than 34?
Hence the sum of those numbers is 80.

1) the largest number in the set is greater than 20.
Lets assume that it has the value of 20 (the least possible), so the sum of the four remaining numbers will be 60. A+B+C+D=60, D (the greatest number) must be positive and will equal at least 15 (if every number is equal), so $$20+15=35>34$$
If this holds true for the worst case scenario, it will hold true for the others as well.

2) The median of the set is 16.
Consider A=[$$16,16,16,16,16$$], the answer is no; or consider A=[$$1,2,3,4,70$$] and the answer is yes.
Not sufficient
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Zarrolou I think the answer should be C.

Statement 1 can be made false as well. Consider this example:

Largest number is 21. Second largest 13. Their sum will be 34. Other numbers can be 10,12,12,12. As the average of 5 numbers is 16 then their sum will be 80. These numbers satisfy all constraints as 10+12+12+12+13+21 = 80 averaging to 16. And nowhere does the question mention that numbers should be distinct.
Hence the answer is NO.

Similarly we can get a Yes answer. let largest number be 21 and second largest 14 to sum to 35. rest of numbers can be 10,11,12,12.

Statement 2 you showed already to be insufficient.

C) Middle number 16 then Second largest lets say is smallest (16) and largest is greater than 20 hence (21). then smallest sum will be 37.
So we will have a definite Yes answer

Bunuel correct me if I am wrong
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Re: The average of five number is 16. Is the sum of the two larg  [#permalink]

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1
For simplicity, consider the five numbers are $$n_1, n_2, n_3, n_4$$ and $$n_5$$, where $$n_1$$ is the smallest and $$n_5$$ is the largest number.
We are given - $$\frac{n_1+n_2+n_3+n_4+n_5}{5}=16$$.

Statement 1: Consider $$n_5 = 21$$.
$$\frac{n_1+n_2+n_3+n_4+21}{5}=16$$

$$\frac{n_1+n_2+n_3+n_4}{5}+4.2=16$$

$$\frac{n_1+n_2+n_3+n_4}{5}=11.8$$

$$n_1+n_2+n_3+n_4=59$$
Therefore, for the sum of above four numbers to be equal to 59 the largest among 4 should at least be >= 15. Thus, 21+15=36.
Sufficient.

Statement 2: The median is 16 and also the average is 16. This means that either all numbers have the same value of 16 or they are consecutive numbers.
If its the former case then the sum of two largest numbers is 32, however if its the latter case then the sum can be 35 or 38, etc.
Not Sufficient.

Ans - A
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The average of five number is 16. Is the sum of the two larg  [#permalink]

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harasali91 wrote:
Zarrolou I think the answer should be C.

Statement 1 can be made false as well. Consider this example:

Largest number is 21. Second largest 13. Their sum will be 34. Other numbers can be 10,12,12,12. As the average of 5 numbers is 16 then their sum will be 80. These numbers satisfy all constraints as 10+12+12+12+13+21 = 80 averaging to 16. And nowhere does the question mention that numbers should be distinct.
Hence the answer is NO.

Similarly we can get a Yes answer. let largest number be 21 and second largest 14 to sum to 35. rest of numbers can be 10,11,12,12.

Statement 2 you showed already to be insufficient.

C) Middle number 16 then Second largest lets say is smallest (16) and largest is greater than 20 hence (21). then smallest sum will be 37.
So we will have a definite Yes answer

Bunuel correct me if I am wrong

harasali91

In your logic for statement 1, you are considering 6 numbers - 10, 12, 12, 12, 13 and 21. It should be five numbers.

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Re: The average of five number is 16. Is the sum of the two larg  [#permalink]

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GMATMBA5 yes, thank you for clarifying. I should be vary of these careless mistakes. Re: The average of five number is 16. Is the sum of the two larg   [#permalink] 28 Mar 2019, 07:29
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