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The average (arithmetic mean) of integers r, s, t, u, and v is 100. Ar

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Bunuel
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The average (arithmetic mean) of integers r, s, t, u, and v is 100. Ar [#permalink] New post   11 Jul 2017, 02:52
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The average (arithmetic mean) of integers r, s, t, u, and v is 100. Are exactly two of the integers greater than 100?

(1) Three of the integers are less than 50.
(2) None of the integers is equal to 100.
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Re: The average (arithmetic mean) of integers r, s, t, u, and v is 100. Ar [#permalink] New post   11 Jul 2017, 03:43
Bunuel wrote:
The average (arithmetic mean) of integers r, s, t, u, and v is 100. Are exactly two of the integers greater than 100?

(1) Three of the integers are less than 50.
(2) None of the integers is equal to 100.


We have \(r+s+t+u+v=500\)

(1) Since we have \(r,s,t < 50 \implies r+s+t < 150 \implies u+v>350\)

If \(u = 50 \implies v > 300 > 100\). There is only one integer greater than 100
If \(u=150 \implies v > 200 > 100\). There are two integers greater than 100

Hence insufficient.

(2) We can't know how many numbers are greater than 100. Insufficient.

Combine (1) and (2) we still have either one or two integers greater than 100. Insufficient.

The answer is E
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Re: The average (arithmetic mean) of integers r, s, t, u, and v is 100. Ar [#permalink] New post   21 Nov 2020, 18:16
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Bunuel wrote:
The average (arithmetic mean) of integers r, s, t, u, and v is 100. Are exactly two of the integers greater than 100?

(1) Three of the integers are less than 50.
(2) None of the integers is equal to 100.


The total of the 5 integers is 500.

Statement 1:

We could have 2 integers greater than 100, or we could have 3 integers less than 50, one integer between 50 and 100, and only one integer greater than 100. Insufficient.

Statement 2:

This is basically useless information so insufficient.

Combined:

Since statement 2 barely provides information combined still insufficient.

Ans: E
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Re: The average (arithmetic mean) of integers r, s, t, u, and v is 100. Ar [#permalink] New post   29 Nov 2020, 22:51
Best way is to think of one negative integer, that ways A and B are ruled and so is C. E is clearly the answer.

Say U + V has to be 350. It can be either 150 + 200 (answers the Q) OR -100 + 450 (does not answer the Q)

St 2 says none of the integers is equal to 100. Well we can always have 99 and 101 (answering the Q) and we can also have 150 + rest of the integers as less than 100 (not answering the Q).

Merging the two statements, nothing new will be obtained. E is the answer.
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Re: The average (arithmetic mean) of integers r, s, t, u, and v is 100. Ar [#permalink]
29 Nov 2020, 22:51
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Bunuel
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