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

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

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11 Jul 2017, 02:52
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Difficulty:

35% (medium)

Question Stats:

57% (01:22) correct 43% (01:19) wrong based on 45 sessions

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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]

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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.

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Re: The average (arithmetic mean) of integers r, s, t, u, and v is 100. Ar   [#permalink] 11 Jul 2017, 03:43
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