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# If the average (arithmetic mean) of three positive numbers is 30, how

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Joined: 02 Sep 2009
Posts: 58424
If the average (arithmetic mean) of three positive numbers is 30, how  [#permalink]

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01 Jan 2018, 10:44
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45% (medium)

Question Stats:

65% (01:26) correct 35% (01:21) wrong based on 43 sessions

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If the average (arithmetic mean) of three positive numbers is 30, how many of the numbers are greater than 30?

(1) The largest number is 50.
(2) The smallest number is greater than 10.

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Joined: 23 Feb 2017
Posts: 58
Re: If the average (arithmetic mean) of three positive numbers is 30, how  [#permalink]

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01 Jan 2018, 23:20
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Average of three positive terms is 30
Sum of three terms is 30*3 =90

Statement 1 The largest number is 50.
Terms can be 20,20,50 (only one term greater than 30)
or 8,32, 50 (two terms greater than 30) not sufficient

Statement 2 The smallest number is greater than 10.
Terms can be 11, 11, 68 (only one term greater than 30)
or 11, 39,40 (two terms greater than 30) not sufficient

Combined Statement 1 & 2
Terms 50, 11, 29 (only one term greater than 30) Sufficient

Ans C
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If the average (arithmetic mean) of three positive numbers is 30, how  [#permalink]

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06 Jun 2019, 13:45
Bunuel wrote:
If the average (arithmetic mean) of three positive numbers is 30, how many of the numbers are greater than 30?

(1) The largest number is 50.
(2) The smallest number is greater than 10.

Statement 1:

x, y, 50 = avg 30

put them on number line

----x-------y--------50-----

let one of the numbers be 30 (equal to avg to get the lowest possible value of x)
----x------30------50-----

if x is <10; then the avg will fall below 30 (since the gap b/w x and y will be more than gap b/w y and 50=20 ). If x>10; avg will be above 30

Not sufficient.

Statement 2:
If x>10,

-----10------y-------z----
Not sufficient

Combining 1 &2
-----10-----y------50-----
yes, one number can be greater than 30, i.e. y (and not both because then the avg can't be 30)

sufficient

Option C.
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If the average (arithmetic mean) of three positive numbers is 30, how   [#permalink] 06 Jun 2019, 13:45
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