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if the average of three numbers is 37 and least number is 18

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if the average of three numbers is 37 and least number is 18 [#permalink] New post 15 Sep 2018, 23:48
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Question Stats:

50% (01:06) correct 50% (01:25) wrong based on 38 sessions
if the average of three distinct numbers is 37 and least number is 18 which of the following could be greatest number?

Select all that applies.

A:40
B:46
C:49
D:58
E:74
F:77
[Reveal] Spoiler: OA
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Re: if the average of three numbers is 37 and least number is 18 [#permalink] New post 16 Sep 2018, 00:08
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x+y+z/3= 37

sum of 3 nos = 111

since least number is x=18

y+z=93

check each option
1) 40 : 93-40=53 , therefore wrong choice (53 > 40)
2) 58 : 93-58=35 , therefore correct (58 > 35)
similarly check other options
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Re: if the average of three numbers is 37 and least number is 18 [#permalink] New post 02 Jul 2020, 22:28
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The average means that we have (x+y+z)/3

If this arithmetic mean is 37 and the least number is 18.

(x+y+18)/3=37

(x+y)=93

Now for this sum,

a)The greatest number must be greater than the half of the quantity.
b)At the same time, the least value of this sum, must be greater than 18. That means must be at least 19.

So, solving:

a)93/2= 46.5 rounded ---> 47. So the least value for the greatest number is 47
b)x+19=93 ----> 74. So the maximum value of the greatest number is 74.

As a result the only options that can be between this two numbers are: 49,58 and 74.

Answer: C, D, E
Re: if the average of three numbers is 37 and least number is 18   [#permalink] 02 Jul 2020, 22:28
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if the average of three numbers is 37 and least number is 18

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