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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The average of 63, 37 and x is greater than the average of the

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Senior Manager  V
Joined: 25 Sep 2018
Posts: 446
Location: United States (CA)
Concentration: Finance, Strategy
GMAT 1: 640 Q47 V30 GPA: 3.97
WE: Investment Banking (Investment Banking)
The average of 63, 37 and x is greater than the average of the  [#permalink]

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Question Stats: 49% (02:24) correct 51% (02:37) wrong based on 45 sessions

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The average of 63, 37 and x is greater than the average of the multiples of 3 between 1 and 111, inclusive. Which of the following is a possible value of x?
I. 64 II. 71 III. 75 IV. 85
A) I, II, Ill, and IV
B) IV only
C) II, Ill and IV
D) III and IV
E). None of these

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Why do we fall?...So we can learn to pick ourselves up again
Director  S
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 531
Location: India
Re: The average of 63, 37 and x is greater than the average of the  [#permalink]

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1
Hi,

It is a simple question testing the concept of Average.

Average = Total / Number of elements

So, average of three numbers 63,37 and x is

(100+x)/3

Average of multiples of 3 between 1 and 111(inclusive) is,

Multiples of 3 are,

3 ,6, 9, …111

We can find the average of multiples of 3 in using different ways,

One such way is,

Average = (3+111)/2

Rule: If a list of numbers were evenly spaced (common difference) then Average of the entire list is equal to the average of first element and last element of the set.

So average = 57

Given,

(100+x)/3 > 57

100 + x > 171

x > 71

So the answers are 75 and 85.

Hope this helps.
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GMAT Mentors Director  P
Joined: 24 Nov 2016
Posts: 758
Location: United States
Re: The average of 63, 37 and x is greater than the average of the  [#permalink]

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Abhi077 wrote:
The average of 63, 37 and x is greater than the average of the multiples of 3 between 1 and 111, inclusive. Which of the following is a possible value of x?
I. 64 II. 71 III. 75 IV. 85
A) I, II, Ill, and IV
B) IV only
C) II, Ill and IV
D) III and IV
E). None of these

rule: avg=sum•n
rule: multiple(x) between range: greatestm(x)-leastm(x)/x+1
rule: average of an arithmetic progression: greatestm(x)+leastm(x)/2
rule: any number is divisible by 3 if the sum of its digits is divisibly by 3

avg m(3) from 1 to 111 inclusive: greatestm(3)=111, leastm(3)=3, avg=111+3/2=57

given:
[63+37+x]/3>57
100+x>171
x>71 Re: The average of 63, 37 and x is greater than the average of the   [#permalink] 30 Jul 2019, 06:55
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# The average of 63, 37 and x is greater than the average of the  