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If the average (arithmetic mean) of 4 numbers is 50, how man

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If the average (arithmetic mean) of 4 numbers is 50, how man  [#permalink]

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New post 20 Feb 2014, 00:11
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If the average (arithmetic mean) of 4 numbers is 50, how many of the numbers are greater than 50 ?

(1) None of the four numbers is equal to 50.
(2) Two of the numbers are equal to 25.

Data Sufficiency
Question: 101
Category: Arithmetic Statistics
Page: 160
Difficulty: 650


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Re: If the average (arithmetic mean) of 4 numbers is 50, how man  [#permalink]

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New post 20 Feb 2014, 00:12
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SOLUTION

If the average (arithmetic mean) of 4 numbers is 50, how many of the numbers are greater than 50 ?

It's almost always better to express the average in terms of the sum, so we are given that the sum of the 4 numbers is 4*50 =200.

(1) None of the four numbers is equal to 50. Clearly insufficient.

(2) Two of the numbers are equal to 25. Also insufficient, consider {25, 25, 30, 120} and {25, 25, 75, 75}.

(1)+(2) The sets from (2) are still OK to consider, since they do not contradict (1), which means that even taken together the statements are not sufficient to answer the question.

Answer: E.
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Re: If the average (arithmetic mean) of 4 numbers is 50, how man  [#permalink]

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New post 20 Feb 2014, 22:45
Option E.
From Statement 1:Let the 4 nos. be a,b,c,d
Given;a+b+c+d=200
None of the 4 nos. is 50.
a=40;
b=40
c=60
d=60
Ans to the question=2
But if a=40
b=51
c=51
d=58
Ans to the ques=3.
Not suff.

From S2:Let the two nos a=b=25
Therefore c+d=200-50=150
Case 1:c=40 and d=110
Ans to the ques=1

Case 2:c=55 and d=95
Ans to the ques=2
Not suff.

Combining the two statements.
a=b=25
therefore c+d=150 (None of the values=50)
We can consider the same two cases as in S2 to get different answers.Not sufficient.
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Re: If the average (arithmetic mean) of 4 numbers is 50, how man  [#permalink]

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New post 21 Feb 2014, 00:41
1
Average = Sum/Number;
Therefore, Sum = 50 * 4 = 200;

Let the nos. be a, b, c and d.
a + b + c + d = 200;

Statement 1:
Since none of the 4 numbers is equal to 50, they can have a wide range such as a, b = 25 & c,d=75; etc...

Not sufficient.

Statement 2:
Lets say a & b = 25;
So, c + d = 200 - 150 = 150;
Not sufficient, since c & d can have different possibilites.

Combining the statements, we still have a scenario similar to Statement 2.

Ans is (E).
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Re: If the average (arithmetic mean) of 4 numbers is 50, how man  [#permalink]

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New post 21 Feb 2014, 06:01
1
The sum of these numbers,n, is 200=n/4=50.
1) if non of the numbers equal 50, then the set can be as follows: (1;1;1;197) or (60,70,35,35)
2) if two of the numbers are 25 and 25, the sets can still be (25;25;99;51) or (25;25;30;120)

Together (1) and (2): we can take the example in (2) above. Still insufficient.

Answer E.
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Re: If the average (arithmetic mean) of 4 numbers is 50, how man  [#permalink]

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New post 26 Jun 2018, 12:11
Sum=200

25, 25, 30, 120
25, 25, 60, 90

Statements combined are insufficient. E
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Re: If the average (arithmetic mean) of 4 numbers is 50, how man &nbs [#permalink] 26 Jun 2018, 12:11
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