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Difficulty: 555-605 Level,    Statistics and Sets Problems,                      
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Re: If the average (arithmetic mean) of 4 numbers is 50, how man [#permalink]
1
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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]
1
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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]
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 [#permalink]
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.

I attempted the question in 1:12 Mins and choose incorrect option B. However, after careful reading again, I thought the logic would be as below -

(1) says all the four nos are either >50 or <50. But dont know the answer. NOT SUFFICIENT.

(2) says, 2*25=50, Sum of balance two = 200-50=150. Now this is where I did wrong.I took an average of the balance two, 150/2=75 and considered B as the right answer.

However, after going through the question again, I found, no where it is written both the nos. are equal or not. Further I dont know any of the no, so that I can deduce the other no. So even though sum of both coming 150, it can be as 75+75, 40+110, 50+100.....etc.

(1) + (2) is out of question.

Thus E should be the correct answer choice.
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Re: If the average (arithmetic mean) of 4 numbers is 50, how man [#permalink]
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Re: If the average (arithmetic mean) of 4 numbers is 50, how man [#permalink]
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