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

Question

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.

Bunuel · Accepted Answer

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.

AKG1593 · Answer

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.

nutshell · Answer

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).

Cosmas · Answer

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.

gmatzpractice · Answer

Sum=200

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

Statements combined are insufficient. E

merajul · Answer

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.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards