In a certain group, the average (arithmetic mean) age of the males is

Question

In a certain group, the average (arithmetic mean) age of the males is 28, and the average age of the females is 30. If there are 100 people in the group, how many of them are males?

(1) The average age of all 100 people is 28.9

(2) There are 10 more males than there are females.

StudiosTom · Answer

Statement 1:Since total 100 people ,so total age=100 *28.9 =2890
Men's mean=28 women's mean+30 ,looking at the total mean it is clear that there are more men than women.
Using basic math,if there are 50 men-50*28=1400 and 50 women -50*30=1500
total=1500+1400 =2900 which is greater than 2890 totaled above.So increasing one men decreases the average by 2,so total men=55,women=45
Hence  Sufficient

Statement 2:suppose there are w women .So men=10+w
Also m+w=100 ,
so using these equation it is clear to find the answer which is not required.

Hence  Sufficient

chetan2u · Answer

In a certain group, the average (arithmetic mean) age of the males is 28, and the average age of the females is 30. If there are 100 people in the group, how many of them are males?

(1) The average age of all 100 people is 28.9
We know to average age of both group and now the overall average group, we can find the ratio of two groups and thus the numbers.
 \frac{30-28.9}{30-28}*100=M......M=1.1*50=55 
Sufficient

(2) There are 10 more males than there are females.
M=10+F
M+F=100..
Two equation two variables..
Sufficient

D

Crytiocanalyst · Answer

(1) The average age of all 100 people is 28.9
We can find the number of men by 30-28.9/30-28 *100 = 1.1*50=55
and the women being 45
clearly sufficient

(2) There are 10 more males than there are females.
Since this is solving for 2 eqn in 2 variable we can conclusively arrive at an answer

Therefore IMO D

AshleyAshley · Answer

In a certain group, the average (arithmetic mean) age of the males is 28, and the average age of the females is 30. If there are 100 people in the group, how many of them are males?
 
(1) The average age of all 100 people is 28.9
 
(2) There are 10 more males than there are females.

Okay in this situation we should start from statement 2.

(2) There are 10 more males than there are females. So females + (females+10)=100. females=X => X+(X+10)=100
2x=90=> X=45 is females. So males are 55.

Now let's calculate the average age.

(1) The average age of all 100 people is 28.9

Males- 55*28=1540
Females - 45*30=1350 
Sum is 2890. Average is 28.9

The answer is C.

Shrutiv134 · Answer

Is there a better way to figure out for statement (1)?

Bunuel · Answer

The average age of males is 28, which is 0.9 below the overall average of 28.9.
The average age of females is 30, which is 1.1 above the overall average of 28.9.

This means the ratio of males to females must be in the reverse ratio of these differences:

males/females = 1.1/0.9 = 11/9.

So the group must have 55 males and 45 females to maintain the overall average. Basically, there must be more males to pull the overall average closer to their average than to that of the females.

General rule:

When two groups with different averages are combined, the sizes of the two groups are in the inverse ratio of the absolute differences between each group’s average and the overall average. The group whose average is closer to the overall average must be larger to pull the combined average in that direction.

adithya000 · Answer

Statement (1): The average age of all 100 people is 28.9 
 Let: 
 
  m = number of males  
  f = number of females   
  f=100−m
   
 The total age of the group:
28×m + 30×(100−m) = 28.9×100
 
 Solving: 
  28m+30(100−m)=2890
28m+3000−30m=2890
−2m=−110
m=55  
  Statement (1) alone is sufficient   
 
Statement (2): There are 10 more males than females 
 Let: 
 
  m=f+10  
  We know that m+f=100. So, f=m- 10.  
 Solving: 
  m+(m−10)=100
2m=110
m=55  
 Statement (2) alone is sufficient  
Therefore,  D .

In a certain group, the average (arithmetic mean) age of the males is

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

In a certain group, the average (arithmetic mean) age of the males is

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