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

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Math Expert
Joined: 02 Sep 2009
Posts: 47977
In a certain group, the average (arithmetic mean) age of the males is  [#permalink]

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25 Jul 2018, 04:15
00:00

Difficulty:

55% (hard)

Question Stats:

67% (01:26) correct 33% (01:41) wrong based on 38 sessions

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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.

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In a certain group, the average (arithmetic mean) age of the males is  [#permalink]

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Updated on: 25 Jul 2018, 04:36
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
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Originally posted by AnkitOrYadav on 25 Jul 2018, 04:31.
Last edited by AnkitOrYadav on 25 Jul 2018, 04:36, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 6544
Re: In a certain group, the average (arithmetic mean) age of the males is  [#permalink]

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25 Jul 2018, 04:31
1
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
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: In a certain group, the average (arithmetic mean) age of the males is &nbs [#permalink] 25 Jul 2018, 04:31
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