In a survey of X people it was found that 40% are men and the earnings

Question

In a survey of X people it was found that 40% are men and the earnings of 75% of the men are greater than $75000 per annum. 2/5 of the people surveyed earned more than $75000 per annum. What fraction of the total females earn less than or equal to $75000?

A) $\frac{2}{3}$

B) $\frac{1}{6}$

C) $\frac{5}{6}$

D) $\frac{1}{2}$

E) $\frac{1}{5}$

A)  \frac{2}{3}

B)  \frac{1}{6}

C)  \frac{5}{6}

D)  \frac{1}{2}

E)  \frac{1}{5}

gsingh0711 · Answer

Explanation:

Let the total number of people be 100. Using the given information we can fill the following table

Men Women Total
Earn > 75000 75% of 40 = 30 (2/5) of 100 = 40
Earn ≤ 75000 
Total 4
0

60 100
The table can be completed as below:

Men Women Total
Earn > 75000 30 10 40
Earn ≤ 75000 10 50 60
Total 4
0

60 100
From the table, 50 females out of 60 earn less or equal to $75000.
⇒ The required fraction = 5/6

Answer: C.

I think, I deserve a kudus LOL

PKN · Answer

Hi  gsingh0711 ,
Kindly allow us to solve your posted questions.
You may post the official explanation later.

Anticipating your kind co-operation.

GMAT215 · Answer

In a survey of X people it was found that 40% are men and the earnings of 75% of the men are greater than $75000 per annum. 2/5 of the people surveyed earned more than $75000 per annum. What fraction of the total females earn less than or equal to $75000?

A) $\frac{2}{3}$

B) $\frac{1}{6}$

C) $\frac{5}{6}$

D) $\frac{1}{2}$

E) $\frac{1}{5}$

more than 75 less than 75 Total
men 0.3(given :75% of men) 0.1(balance) 0.4 (given)
women 0.1 (balance) 0.5 (balance) 0.6 (balance)
Total 0.4 (given)

hope it helps!!!

adstudy · Answer

Men = 40% of total population

Hence,
  Women = 60% of total population

Now question says, 
75% of the men earn greater than $75000 per annum

That means, 75% of 40% of men earn greater than $75000 per annum =   30% of all men   ------ (1)

Now question also says,
 \frac{2}{5}  of the people surveyed earned more than $75000 per annum.

Now  \frac{2}{5}  of 100% =   40%
  
Out of the 40%, 30% are men --------- From (1)

That is   remaining 10% are women  . ----- (2)

Now we need to find,

fraction of the total females earn less than or equal to $75000.

If 10% out of the 60% women earned more than $75000 per annum, then,

50% out of 60% women earned less than or equal to $75000 per annum  .

that makes it  \frac{5}{6}

Hence C.

GyMrAT · Answer

Hi Mods  Bunuel   chetan2u

Please move the question to PS forum.

Thanks,
GyM

Bunuel · Answer

______________
Done. Thank you.

Abhishek009 · Answer

Let the total Population be 100 , So Men = 40 & Women = 60

75% of the men ie 30 men earns > 75000

Further 2/5th (Or 40people ) earn > 75000 ; Or we have 10 women earns > 75000

Hence we have 50 women earning < 75000

Thus, the fraction of the total females earn less than or equal to $75000 = 50/60 = 5/6, Answer must be (C)

Kinshook · Answer

Given: 1. In a survey of X people it was found that 40% are men and the earnings of 75% of the men are greater than $75000 per annum. 2. 2/5 of the people surveyed earned more than $75000 per annum. Asked: What fraction of the total females earn less than or equal to $75000? Screenshot 2020-04-29 at 7.48.48 PM.png Fraction of the total females that earn less than or equal to $75000 = 50%/60% = 5/6 IMO C Hqv77dz3ClE

bumpbot · Answer

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In a survey of X people it was found that 40% are men and the earnings

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In a survey of X people it was found that 40% are men and the earnings

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