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

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Manager
Joined: 02 Mar 2018
Posts: 56
Location: India
GMAT 1: 640 Q51 V26
GPA: 3.1
In a survey of X people it was found that 40% are men and the earnings  [#permalink]

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Updated on: 05 Aug 2018, 10:47
5
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Difficulty:

65% (hard)

Question Stats:

61% (02:08) correct 39% (02:44) wrong based on 94 sessions

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) $$\frac{1}{5}$$ Originally posted by gsingh0711 on 05 Aug 2018, 09:49. Last edited by generis on 05 Aug 2018, 10:47, edited 1 time in total. Edited and formatted the question, renamed the topic Manager Joined: 02 Mar 2018 Posts: 56 Location: India GMAT 1: 640 Q51 V26 GPA: 3.1 Re: In a survey of X people it was found that 40% are men and the earnings [#permalink] ### Show Tags 05 Aug 2018, 09:49 1 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

I think, I deserve a kudus LOL
Director
Joined: 14 Dec 2017
Posts: 505
Location: India
In a survey of X people it was found that 40% are men and the earnings  [#permalink]

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07 Aug 2018, 10:58
1
Hi Mods Bunuel chetan2u

Please move the question to PS forum.

Thanks,
GyM
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Joined: 01 Oct 2017
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WE: Supply Chain Management (Energy and Utilities)
Re: In a survey of X people it was found that 40% are men and the earnings  [#permalink]

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05 Aug 2018, 09:54
gsingh0711 wrote:
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? 2/3 1/6 5/6 1/2 1/5 Hi gsingh0711, Kindly allow us to solve your posted questions. You may post the official explanation later. Anticipating your kind co-operation. _________________ Regards, PKN Rise above the storm, you will find the sunshine Manager Joined: 01 Feb 2018 Posts: 73 Location: India Concentration: Entrepreneurship, Marketing GPA: 4 WE: Consulting (Consulting) Re: In a survey of X people it was found that 40% are men and the earnings [#permalink] ### Show Tags 07 Aug 2018, 10:26 [quote="gsingh0711"]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?

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!!!
Manager
Joined: 11 Mar 2018
Posts: 157
Re: In a survey of X people it was found that 40% are men and the earnings  [#permalink]

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07 Aug 2018, 10:42
gsingh0711 wrote:
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) $$\frac{1}{5}$$ 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. Math Expert Joined: 02 Sep 2009 Posts: 60647 Re: In a survey of X people it was found that 40% are men and the earnings [#permalink] ### Show Tags 08 Aug 2018, 03:04 GyMrAT wrote: Hi Mods Bunuel chetan2u Please move the question to PS forum. Thanks, GyM ______________ Done. Thank you. _________________ Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4871 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: In a survey of X people it was found that 40% are men and the earnings [#permalink] ### Show Tags 08 Aug 2018, 07:43 1 gsingh0711 wrote: 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) $$\frac{1}{5}$$

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)
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Re: In a survey of X people it was found that 40% are men and the earnings   [#permalink] 08 Aug 2018, 07:43
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# In a survey of X people it was found that 40% are men and the earnings

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