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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  [#permalink]

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New post Updated on: 05 Aug 2018, 10:47
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  65% (hard)

Question Stats:

57% (01:44) correct 43% (02:38) wrong based on 77 sessions

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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
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Re: In a survey of X people it was found that 40% are men and the earnings  [#permalink]

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New post 05 Aug 2018, 09:49
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
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Re: In a survey of X people it was found that 40% are men and the earnings  [#permalink]

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New post 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.
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Re: In a survey of X people it was found that 40% are men and the earnings  [#permalink]

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New post 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!!!
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    Re: In a survey of X people it was found that 40% are men and the earnings  [#permalink]

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    New post 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.
    _________________

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

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

    Please move the question to PS forum.


    Thanks,
    GyM
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    Re: In a survey of X people it was found that 40% are men and the earnings  [#permalink]

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    New post 08 Aug 2018, 03:04
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    Re: In a survey of X people it was found that 40% are men and the earnings  [#permalink]

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    New post 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 &nbs [#permalink] 08 Aug 2018, 07:43
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