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The eSoroban device is available in two colors, orange and green.

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The eSoroban device is available in two colors, orange and green.  [#permalink]

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New post 25 May 2019, 13:07
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The eSoroban device is available in two colors, orange and green. In 2013, 60% of the eSoroban devices sold were purchased by women, \(\frac{5}{12}\) of whom purchased the orange device. If an equal number of orange and green eSoroban devices were sold in 2013, what fraction of men who purchased an eSoroban in 2013 purchased the green device?

A. \(\frac{3}{10}\)

B. \(\frac{3}{8}\)

C. \(\frac{5}{12}\)

D. \(\frac{1}{2}\)

E. \(\frac{5}{7}\)
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Re: The eSoroban device is available in two colors, orange and green.  [#permalink]

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New post 25 May 2019, 14:41
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Let the total number of devices sold= lcm(5,12)=60
Orange devices=30, Green devices=30
Devices sold to women= (3/5)*60=36
orange devices sold to women= (5/12)*36= 15
green devices sold to women= 36-15=21

green devices sold to men=30-21=9
devices sold to men= 60-36=24

fraction of men who purchased an eSoroban in 2013 purchased the green device=9/24=3/8
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Re: The eSoroban device is available in two colors, orange and green.  [#permalink]

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New post 26 May 2019, 05:37
nick1816 wrote:
Let the total number of devices sold= lcm(5,12)=60
Orange devices=30, Green devices=30
Devices sold to women= (3/5)*60=36
orange devices sold to women= (5/12)*36= 15
green devices sold to women= 36-15=21

green devices sold to men=30-21=9
devices sold to men= 60-36=24

fraction of men who purchased an eSoroban in 2013 purchased the green device=9/24=3/8


Question here.

Where in the problem state that the product is produced equally in two colors?

There could have been more green and vice versa, right?

So how did you know it was a 50/50 split?
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The eSoroban device is available in two colors, orange and green.  [#permalink]

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New post 26 May 2019, 06:05
The eSoroban device is available in two colors, orange and green. In 2013, 60% of the eSoroban devices sold were purchased by women, 5/12 of whom purchased the orange device. If an equal number of orange and green eSoroban devices were sold in 2013, what fraction of men who purchased an eSoroban in 2013 purchased the green device?

Question here.

Where in the problem state that the product is produced equally in two colors?

There could have been more green and vice versa, right?

So how did you know it was a 50/50 split?[/quote]

Posted from my mobile device
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Re: The eSoroban device is available in two colors, orange and green.  [#permalink]

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New post 11 Aug 2019, 01:19
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energetics wrote:
The eSoroban device is available in two colors, orange and green. In 2013, 60% of the eSoroban devices sold were purchased by women, \(\frac{5}{12}\) of whom purchased the orange device. If an equal number of orange and green eSoroban devices were sold in 2013, what fraction of men who purchased an eSoroban in 2013 purchased the green device?

A. \(\frac{3}{10}\)

B. \(\frac{3}{8}\)

C. \(\frac{5}{12}\)

D. \(\frac{1}{2}\)

E. \(\frac{5}{7}\)



org green Total
Men 25 15 40
women 25 35 60
Total 50 50 100



Required Fraction: 15/40 = 3/5
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The eSoroban device is available in two colors, orange and green.  [#permalink]

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New post 11 Aug 2019, 02:38
It takes me 9min to sort out:(
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Re: The eSoroban device is available in two colors, orange and green.  [#permalink]

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New post 11 Aug 2019, 02:58
energetics wrote:
The eSoroban device is available in two colors, orange and green. In 2013, 60% of the eSoroban devices sold were purchased by women, \(\frac{5}{12}\) of whom purchased the orange device. If an equal number of orange and green eSoroban devices were sold in 2013, what fraction of men who purchased an eSoroban in 2013 purchased the green device?

A. \(\frac{3}{10}\)

B. \(\frac{3}{8}\)

C. \(\frac{5}{12}\)

D. \(\frac{1}{2}\)

E. \(\frac{5}{7}\)


Let Total People, who purchased devices, be 100.

Therefore Women who purchased devices = 60 (According to question)

and hence Men who purchased devices = 40 (100 - 60) -- (1)

Now \(\frac{5}{12}\) is the fraction of orange device of devices purchased by women. That is equal to 25

Hence remaining devices, purchased by women, are green and are equal to = 60 - 25 = 35

Now from question we know, Total Green devices = Total Orange devices

Hence 35(Green devices with women) + G(Green devices with men) = 25(Orange devices with women) + O(Orange devices with men)

which we can write as O - G = 10 -- (2)

And also O + G = 40 -- (3) [From (1)]

From (2) and (3), we get

O = 25
G = 15

fraction of men who purchased an eSoroban in 2013 purchased the green device = \(\frac{Green devices purchased by men}{Total Men who purchased eSorban Devices}\)

Hence \(\frac{15}{40}\)

=> \(\frac{3}{8}\) ------- Answer (B)
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The eSoroban device is available in two colors, orange and green.  [#permalink]

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New post 15 Sep 2019, 02:30
energetics wrote:
The eSoroban device is available in two colors, orange and green. In 2013, 60% of the eSoroban devices sold were purchased by women, \(\frac{5}{12}\) of whom purchased the orange device. If an equal number of orange and green eSoroban devices were sold in 2013, what fraction of men who purchased an eSoroban in 2013 purchased the green device?

A. \(\frac{3}{10}\)

B. \(\frac{3}{8}\)

C. \(\frac{5}{12}\)

D. \(\frac{1}{2}\)

E. \(\frac{5}{7}\)


Given:
1. The eSoroban device is available in two colors, orange and green.
2. In 2013, 60% of the eSoroban devices sold were purchased by women, \(\frac{5}{12}\) of whom purchased the orange device.
3. An equal number of orange and green eSoroban devices were sold in 2013

Asked: What fraction of men who purchased an eSoroban in 2013 purchased the green device?

-----------Orange----------Green--------------Total
Men---------15%-------------25%-------------40%
Women------25%-------------35%----------------60%
Total --------50%------------50%--------------100%

Fraction of men purchasing green device = 15%/40% = 3/8

IMO B
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Re: The eSoroban device is available in two colors, orange and green.  [#permalink]

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New post 23 Nov 2019, 03:23
Kinshook wrote:
energetics wrote:
The eSoroban device is available in two colors, orange and green. In 2013, 60% of the eSoroban devices sold were purchased by women, \(\frac{5}{12}\) of whom purchased the orange device. If an equal number of orange and green eSoroban devices were sold in 2013, what fraction of men who purchased an eSoroban in 2013 purchased the green device?

A. \(\frac{3}{10}\)

B. \(\frac{3}{8}\)

C. \(\frac{5}{12}\)

D. \(\frac{1}{2}\)

E. \(\frac{5}{7}\)


Given:
1. The eSoroban device is available in two colors, orange and green.
2. In 2013, 60% of the eSoroban devices sold were purchased by women, \(\frac{5}{12}\) of whom purchased the orange device.
3. An equal number of orange and green eSoroban devices were sold in 2013

Asked: What fraction of men who purchased an eSoroban in 2013 purchased the green device?

-----------Orange----------Green--------------Total
Men---------15%-------------25%-------------40%
Women------25%-------------35%----------------60%
Total --------50%------------50%--------------100%

Fraction of men purchasing green device = 15%/40% = 3/8

IMO B


But in the vertical columns of both orange and green the addition becomes

Orange = 15% + 25% = 40%, which is not equal to 50%

Same goes for green devices?

Can you explain?
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Re: The eSoroban device is available in two colors, orange and green.   [#permalink] 23 Nov 2019, 03:23
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