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Martina earns one-sixth of her annual income during the mont [#permalink]

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21 Jul 2010, 22:22

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Martina earns one-sixth of her annual income during the month of June and one-eighth in August. Pam earns one-third of her annual income in June and one-fourth in August. Martina's earnings for June and August equal Pam's earnings for the same period. What portion of their combined annual income do the two girls earn during the ten months NOT including June and August?

Martina earns one-sixth of her annual income during the month of June and one-eighth in August. Pam earns one-third of her annual income in June and one-fourth in August. Martina's earnings for June and August equal Pam's earnings for the same period. What portion of their combined annual income do the two girls earn during the ten months NOT including June and August? (A) 1/8 (B) 7/24 (C) 7/18 (D) 11/18 (E) 7/8

Solution:

Lets assume that Martina earns 6000 in the entire year and Pam earns 3000 during the annual year. So, Martina: June = 1000 (1/6) August = 750 (1/8)

For Pam: June = 1000 (1/3) August = 750 (1/4) Since both their earnings are same for these 2 months (If you carefully observe, the ratios for Martina in those 2 months have just been halved for respective months as compared to Pam's). so net earnings for the entire year would be double for the income in those 2 months to be same.

So total earnings for both in the annual year = 9900 Earnings from June & August = 1750 + 1750 = 3500 Earnings during rest of the year = 5500

= 5500/9000 = 11/18.

I hope everything is clear..
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Martina's earnings for June and August equal Pam's earnings for the same period

=> x/8 + x/6 = y/3 + y/6 where x = martina' earning and y = pam's

=> 7x/24 = 7y/12 => x=2y Their combined income = x+y = 3y

For ten months their combined income = \(x-\frac{7x}{24}+ y-\frac{7y}{12}\)= \(\frac{17x}{24}+ \frac{5y}{12}\) = \(\frac{17y}{12}+ \frac{5y}{12}\)= \(\frac{22y}{12}\)

Required ratio = (22y/12 )/3y =\(\frac{11}{18}\)
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Re: Martina earns one-sixth of her annual income during the mont [#permalink]

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16 Nov 2015, 20:05

Hello from the GMAT Club BumpBot!

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Martina earns one-sixth of her annual income during the mont [#permalink]

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09 Dec 2015, 09:12

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rohitgoel15 wrote:

Martina earns one-sixth of her annual income during the month of June and one-eighth in August. Pam earns one-third of her annual income in June and one-fourth in August. Martina's earnings for June and August equal Pam's earnings for the same period. What portion of their combined annual income do the two girls earn during the ten months NOT including June and August?

(A) 1/8 (B) 7/24 (C) 7/18 (D) 11/18 (E) 7/8

Just pick some smart numbers, and it becomes very easy..... Martina's income = 24 June\(= \frac{1}{6} =4\) August \(= \frac{1}{8} =3\) Pam's income \(=\frac{1}{3} +\frac{1}{4}=\frac{7}{12}\) => \(\frac{7}{12}*x=7\), so\(x=12\) Because Pam's and Martina's income for June&August are equal So, combined income = 12+24=36, and they earned in June&August 14 means in other months 22 -->\(\frac{22}{36}=\frac{11}{18}\) Answer D
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Re: Martina earns one-sixth of her annual income during the mont [#permalink]

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14 Dec 2016, 12:06

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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