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# Martina earns one-sixth of her annual income during the month of June

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Math Expert
Joined: 02 Sep 2009
Posts: 60778
Martina earns one-sixth of her annual income during the month of June  [#permalink]

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07 Nov 2019, 01:52
00:00

Difficulty:

55% (hard)

Question Stats:

63% (03:40) correct 38% (02:44) wrong based on 32 sessions

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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?

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

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Joined: 18 Aug 2017
Posts: 5751
Location: India
Concentration: Sustainability, Marketing
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WE: Marketing (Energy and Utilities)
Re: Martina earns one-sixth of her annual income during the month of June  [#permalink]

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07 Nov 2019, 10:02
1
1
Martina salary = 24
June earned = 4
August earned = 3
balance 10 months = 24-7 ; 17
Pam salary = 12
June earned = 4
August earned = 3
balance 10 months = 12-7 ; 5
Martina's earnings for June and August equal Pam's earnings for the same period ; both are 7
total combined income = 24+12 ; 36
so total 10 months combined salary = 17+5 ; 22
22/36 ; 11/18
IMO D

Bunuel 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

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Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9167
Location: United States (CA)
Re: Martina earns one-sixth of her annual income during the month of June  [#permalink]

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12 Nov 2019, 20:18
Bunuel 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

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Martina earns 1/6 + 1/8 = 4/24 + 3/24 = 7/24 of her total annual income in June and August.

Pam earns ⅓ + 1/4 = 4/12 + 3/12 = 7/12 = 14/24 of her annual income in June and August.

Even though they earn the same in those months, we see that Martina’s annual income is twice Pam’s. Thus, we can let Pam’s salary = 24 and Martina’s = 48.

Thus, in the months not including June and August, Martina earns 17/24 x 48 = 34 and Pam earns 10/24 x 24 = 10.

So the fraction of their combined annual income earned in the other months is:

(34 + 10)/( 48 + 24) = 44/72 = 11/18

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Re: Martina earns one-sixth of her annual income during the month of June   [#permalink] 12 Nov 2019, 20:18
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