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Maria pays 1/8 of her monthly income for food, 1/8 for utilities, 1/8

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Maria pays 1/8 of her monthly income for food, 1/8 for utilities, 1/8 [#permalink]

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New post 16 Aug 2017, 21:58
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Maria pays \(\frac{1}{8}\) of her monthly income for food, \(\frac{1}{8}\) for utilities, \(\frac{1}{8}\) for student loans, and \(\frac{4}{5}\) of the remainder for rent. If at the end of each month Maria puts \(\frac{1}{2}\) of her remaining income into a CD account, what portion of her monthly income does she puts into the account?


A. \(\frac{1}{8}\)

B. \(\frac{1}{10}\)

C. \(\frac{7}{80}\)

D. \(\frac{1}{16}\)

E. \(\frac{1}{20}\)
[Reveal] Spoiler: OA

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Last edited by Bunuel on 16 Aug 2017, 23:28, edited 1 time in total.
Renamed the topic and edited the question.

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Re: Maria pays 1/8 of her monthly income for food, 1/8 for utilities, 1/8 [#permalink]

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New post 16 Aug 2017, 22:14
Assume her income as 80
so payment for
Food = \(\frac{1}{8}\) * 80 = 10
Utilities = \(\frac{1}{8}\) * 80 = 10
Student Loan = \(\frac{1}{8}\) * 80 =10
Remainder = 80-(10+10+10) = 50
Rent = \(\frac{4}{5}\) * 50 = 40
Remainder = 50-40=10
Account = \(\frac{1}{2}\) * 10 =5
Fraction of Income into account = \(\frac{5}{80}\) = \(\frac{1}{16}\)
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Re: Maria pays 1/8 of her monthly income for food, 1/8 for utilities, 1/8 [#permalink]

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New post 16 Aug 2017, 23:34
HolaMaven wrote:
Maria pays \(\frac{1}{8}\) of her monthly income for food, \(\frac{1}{8}\) for utilities, \(\frac{1}{8}\) for student loans, and \(\frac{4}{5}\) of the remainder for rent. If at the end of each month Maria puts \(\frac{1}{2}\) of her remaining income into a CD account, what portion of her monthly income does she puts into the account?


A. \(\frac{1}{8}\)

B. \(\frac{1}{10}\)

C. \(\frac{7}{80}\)

D. \(\frac{1}{16}\)

E. \(\frac{1}{20}\)


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Hope it helps.
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Maria pays 1/8 of her monthly income for food, 1/8 for utilities, 1/8 [#permalink]

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HolaMaven wrote:
Maria pays \(\frac{1}{8}\) of her monthly income for food, \(\frac{1}{8}\) for utilities, \(\frac{1}{8}\) for student loans, and \(\frac{4}{5}\) of the remainder for rent. If at the end of each month Maria puts \(\frac{1}{2}\) of her remaining income into a CD account, what portion of her monthly income does she puts into the account?

A. \(\frac{1}{8}\)

B. \(\frac{1}{10}\)

C. \(\frac{7}{80}\)

D. \(\frac{1}{16}\)

E. \(\frac{1}{20}\)

I think HolaMaven 's approach is the quickest. IMO this problem's challenge is to be meticulous regardless of approach. Easiest for me after reading the prompt: track on what remains after each deduction.

1) What portion is left after Maria pays for food, utilities, and loans? Each is \(\frac{1}{3}\) of her total monthly income ( = 1).

1 - [3 * \((\frac{1}{8})\)]

1 - \(\frac{3}{8}\)= \(\frac{5}{8}\) remains

2) Rent = \(\frac{4}{5}\) of the remaining \(\frac{5}{8}\) -- what portion is left after she pays rent?

\(\frac{5}{8}\) -\((\frac{4}{5}\) *\(\frac{5}{8})\) =

\(\frac{5}{8}\) - \(\frac{1}{2}\) = \(\frac{1}{8}\) remaining

3) CD = \(\frac{1}{2}\) of the remaining \(\frac{1}{8}\)

\(\frac{1}{2}\) * \(\frac{1}{8}\) = \(\frac{1}{16}\)

\(\frac{1}{16}\) is the portion of her monthly income that goes to her CD account

Answer D

Kudos [?]: 182 [1], given: 494

Maria pays 1/8 of her monthly income for food, 1/8 for utilities, 1/8   [#permalink] 17 Aug 2017, 08:18
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Maria pays 1/8 of her monthly income for food, 1/8 for utilities, 1/8

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