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John invested 1/4 of A dollars in an investment fund, and placed the r

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John invested 1/4 of A dollars in an investment fund, and placed the r  [#permalink]

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New post 06 Jul 2018, 00:46
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[GMAT math practice question]

John invested \(\frac{1}{4}\) of A dollars in an investment fund, and placed the remaining \(\frac{3}{4}\) of A dollars in a savings account. If he made a 4p% loss on the fund, and a p% profit on the savings account, what was his total profit (or loss), in terms of A and p? (A negative value represents a loss.)

\(A. \frac{–Ap}{400}\)
\(B. 0\)
\(C. \frac{Ap}{400}\)
\(D. \frac{Ap}{200}\)
\(E. \frac{Ap}{100}\)

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Re: John invested 1/4 of A dollars in an investment fund, and placed the r  [#permalink]

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New post 06 Jul 2018, 01:05
MathRevolution wrote:
[GMAT math practice question]

John invested \(\frac{1}{4}\) of A dollars in an investment fund, and placed the remaining \(\frac{3}{4}\) of A dollars in a savings account. If he made a 4p% loss on the fund, and a p% profit on the savings account, what was his total profit (or loss), in terms of A and p? (A negative value represents a loss.)

\(A. \frac{–Ap}{400}\)
\(B. 0\)
\(C. \frac{Ap}{400}\)
\(D. \frac{Ap}{200}\)
\(E. \frac{Ap}{100}\)


Take A as 400, so two parts 1/4 = 100 and 3/4=300...
And let p be 10%
So 4*10=40% loss on 100= 40
10% profit on 300 = 30
So loss =40-30=10

Put in the choices..
A. -Ap/400=-400*10/400=-10

Ans A
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Re: John invested 1/4 of A dollars in an investment fund, and placed the r  [#permalink]

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New post 06 Jul 2018, 02:29
MathRevolution wrote:
[GMAT math practice question]

John invested \(\frac{1}{4}\) of A dollars in an investment fund, and placed the remaining \(\frac{3}{4}\) of A dollars in a savings account. If he made a 4p% loss on the fund, and a p% profit on the savings account, what was his total profit (or loss), in terms of A and p? (A negative value represents a loss.)

\(A. \frac{–Ap}{400}\)
\(B. 0\)
\(C. \frac{Ap}{400}\)
\(D. \frac{Ap}{200}\)
\(E. \frac{Ap}{100}\)


Algebra Approach:-

Head:- Investment--------------------------------------------------Saving

Dollar:- \(\frac{A}{4}\)------------------------------------------------------------------\(\frac{3A}{4}\)
Loss or Profit:- \(\frac{A}{4}*4p%\)----------------------------------------------------------\(\frac{3}{4A}*p%\)
Amount with John
after loss
or profit :-\(\frac{A}{4}\)-\(\frac{4Ap}{400}\)------------------------------------------------------\(\frac{3A}{4}\)*+\(\frac{3Ap}{400}\)

Total profit or loss=(Amount with John after loss or profit)-A=\((\frac{A}{4}-\frac{4Ap}{400}+\frac{3A}{4}+\frac{3Ap}{400})-A\)
=\(A-\frac{Ap}{400}-A\)
=\(\frac{-Ap}{400}\)
Ans. Option (A) Loss case.
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John invested 1/4 of A dollars in an investment fund, and placed the r  [#permalink]

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New post 06 Jul 2018, 02:36
MathRevolution wrote:
[GMAT math practice question]

John invested \(\frac{1}{4}\) of A dollars in an investment fund, and placed the remaining \(\frac{3}{4}\) of A dollars in a savings account. If he made a 4p% loss on the fund, and a p% profit on the savings account, what was his total profit (or loss), in terms of A and p? (A negative value represents a loss.)

\(A. \frac{–Ap}{400}\)
\(B. 0\)
\(C. \frac{Ap}{400}\)
\(D. \frac{Ap}{200}\)
\(E. \frac{Ap}{100}\)


Let \(A=40\)

Amount invested in the fund = \(\frac{1}{4} * 40 = 10\)
Since \(4p = 4*10 = 40\), John loses 40% of his investment in the fund:
Loss = \(\frac{40}{100}(10) = -4\)

Amount placed in the savings account = \(40-10=30\)
Since \(p=10\), John earns 10% of the amount placed in the savings account:
Gain = \(\frac{10}{100}(30)= 3\)

Loss + Gain = \(-4+3 = -1\)
The correct answer must be NEGATIVE.


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John invested 1/4 of A dollars in an investment fund, and placed the r  [#permalink]

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New post 06 Jul 2018, 07:16
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MathRevolution wrote:
John invested \(\frac{1}{4}\) of A dollars in an investment fund, and placed the remaining \(\frac{3}{4}\) of A dollars in a savings account. If he made a 4p% loss on the fund, and a p% profit on the savings account, what was his total profit (or loss), in terms of A and p? (A negative value represents a loss.)

\(A. \frac{–Ap}{400}\)
\(B. 0\)
\(C. \frac{Ap}{400}\)
\(D. \frac{Ap}{200}\)
\(E. \frac{Ap}{100}\)


Profit on Savings fund is \(\frac{3Ap}{400}\)

Loss on the investment fund is \(\frac{p}{100}\)

So, Net profit is \(\frac{3Ap}{400}\) \(-\) \(\frac{p}{100}\)

Or, Net profit is \(\frac{–Ap}{400}\), Answer must be (A)
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Re: John invested 1/4 of A dollars in an investment fund, and placed the r  [#permalink]

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New post 08 Jul 2018, 03:20
=>
Total profit = profit on investment fund + profit on savings account
\(= (\frac{1}{4})A*(\frac{-4p}{100}) + (\frac{3}{4})A*(\frac{p}{100})\)
\(=-\frac{4Ap}{400} + \frac{3Ap}{400} = \frac{-Ap}{400}\)

Therefore, the answer is A.
Answer: A
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Re: John invested 1/4 of A dollars in an investment fund, and placed the r  [#permalink]

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New post 13 Jul 2018, 13:21
MathRevolution wrote:
[GMAT math practice question]

John invested \(\frac{1}{4}\) of A dollars in an investment fund, and placed the remaining \(\frac{3}{4}\) of A dollars in a savings account. If he made a 4p% loss on the fund, and a p% profit on the savings account, what was his total profit (or loss), in terms of A and p? (A negative value represents a loss.)

\(A. \frac{–Ap}{400}\)
\(B. 0\)
\(C. \frac{Ap}{400}\)
\(D. \frac{Ap}{200}\)
\(E. \frac{Ap}{100}\)


We express p% as p/100 and 4p% as 4p/100. Thus, for the investment fund, he lost A/4 x 4p/100 = Ap/100 dollars. For the savings account, he made 3A/4 x p/100 = 3Ap/400 dollars. Thus his profit (or loss) is:

3Ap/400 - Ap/100 = 3Ap/400 - 4Ap/400 = -Ap/400

Answer: A
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Re: John invested 1/4 of A dollars in an investment fund, and placed the r &nbs [#permalink] 13 Jul 2018, 13:21
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