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Company R's annual profit has increased by a constant amount each cale

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Bunuel
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Company R's annual profit has increased by a constant amount each cale [#permalink] Company R's annual profit has increased by a constant amount each cale   26 Jun 2018, 06:19
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Company R's annual profit has increased by a constant amount each calendar year since 1985. What was Company R's annual profit in 1991?

(1) In 1985 Company R's annual profit was $212,000; in 1989 Company R's annual profit was $242,000.
(2) Company R's annual profit has increased by $7,500 each year since 1985.
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Company R's annual profit has increased by a constant amount each cale [#permalink] Company R's annual profit has increased by a constant amount each cale   Updated on: 24 May 2021, 21:58
Bunuel wrote:
Company R's annual profit has increased by a constant amount each calendar year since 1985. What was Company R's annual profit in 1991?

(1) In 1985 Company R's annual profit was $212,000; in 1989 Company R's annual profit was $242,000.
(2) Company R's annual profit has increased by $7,500 each year since 1985.


As the profit increases every year by a fixed amount, the profit can be analysed through AP series.

Let \(p\) be the profit in 1985. Time period \(n=1991-1985=16\) years. Let \(d\) be the common difference.

Hence Profit in 1991 \(= p + (n-1)d = p + (16-1)d\)

we need the value of \(p\) & \(d\)

Statement 1: implies \(p=212,000\)

Profit in 1989 i.e \(4\) years since 1985 will be \(=212000 + (4-1)d=242000\).

From this statement, we get the value of \(p & d\).

This statement gives all the required values. Sufficient

Statement 2: we know the increase in profit but we do not know the profit amount. hence \(p\) & \(d\) cannot be calculated. Insufficient

Option A

Originally posted by niks18 on 26 Jun 2018, 08:26.
Last edited by niks18 on 24 May 2021, 21:58, edited 1 time in total.
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Re: Company R's annual profit has increased by a constant amount each cale [#permalink] Company R's annual profit has increased by a constant amount each cale   27 Jun 2018, 04:28
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Bunuel wrote:
Company R's annual profit has increased by a constant amount each calendar year since 1985. What was Company R's annual profit in 1991?

(1) In 1985 Company R's annual profit was $212,000; in 1989 Company R's annual profit was $242,000.
(2) Company R's annual profit has increased by $7,500 each year since 1985.


Question stem: Company R's annual profit has increased by a constant amount each calendar year since 1985
It means that the profit in each subsequent year since 1985 is in an AP.

Statement 1:In 1985 Company R's annual profit was $212,000; in 1989 Company R's annual profit was $242,000
We can compute the common difference of the progression and add two more such common differences to compute the value for 1991.
We will get a unique answer.

That will suffice. We need not compute the value as it is a DS question.

However, this is the value. The annual increase in profit = (profit in 1989 - profit in 1985)/4 = (242,000 - 212,000)/4 = 7500.
So, profit in 1991 = Profit in 1989 + 2 * common difference = 242,000 + 2*7500 = $257,000

Statement 1 is sufficient.

Statement 2: Company R's annual profit has increased by $7,500 each year since 1985

We do not know the profit in 1985 or any of the years between 1985 and 1991 to find the answer.

Statement 2 is NOT sufficient.

Choice A.
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Re: Company R's annual profit has increased by a constant amount each cale [#permalink] Company R's annual profit has increased by a constant amount each cale   27 Jun 2018, 06:06
Company R's annual profit has increased by a constant amount each calendar year since 1985 - arithmetic progression.
If profit in 1985 = a(1), then every profit (on 7th year) in 1991 a(7)= a(1)+(7-1)*K =a(1)+6K=?

(1) In 1985 Company R's annual profit was $212,000; in 1989 Company R's annual profit was $242,000.

a(1)=$212,000 and a(5)=$242,000 - from this point you may stop calculations because when we know two numbers of arithmetic progression, we can find any other number. Suff

(2) Company R's annual profit has increased by $7,500 each year since 1985

K=$7,500 and we need to find a(7)=a(1)+6K - clearly Not Suff because we don't know starting ammount.

Answer (A)
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Re: Company R's annual profit has increased by a constant amount each cale [#permalink] Company R's annual profit has increased by a constant amount each cale   01 Apr 2021, 23:36
niks18 wrote:
Bunuel wrote:
Company R's annual profit has increased by a constant amount each calendar year since 1985. What was Company R's annual profit in 1991?

(1) In 1985 Company R's annual profit was $212,000; in 1989 Company R's annual profit was $242,000.
(2) Company R's annual profit has increased by $7,500 each year since 1985.


As the AMOUNT of profit increases every year hence the Total Profit is Compounded.

Let \(p\) be the profit in 1985. Time period \(=1991-1985=16\) years. Let \(r\) be the growth rate.

Hence Profit in 1991 \(= p*(1+\frac{r}{100})^{16}\)

we need the value of \(p\) & \((1+\frac{r}{100})\)

Statement 1: implies \(p=212,000\)

Profit in 1989 i.e \(4\) years since 1985 will be \(=p*(1+\frac{r}{100})^4=242000\)

\(=>(1+\frac{r}{100})^4=\frac{242000}{212000}=\frac{121}{106}\). Now raise both sides to the power \(4\) to get,

Hence \((1+\frac{r}{100})^{16}=(\frac{121}{106})^4\)

This statement gives all the required values. Sufficient

Statement 2: we know the increase in profit but we do not know the profit amount. hence \(p\) & \(r\) cannot be calculated. Insufficient

Option A



May I know the thought behind using compound interest to calculate the amount when it clearly says that the profit has increased by a constant amount each year?
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Re: Company R's annual profit has increased by a constant amount each cale [#permalink] Company R's annual profit has increased by a constant amount each cale   24 May 2021, 22:00
tanya0630 wrote:
niks18 wrote:
Bunuel wrote:
Company R's annual profit has increased by a constant amount each calendar year since 1985. What was Company R's annual profit in 1991?

(1) In 1985 Company R's annual profit was $212,000; in 1989 Company R's annual profit was $242,000.
(2) Company R's annual profit has increased by $7,500 each year since 1985.


As the AMOUNT of profit increases every year hence the Total Profit is Compounded.

Let \(p\) be the profit in 1985. Time period \(=1991-1985=16\) years. Let \(r\) be the growth rate.

Hence Profit in 1991 \(= p*(1+\frac{r}{100})^{16}\)

we need the value of \(p\) & \((1+\frac{r}{100})\)

Statement 1: implies \(p=212,000\)

Profit in 1989 i.e \(4\) years since 1985 will be \(=p*(1+\frac{r}{100})^4=242000\)

\(=>(1+\frac{r}{100})^4=\frac{242000}{212000}=\frac{121}{106}\). Now raise both sides to the power \(4\) to get,

Hence \((1+\frac{r}{100})^{16}=(\frac{121}{106})^4\)

This statement gives all the required values. Sufficient

Statement 2: we know the increase in profit but we do not know the profit amount. hence \(p\) & \(r\) cannot be calculated. Insufficient

Option A



May I know the thought behind using compound interest to calculate the amount when it clearly says that the profit has increased by a constant amount each year?


Hi tanya0630

Apologies for the late reply. My previous solution was incorrect and hence I have edited the solution. It seems I had mistaken the profit increase with growth in profit.
I hope your doubt is clear now.

Thanks
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Re: Company R's annual profit has increased by a constant amount each cale [#permalink] Company R's annual profit has increased by a constant amount each cale   30 Jul 2024, 00:24
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Re: Company R's annual profit has increased by a constant amount each cale [#permalink]
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