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

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

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.

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)

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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