Data Sufficiency

GMAT Paper Tests

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.

OA A

As the profit increase annually, total profit is compounded. so, let 1985 profit = p;
Time = 1991 - 1985 = 16 years
Let growth rate = r
$$Therefore,\ profit\ in\ 1991=p\cdot\left(1+\frac{r}{100}\right)^{16}$$
Question=> What was company R's annual profit in 1991?
Statement 1: In 1985 company R's annual profit was $212,000 while in 1989, the company R's annual profit was $242,000.
$$profit\ in\ 1991=p\cdot\left(1+\frac{r}{100}\right)^{16}$$
p=$212,000
Time period = 1989 - 1985 = 4 years
$$profit\ in\ 1989=p\cdot\left(1+\frac{r}{100}\right)^4=\text{242,000}$$
$$=>\left(1+\frac{r}{100}\right)^4=\frac{\left(242000\right)}{212000}=\frac{121}{106}$$
$$=>\left(1+\frac{r}{100}\right)^{16}=>\left(1+\frac{r}{100}\right)^{4\cdot4}\ where\ \left(1+\frac{r}{100}\right)^4=\frac{121}{106}$$
$$Therefore,\ \left(\frac{121}{106}\right)^4\ and\ \ p=\text{212000}$$
$$profit\ in\ 1991=p\cdot\left(1+\frac{r}{100}\right)^{16}\ =>212000\cdot\ \left(\frac{121}{106}\right)^4$$
STATEMENT 1 IS SUFFICIENT

Statement 2:: Company R's annual profit has increased by $7500 each year since 1985. The value of profit amount is unknown. Hence, 'p' and 'r' cannot be calculated.
STATEMENT 2 IS INSUFFICIENT

Therefore, statement 1 alone is SUFFICIENT

Answer is option A....

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