GMAT Quantitative - Calculating percents

is of . Which of the following expressions is equal to ?

$N = \frac{25M}{21}$

$N = \frac{21M}{25}$

$N = \frac{25}{21M}$

$N = \frac{21}{25M}$

None of the other responses is correct.

Explanation

If is of , then $M = \frac{84}{100}N = \frac{21}{25}N$ .

Equivalently,

$\frac{25}{21} \cdot \frac{21}{25}N = \frac{25}{21} \cdot M$

$N = \frac{25M}{21}$

Gary weighs 20 percent more than Harry who's weight is 80 percent of James' weight. If James weighs 172 pounds, how much would Gary weigh if he lost 12 pounds? (Rounded to the nearest pound).

$153\ lbs.$

$165\ lbs.$

$138\ lbs.$

$206\ lbs.$

$194\ lbs.$

Explanation

If James weighs 172 pounds, and Harry weighs 80% of that, then

$H = 0.8\times172$ pounds. If Gary weighs 20% more than Harry, then

he is 120% Harry's weight $= 1.2\times137.6=165.12$ . If he loses 12 pounds,

he would weigh 153.12 or 153 pounds.

In a bag, Mary has red marbles, blue marbles, and green marbles. What percent of the marbles are blue?

Explanation

To calculate the percentage, you must first find the fraction of marbles that are blue and then convert the fraction to a percent.

$% \textup{blue}= \frac{40}{32+40+8}=\frac{40}{80}=\frac{5}{10}=50%$

is 75% of .

is what percent of ?

$62\frac{1}{2} %$

$56\frac{1}{4}%$

$66 \frac{2}{3}%$

Explanation

is 75% of , so

$M -N = \frac{3}{4}M$

and

$\frac{1}{4}M = N$

$M + N = M +\frac{1}{4}M = \frac{5}{4}M$

The question can be rewritten as

is what percent of $\frac{5}{4}M$ ?

The answer is found as follows:

$\frac{N}{\frac{5}{4}N} \times 100 % = \frac{4}{5} \times 100 % = 80 %$ .

A number is divided by two; then its decimal point is moved to the left two spaces. This is the same as taking what percent of the number?

$\frac{1}{2}$ %

$\frac{1}{20}$ %

$\frac{1}{5}$ %

$\frac{1}{50}$ %

$\frac{1}{200}$ %

Explanation

Let's do these two things to 100. Dividing 100 by 2 yields 50; moving the decimal point two places left changes 50, or 50.0, to 0.50.

This means that the new number is 0.50% , or $\frac{1}{2}$ %, of the original number.

Given a number , which of these is the greatest quantity of the three?

(a) 30% of 40% of 50% of

(b) 40% of 50% of 30% of

All three are equal to one another

30% of 40% of 50% of

40% of 50% of 30% of

50% of 30% of 40% of

It is impossible to tell without knowing the value of

Explanation

All three are equal.

30% of 40% of 50% of is $\frac{3}{10}$ of $\frac{2}{5}$ of $\frac{1}{2}$ of : that is, $\frac{3}{10} \cdot\frac{2}{5}\cdot\frac{1}{2} \cdot x = \frac{6}{100} x$

40% of 50% of 30% of is $\frac{2}{5}$ of $\frac{1}{2}$ of $\frac{3}{10}$ of : that is, $\frac {2}{5} \cdot\frac{1}{2} \cdot\ \frac{3}{10} \cdot x = \frac{6}{100} x$

50% of 30% of 40% of is $\frac{1}{2}$ of $\frac{3}{10}$ of $\frac{2}{5}$ of : that is $\frac{1}{2} \cdot\ \frac{3}{10} \cdot \frac {2}{5} \cdot x = \frac{6}{100} x$

A randomly selected study sample includes women. Of all the women in the sample, have an income greater than . What is the percentage of women in the sample who have an income greater than ?

Not enough information

Explanation

The percentage of women who have an income greater than in the sample is simply the product of the percentage of women in the sample and the percentage of these women who earn more than .

$0.6\times 0.3=0.18$

The percentage of women who earn more than in the sample is .

Or, we could assume there are people in the sample. The number of women in the sample would then be $100\cdot0.6=60$ . And the number of women who earn more than in the sample would be $60 \cdot 0.3=18$ .

The percentage of women who earn more than in the sample is $\frac{18}{100}=18%$ .

Let's verify this answer by taking another sample size, let's say there are people in the sample.

The number of women who earn more than in the sample would then be $150 \cdot 0.6 \cdot 0.3=90 \cdot 0.3=27$ .

The percentage of women who earn more than in the sample is $\frac{27}{150}=18%$ .

We still get the same result because the number of people in the sample is not necessary to find that percentage since we are given the percentage of women in the sample and the percentage of these women in the sample who earn more than .

In a bag, Mary has red marbles, blue marbles, and green marbles. What percent of the marbles are green?

Explanation

To calculate the percentage, you must first find the fraction of marbles that are green and then convert the fraction to a percent.

$% \textup{green} = \frac{8}{32+40+8}=\frac{8}{80}=\frac{1}{10}=10%$

The percentage of accountants at a company that has 10,000 employees dropped from at the end of last year to at the end of this year. If the number of employees at the end of this year is 9,500, what is the approximate change in the number of accountants over this period?

Explanation

The number of accountants at the end of last year is:

$10000\times0.1=1000$

The number of accountants at the end of this year is:

$9500\times0.06=570$

The approximate change in the number of accountants from the end of last year to the end of this year is:

$\frac{570-1000}{1000}=-0.43$

There was a 43% decrease in the number of accountants over this period.

You bought worth of a stock two years ago. After the first year, the value of the stock decreased by an average . During the second year, the value of the stock increased by an average . What is the value of your investment today?