Calculating percents

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GMAT Quantitative › Calculating percents

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

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

CORRECT

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

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

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

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).

$153\ lbs.$

CORRECT

$165\ lbs.$

$138\ lbs.$

$206\ lbs.$

$194\ lbs.$

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.

A number is multiplied by one-sixth; the product is divided by one-seventh; that quotient is multiplied by seven-tenths. What percent of the original number is the final result?

$81 \frac{2}{3} %$

CORRECT

$1 \frac{2}{3} %$

$166 \frac{2}{3} %$

$8 \frac{1}{6} %$

$16 \frac{2}{3} %$

Explanation

The best way to do this is to start with 100 and to calculate the final result, which will be the correct answer.

The final result will be as follows:

$100 \cdot \frac{1}{6} \div \frac{1}{7} \cdot \frac{7}{10}$

$= \frac{100 }{1}\cdot \frac{1}{6} \cdot \frac{7}{1} \cdot \frac{7}{10}$

$= \frac{100 }{1}\cdot \frac{1}{6} \cdot \frac{7}{1} \cdot \frac{7}{10} = \frac{245}{3} = 81 \frac{2}{3}$

The final number will be $81 \frac{2}{3} %$ of the original number.

The price of an item is decreased by 10%, then by 20%, then by 30%. This is equivalent to doing what?

Decreasing the price by 49.6%

CORRECT

Decreasing the price by 50.4%

Decreasing the price by 60%.

Decreasing the price by 40%

Decreasing the price by 50%.

Explanation

Decreasing a price by 10%, then by 20%, then by 30% is equivalent to taking 90% of a price, then taking 80% of that, then taking 70% of that. That, in turn, is equivalent to multiplying the price by 0.90, then by 0.80, then by 0.70.

For simplicity's sake, assume the initial price was \$100. Then we can calculate the final price as follows:

$100 \cdot 0.9 \cdot 0.8 \cdot 0.7 = 50.4$

The final price is \$50.40, so we essentially discounted the price by \$49.60, which is 49.6%.

Untitled

The above is an annual income tax table for single persons in a given state.

Between January 1 and July 1, Mr. Smith earned \$722 per month from a part time job. He earned a raise beginning on July 1, but he ended up not paying any income tax for the year. Assuming he had no other income, what percent was the highest possible raise in his salary? Choose the answer that is closest to the maximum possible raise.

CORRECT

Explanation

Since Mr. Smith did not pay any income tax, his income was at most \$10,000.

He earned \$722 per month over six months for a total of

$$722 \times 6 = $4,332$

The maximum he earned over the remaining six months is

$$10,000 - $4,332 = \$5,668$ , which is

$\$5,668 \div 6 = \$944.67$ per month.

This represents a

$\frac{\$944.67 - $722 }{$722 } \times 100 % = \frac{$222.67 }{$722 } \times 100 % \approx 31 %$

maximum raise.

The closest choice is 30%.

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

CORRECT

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 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?

$\frac{1}{2}$ %

CORRECT

$\frac{1}{20}$ %

$\frac{1}{5}$ %

$\frac{1}{50}$ %

$\frac{1}{200}$ %

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.

Total sales at XYZ Corporation increased by this year. What is the amount of sales for this year if last year's sales were $\$200,000$ ?

$\$250,000$

CORRECT

$\$50,000$

$\$225,000$

$\$450,000$

$\$125,000$

Explanation

The amount of sales for this year is 125% of last year's sales. Therefore, we can calculate in the following way:

$200000\times1.25=250,000$

Or:

$200,000+0.25\times200000=200,000+\frac{200000}{4}=250000$

Rob, Tim, and Peggy are the three managers at a local restaurant. Peggy's salary is less than Tim's salary. Tim's salary is less than Rob's salary. What percent of Rob's salary is Peggy's salary?

CORRECT

Explanation

Let be Rob's salary.

Then, since Tim's salary is 10% less than Rob's salary, we can write Tim's salary as .

Since Peggy's salary is 20% less than Tim's salary, we can write Peggy's salary as .

Peggy's salary is 72% of Rob's salary as we can write:

Peggy salary/ Rob salary =

Making the answer into a percent we get,

$0.72 \times 100=72%$ .

A randomly selected study sample includes women. Of all the women in the sample, have an income greater than $\$50,000$ . What is the percentage of women in the sample who have an income greater than $\$50,000$ ?

CORRECT

Not enough information

Explanation

The percentage of women who have an income greater than $\$50,000$ 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 $\$50,000$ .

$0.6\times 0.3=0.18$

The percentage of women who earn more than $\$50,000$ 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 $\$50,000$ 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 $\$50,000$ 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 $\$50,000$ 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 $\$50,000$ .

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