GMAT Quantitative - Calculating ratio and proportion

On a map, one and a half inches represents sixty actual miles. In terms of , what distance in actual miles is represented by inches on the map?

$40N ; \textrm{mi}$

$\frac{40 }{N}; \textrm{mi}$

$90N ; \textrm{mi}$

$45N ; \textrm{mi}$

$\frac{90 }{N}; \textrm{mi}$

Explanation

Let be the number of actual miles. Then the proportion statement to be set up, with each ratio being number of actual miles to number of map inches, is:

$\frac{60}{1\tfrac{1}{2}} = \frac{x}{N}$

Simplify the left expression and solve for

$\frac{x}{N} = \frac{60}{1\tfrac{1}{2}} = 60 \div \frac{3}{2} =60 \cdot \frac{2}{3}$

$\frac{x}{N} = 40$

A furlong is a measure of length used in horse racing. Eight furlongs are equal to one mile.

Express 20 furlongs in feet.

$13,200 \textrm{ ft}$

$10,560 \textrm{ ft}$

$10,700 \textrm{ ft}$

$15,840 \textrm{ ft }$

$7,920 \textrm{ ft}$

Explanation

Divide 20 furlongs by 8 furlongs per mile, then multiply by 5,280 feet per mile.

$\frac{20}{8} \times 5,280 = 2.5 \times 5,280 = 13,200$

A clothing store is having a sales for the holiday season. They mark down all items by $43\frac{4}{5}%$ . What is the sales price of a suit whose original price is ?

Explanation

We start by finding the value of the mark down:

$43\frac{4}{5}=43+\frac{4}{5}=43+0.80=43.8%$

Therefore, the mark down is 43.8% or 0.438, which means that the new price of the suit is:

$340\cdot (1-0.438)=191.08$

The annual budget for a road construction project is $25,200 budgeted equally over 12 months. If by the end of the third month the actual expenses have been $7,420, how much has the construction project gone over budget?

$\dpi{100} \small $ 1120$

$\dpi{100} \small $ 980$

$\dpi{100} \small $2150$

$\dpi{100} \small $1640$

$\dpi{100} \small $3340$

Explanation

The monthly budget is found by:

$\frac{25,200}{12}=2,100$

which for 3 months is a budget of:

$2,100\cdot 3= 6,300$

To find out how much they are over budget the budgeted amount is subtracted from the actual expenses.
$7,420 - 6,300 = 1,120$

Nishita has necklaces, bracelets, and rings in a ratio of 7:5:4. If she has 64 jewelry items total, how many bracelets does she have?

Explanation

bracelets:

127 people signed up for a subscription service. 45 signed up for weekly deliveries, 34 for monthly deliveries, and the rest for annual deliveries. What is the ratio of weekly subscribers to annual subscribers?

Explanation

Let's first find the number of annual subscribers:

The ratio of weekly subscribers to annual subscribers is therefore .

Company sells liters of soda for , and Company sells liters of soda for .

If the amount of soda sold per dollar is the same for each company, what is ?

Explanation

Since the amount of soda per dollar is the same for each company, we can equate the 2 ratios

$\frac{5liters}{2dollars} = \frac{3liters}{xdollars}$

And solve

$\frac{5}{2} = \frac{3}{x}$

(Cross multiply)

$x = \frac{6}{5} = 1.2$

The ratio $\dpi{100} \small 3$ to $\dpi{100} \small \frac{1}{2}$ is equal to the ratio:

$\dpi{100} \small 6\ to\ 1$

$\dpi{100} \small 5\ to\ 1$

$\dpi{100} \small 3\ to\ 2$

$\dpi{100} \small 2\ to\ 3$

$\dpi{100} \small 1\ to\ 6$

Explanation

The ratio $\dpi{100} \small 3$ to $\dpi{100} \small \frac{1}{2}$ is the same as $\dpi{100} \small \frac{3}{\frac{1}{2}}=3\times \frac{2}{1}=6$ ,
which equals a ratio of $\dpi{100} \small 6$ to $\dpi{100} \small 1$ .

Also, if you double both sides of the ratio, you get $\dpi{100} \small 6$ to $\dpi{100} \small 1$ .

The ratio 4 to $\frac{1}{4}$ is equal to which of the following ratios?

$\dpi{100} \small 16$ to $\dpi{100} \small 1$

$\dpi{100} \small 8$ to $\dpi{100} \small 1$

$\dpi{100} \small 12$ to $\dpi{100} \small 1$

$\dpi{100} \small 16$ to $\dpi{100} \small 3$

$\dpi{100} \small 6$ to $\dpi{100} \small 1$

Explanation

The ratio $\dpi{100} \small 4$ to $\frac{1}{4}$ is equal to $\frac{4}{\frac{1}{4}}$ which is $4\left ( \frac{4}{1} \right )= 16$ .

$\dpi{100} \small 16$ can be written as the ratio $\dpi{100} \small 16$ to $\dpi{100} \small 1$ .

In a certain classroom all of the students are either sophomores or juniors. The number of boys and girls in the classroom are equal. Of the girls, $\dpi{80} \frac{3}{7}$ are sophomores, and there are 24 junior boys. If the number of junior boys in the classroom are in the same proportion to the total amount of boys as the number of sophomore girls are to the total number of girls, how many students are in the classroom?

Explanation

This question seems convoluted but is actually more simple than it seems. We are told that the number of girls and boys in the classroom are equal and that $\frac{3}{7}$ of the girls are sophomores. We are then told that 24 of the boys are juniors, and that they represent a proportion of total boys equal to the proportion of sophomore girls to total girls. This means that: