Understanding measurement - GMAT Quantitative Reasoning

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Question

Fill in the blank:

$3\frac{1}{4} \textup{ pounds } = \underline{ : : : : : : : : : : : : }\textup{ounces}$

Answer

One pound is equal to 16 ounces.

Multiply:

$3 \frac{1}{4} \times 16 = 52$

52 ounces is the correct choice.

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Question

A baseball travels at a rate of $75\ ft/sec$ . How long does it take to reach a fence that is $110\ yards$ away?

Answer

The first step is to convert the distance into feet:

$110\ yds * \frac{3\ ft}{1\ yd} = 330\ ft.$

Then, divide the distance by the baseball's rate of travel:

$\frac{330 ft}{75\ ft/sec} = 4.4\ sec.$

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Question

Big Bob the, 8-feet tall warehouse foreman is stacking uniformly sized boxes of goods in the warehouse. Big Bob notices that he is the exact same height as 3 boxes stacked on top of each other. If the warehouse ceiling is 55 feet high, what is the maximum number of boxes that he can stack on top of one another before he hits the ceiling?

Answer

To find the height of each box set the 3 boxes equal to the height of Big Bob. So, let be the height of each box. Then,

$3x=8\ feet$ or $x=\frac{8\text{ feet}}{3}= 2.66\text{ feet}$

Therefore to find the maximum number of boxes that fit under the ceiling, we divide the ceiling height by the height of each box. So,

$\frac{55'}{2.66'} = 20.68$ or 20 whole boxes would fit under the ceiling.

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Question

It takes Jim 30 minutes to drive to work and 45 minutes to drive home from work. What is Jim's average driving speed in miles per hour if Jim lives 25 miles from work?

Answer

The formula to find the average speed is $avg.\ speed = \frac{total\ distance}{total\ time}$ .

Since the question deals with miles per hour, the time must be converted to hours from minutes:

$\frac{75\ min}{60\ min}= 1.25\ hours$

Plugging the numbers into the equation gives $\frac{50\ miles}{1.25\ hours}= 40\ mph$ .

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Question

A really backward country does not use inches, feet, yards, or meters to measure distance, it uses units called flots, glots, and klots. It takes 17 flots to make a glot, and 7 glots to make a klot.

These units can also be used to form units of area and volume (i.e. square flots, cubic klots).

How many cubic flots make a cubic klot?

Answer

First, multiply to find the number of flots in a klot.

$\frac{17 ; \textrm{flots}}{1 ; \textrm{glot}} \cdot \frac{7 ; \textrm{glots}}{1 ; \textrm{klot}}= \frac{119 ; \textrm{flots}}{1 ; \textrm{klot}}$

Cube that to find the number of cubic flots in a cubic klot.

$\left (\frac{119 ; \textrm{flots}}{1 ; \textrm{klot}} \right )^{3} = \frac{1,685,159 ; \textrm{flots} ^{3}}{1 ; \textrm{klot}^{3}}}$

Therefore, 1,685,159 cubic flots = 1 cubic klot

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Question

Note: Figure NOT drawn to scale.

$DE = \frac{1}{2}\left ( CD \right )$

Give in terms of .

Answer

Since $DE = \frac{1}{2} (CD)$ ,

Since , $BC = CD - 6 = 2 \cdot DE - 6$ , and, subsequently,

$= [2 \left (DE \right ) -6 ]+ [2 \left (DE \right ) -6 ] + 2 \left (DE \right ) + DE$

$= 2 \left (DE \right )+ 2 \left (DE \right ) + 2 \left (DE \right ) + 1\left ( DE \right ) -6 -6$

$= 7 \left (DE \right ) - 12$

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Question

If the length and width of a rectangular room is increased by 20%, what percent has the area increased by?

Answer

$Original\ area=l\cdot w$

$New\ area=1.2l\cdot 1.2w$

$New\ area=1.44\cdot l\cdot w$

$.44\cdot *100=44%$

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Question

Two bedrooms have the same area. Bedroom A is by and the width of Bedroom B is . Find the length of Bedroom B.

Answer

Area of Bedroom A is equal to area of Bedroom B, therefore:

$l=\frac{6'*8'}{10'}$

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Question

Convert $45 ^{\circ }\textrm{ C}$ to Fahrenheit (to the nearest tenth).

$F = \frac{9}{5} C + 32$

Answer

The Celsius-to-Fahrenheit conversion formula is:

$F = \frac{9}{5} C + 32$

Substitute 45 for :

$F = \frac{9}{5} \cdot 45+ 32 = 81 +32 = 113$

The answer is $113 ^{\circ } \textrm{ F}$ .

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Question

Convert $80 ^{\circ } F$ to degrees Celsius (nearest whole degree).

$F = \frac{9}{5} C + 32$

Answer

If is the Fahrenheit temperature, then the equivalent Celsius temperature is

$C = \frac{5}{9} (F - 32)$ .

Substitute into the equation.

$C = \frac{5}{9} (80 - 32)$

$C = \frac{5}{9} \cdot 48 = \frac{5}{9} \cdot \frac{48}{1} = \frac{5}{3} \cdot \frac{16}{1} = \frac{80}{3} =26 \frac{2}{3}$

This rounds up to $27 ^{\circ }C$ .

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Question

Restate 100 miles per hour in feet per second (rounded to the nearest whole number).

Answer

One mile is equal to 5,280 feet, and one hour is equal to 3,600 seconds, The speed can be converted as follows:

$\frac{100 \textrm{ mi}}{1\textrm{ hr}} = \frac{100 \textrm{ mi } \times 5,280 \textrm{ ft / mi } }{1\textrm{ hr} \times 3,600 \textrm{ sec / hr}}$

$= 146 \frac{2}{3} \textrm{ ft / sec }$

or, rounded, 147 feet per second.

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Question

Restate 200 feet per second in miles per hour (nearest whole number).

Answer

One mile is equal to 5,280 feet, and one hour is equal to 3,600 seconds, The speed can be converted as follows:

$\frac{200 \textrm{ ft}}{1\textrm{ sec}} = \frac{200 \textrm{ ft } \times 3,600 \textrm{ sec / hr} }{1\textrm{ sec} \times 5,280 \textrm{ ft / mi } }$

$= 136 \frac{4}{11} \textrm{ mi / hr}$

or, rounded, 136 miles per hour.

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Question

Using the conversion factor 2.54 centimeters = 1 inch, rewrite 100 square inches in square centimeters (nearest tenth).

Answer

1 inch = 2.54 centimeters, so 1 square inch = $2.54 ^{2} = 6.4516$ square centimeters.

100 square inches are equal to $6.4516 \times 100 = 645.16$ square centimeters, which rounds to 645.2 square centimeters.

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Question

A furlong is a unit of length used in horse racing; it is equal to one-eighth of a mile. To the nearest tenth, how many meters are equal to a furlong if 1.609 kilometers are equal to a mile?

Answer

1.609 kilometers, or 1,609 meters, are equal to a mile. One furlong, or one eighth of a mile, is equal to one eighth of 1,609 meters, or

$1,609 \cdot \frac{ 1}{8} = 1,609 \cdot 0.125 = 201.125 \approx 201.1$ meters.

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Question

A unit of distance used in marine navigation is the nautical mile; what we call a mile on land is also referred to as a statute mile.

One nautical mile is defined as 1,852 meters. Using the conversion factor 1.609 kilometers = 1 statute mile, how many statute miles are equal to 1,000 nautical miles (nearest whole number)?

Answer

1,000 nautical miles are equal to $1,852 \times 1,000 = 1,852,000$ meters, or

1 statute mile is equal to 1.609 kilometers, or 1,609 meters; divide 1,852,000 meters by 1,609 meters per statute miles to get

$1,852,000 \div 1,609 \approx 1,151$ statute miles, the equivalent of 1,000 nautical miles.

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Question

If an object travels at a speed of 10 feet per second, how many feet does it travel in half an hour?

Answer

If an object travels at 10 feet per second, then in half an hour it will travel 10 feet for every second there is in 30 minutes. We can set this multiplication up as follows:

$10\frac{feet}{sec}\cdot60\frac{sec}{min}\cdot30:min=18,000:ft$

Here we can see that the units of seconds are cancelled after the first operation, and the units of minutes are cancelled after the second operation, leaving us with the unit of feet for our answer.

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Question

Jason skips a rock across the surface of a pond. The rock bounces three times over the pond's surface. If the second bounce is half the distance of the first bounce, and the third bounce is one quarter of the second bounce, and the total distance between bounces is 65 inches, how many inches did the rock travel on the first bounce?

Answer

We need to translate the words into a mathematical equation. Since we need to solve for the distance the rock travels on the first bounce, let's use a variable to represent that distance.

Let "" = distance traveled on the first bounce.

Notice that we can describe the distances traveled on the 2nd and 3rd bounces in terms of :

Distance traveled on the 2nd bounce is half the distance of the 1st bounce, so 2nd bounce = $\frac{1}{2}x$

Distance traveled on the 3rd bounce is 1/4 of the 2nd bounce, so, 3rd bounce = $\frac{1}{4}*\frac{1}{2}x=\frac{1}{8}x$

The total distance, then, is:

$x+\frac{1}{2}x+\frac{1}{8}x=65$

$\frac{13}{8}x=65$

$x=65\bigg(\frac{8}{13}\bigg)$

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Question

Three years ago, Anna was four times as old as Jeff. Today Anna is three times as old as Jeff.

How old was Anna three years ago?

Answer

First, we set up the variables and the equations. Let:

= Anna's age three years ago

= Jeff's age three years ago. So:

= Anna's age today

= Jeff's age today

Therefore: and . Then we solve for the system of equations:

or

When we solve for J first we get .

Then we solve for A using the first equation of the system:

Therefore Anna was 24 years old three years ago.

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Question

kilometer is approximately $3.9\times10^4$ inches. How many kilometers are there in inches?

Answer

Since

$1 \text{ km}=3.9\times10^4 \text{ inches}$ ,

$1 \text{ inch}= \frac{1}{(3.9\times10^4)} \text{ km}$

Therefore we multiply 1,170,000 by 1/(3.9*104) to obtain the number of kilometers in 1,170,000 inches.

$\frac{1170000}{3.9\times 10^{4}}=\frac{1170}{39}=30$

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Question

If one liter of gasoline costs , how much would eighteen gallons of gasoline cost? (One gallon is approximately liters.)

Answer

One gallon of gasoline is about liters of gasoline. The number of liters in eighteen gallons is:

$18\times 3.8=68.4$

One liter costs . Therefore, eighteen gallons ( liters) will cost:

$68.4\times 1.50=68.4\times 1 +\frac{68.4}{2}=68.4+34.2=102.6=$102.60$

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