GMAT Math : Problem-Solving Questions

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Example Questions

Example Question #3 : Rate Problems

Jerry took a car trip of 320 miles. The trip took a total of six hours and forty minutes; for the first four hours, his average speed was 60 miles per hour. What was his average speed for the remaining time?

Possible Answers:

$30 \textrm{ mph }$

$32 \textrm{ mph }$

$35 \textrm{ mph }$

$25 \textrm{ mph }$

$28 \textrm{ mph }$

Correct answer:

$30 \textrm{ mph }$

Explanation:

Jerry drove 60 miles per hour for 4 hours - that is, $60 \times 4 = 240$ miles.

He drove the remainder of the distance, or 320-240 = 80 miles over a period of $6 \frac{2}{3} - 4 = 2\frac{2}{3}$ hours, so his average speed was

$80 \div 2 \frac{2}{3} = 80 \div \frac{8}{3} = 80 \times \frac{3} {8} = 30$ miles per hour.

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Example Question #1 : Rate Problems

If it takes Sally 3 hours to drive $\dpi{100} \small q$ miles, how many hours will it take her to drive $\dpi{100} \small r$ miles at the same rate?

Possible Answers:

$\dpi{100} \small \frac{qr}{3}$

$\dpi{100} \small \frac{3q}{r}$

$\dpi{100} \small \frac{r}{3q}$

$\dpi{100} \small \frac{3}{qr}$

$\dpi{100} \small \frac{3r}{q}$

Correct answer:

$\dpi{100} \small \frac{3r}{q}$

Explanation:

If Sally drives q miles in 3 hours, her rate is 3/q miles per hour. Plug this rate into the distance equation and solve for the time:

$\dpi{100} \small Distance = rate\times time$

$\dpi{100} \small r=\frac{q}{3}\times t$

$\dpi{100} \small t=\frac{3r}{q}$

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Example Question #2 : Rate Problems

A cat runs at a rate of 12 miles per hour. How far does he run in 10 minutes?

Possible Answers:

$\dpi{100} 10\ miles$

$\dpi{100} 12\ miles$

$\dpi{100} 2\ miles$

$\dpi{100} 1\ mile$

None of the other answers are correct.

Correct answer:

$\dpi{100} 2\ miles$

Explanation:

We need to convert hours into minutes and multiply this by the 10 minute time interval:

$\small \frac{12\ miles}{1\ hour}x\frac{1\ hour}{60\ min}x\frac{10\ min}{1}=\frac{120\ miles}{60}=2\ miles$

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Example Question #2 : Rate Problems

In order to qualify for the next heat, the race-car driver needs to average 60 miles per hour for two laps of a one mile race-track. The driver only averages 40 miles per hour on the first lap. What must be the driver's average speed for the second lap in order to average 60 miles per hour for both laps?

Possible Answers:

120 miles per hour

240 miles per hour

100 miles per hour

80 miles per hour

90 miles per hour

Correct answer:

80 miles per hour

Explanation:

If the driver needs to drive two laps, each one mile long, at an average rate of 60 miles per hour. To find the average speed, we need to add the speed for each lap together then divide by the number of laps. The equation would be as follows:

$\frac{X+Y}{2}=60$

In our case we know lap one was driven at miles per hour. We substitute this value in for and solve for .

$\frac{40+Y}{2}=60$

40+Y=60(2)

40+Y=120

Y=120-40

Y=80

Thus to average miles per hour for two laps with lap one being miles per hour, lap two would have to have a rate of miles per hour.

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Example Question #231 : Word Problems

Randall traveled 75 kilometers in 600 minutes. What was Randall's per hour rate?

Possible Answers:

$0.80\:\frac{km}{hr}$

$7.5\:\frac{km}{hr}$

$8.00\:\frac{km}{hr}$

$1.25\:\frac{km}{hr}$

$0.125\:\frac{km}{hr}$

Correct answer:

$7.5\:\frac{km}{hr}$

Explanation:

We need to pay close attention to some details here.

1) We are given time in minutes, but asked for an answer in hours.

2) A rate can be defined as distance over time.

Taking the first detail, we convert 600 minutes to 10 hours, since there are 60 minutes in one hour.

Taking the second detail, we divide 75 kilometers by 10 hours. This gives us an answer of 7.5 kilometers per hour.

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Example Question #233 : Word Problems

Ray travels $75 \:km$ in three hours. At this rate, how long (in hours) will it take him to travel $375 \:km$ ?

Possible Answers:

$25\:hr$

$45\:hr$

$15\:hr$

$375\:hr$

$225\:hr$

Correct answer:

$15\:hr$

Explanation:

If Ray covers $75 \:km$ in three hours, that means he covers $25 \:km$ in one hour:

$\frac{1\:hr}{3\:hr}=\frac{x\:km}{75\:km}$

$3x=1\cdot75$

$x=\frac{75}{3}=25\:km$

Perform the following calculation to find how long it takes to cover $375 \:km$ .

$\frac{375\:km}{1}*\frac{1\:hr}{25\:km}=\frac{375\:km\cdot hours}{25\:km}=15 \:hours$

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Example Question #11 : Calculating Rate

If a plane flies the 3000 miles from San Francisco to New York at an average speed of 600 mph, and then, buffetted by a hefty headwind, makes the return trip at an average speed of 300 mph. What was its average speed over the entire round trip?

Possible Answers:

400 mph

450mph

500mph

600mph

350mph

Correct answer:

400 mph

Explanation:

In combined rate problems such as this, we must first find units of the desired answer: $\frac{miles}{hour}$ and then find the totals of each piece of those units. Total miles is easy as we can just add together the two legs of the trip:

3000 mi + 3000mi = 6000 total mi

To find total hours, we just have to use each leg's speed:

$\frac{1hour}{600 miles} \cdot 3000 miles = 5 hours$

$\frac{1 hour}{300 miles} \cdot 3000 miles = 10 hours$

The trip therefore took 15 total hours.

Now we simply divide the totals to find the average speed:

$\frac{6000 miles}{15 hours} = 400 miles/hr$

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Example Question #231 : Problem Solving Questions

Frank can eat a huckleberry pie in 15 minutes. His formidable sister, Francine, can eat it in 10 minutes. How long does it take them to eat a pie together?

Possible Answers:

6 minutes

5 minutes

25 minutes

12.5 minutes

8 minutes

Correct answer:

6 minutes

Explanation:

To solve this combined rate problem, we must use the equation: $\frac{AB}{A + B}$

Where A and B are the times it takes Frank and Francine, respectively, to eat a pie.

Therefore, it takes Frank and Francine

$\frac{10\cdot 15}{10 + 15} = \frac{150}{25} = 6 minutes$

to eat the pie.

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Example Question #1 : Geometry

How many degrees does the hour hand on a clock move between 3 PM and 7:30 PM?

Possible Answers:

135

120

180

Correct answer:

135

Explanation:

An hour hand rotates 360 degrees for every 12 hours, so the hour hand moves $\frac{360^{\circ}}{12\ hours}=30^{\circ}/hr$ .

There are 4.5 hours between 3 PM and 7:30 PM, so the total degree measure is

$4.5\ hours*30^{\circ}/hr = 135^{\circ}$ .

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Example Question #1 : Geometry

If a sector covers $20\%$ of a circle, what is the angle of the sector?

Possible Answers:

$72^{\circ}$

$18^{\circ}$

$84^{\circ}$

$90^{\circ}$

$36^{\circ}$

Correct answer:

$72^{\circ}$

Explanation:

One full rotation of a circle is $360^{\circ}$ , so if a sector covers $20\%$ of a circle, its angle will be $20\%$ of $360^{\circ}$ . This gives us:

$\angle=0.20(360^{\circ})=\frac{1}{5}(360^{\circ})=72^{\circ}$

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All GMAT Math Resources

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GMAT Math : Problem-Solving Questions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #3 : Rate Problems

Example Question #1 : Rate Problems

Example Question #2 : Rate Problems

Example Question #2 : Rate Problems

Example Question #231 : Word Problems

Example Question #233 : Word Problems

Example Question #11 : Calculating Rate

Example Question #231 : Problem Solving Questions

Example Question #1 : Geometry

Example Question #1 : Geometry

All GMAT Math Resources

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