SAT Math : Arithmetic

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #31 : Fractions

Vikki is able to complete 4 SAT reading questions in 6 minutes. At this rate, how many questions can she answer in 3 1/2 hours?

Possible Answers:

35

140

150

170

210

Correct answer:

140

Explanation:

First, find how many minutes are in 3 1/2 hours: 3 * 60 + 30 = 210 minutes. Then divide 210 by 6 to find how many six-minute intervals are in 210 minutes: 210/6 = 35. Since Vikki can complete 4 questions every 6 minutes, and there are 35 six-minute intervals we can multiply 4 by 35 to determine the total number of questions that she can complete.

4 * 35 = 140 problems. 

Example Question #32 : Proportion / Ratio / Rate

The price of k kilograms of quartz is 50 dollars, and each kilogram makes s clocks. In terms of s and k, what is the price, in dollars, of the quartz required to make 1 clock?

Possible Answers:
(50s ) / k
s / (50k )
(50k ) / s
(ks ) / 50
50 / (ks )
Correct answer: 50 / (ks )
Explanation:

We want our result to have units of "dollars" in the numerator and units of "clocks" in the denominator. To do so, put the given information into conversion ratios that cause the units of "kilogram" to cancel out, as follows: (50 dollar/k kilogram)* (1 kilogram / s clock) = 50/(ks) dollar/clock.

Since the ratio has dollars in the numerator and clocks in the denominator, it represents the dollar price per clock.

Example Question #11 : How To Find Rate

Minnie can run 5000 feet in 15 minutes.  At this rate of speed, how long will it take her to fun 8500 feet?

Possible Answers:

25.5 min

75.5 min

36.5 min

20 min

18.5 min

Correct answer:

25.5 min

Explanation:

Find the rate of speed.  5000ft/15 min = 333.33 ft per min

Divide distance by speed to find the time needed

8500ft/333.33ft per min = 25.5

Example Question #11 : How To Find Rate

Ruby drives to her grandmother's house and back. On the way there, she travels at an average speed of 40 miles per hour. On the way back, she travels at an average speed of 60 miles per hour. What is Ruby's average speed for the entire round trip?

Possible Answers:

40

50

48

60

52

Correct answer:

48

Explanation:

Remember d=rt where d = distance, r = rate, and t = time.  In this case, the distance to and the distance from are the same, so we know that

d = rt1 and d = r2 t2

Since r1 = 40 and r2 = 60, we can solve for the times and get

t1 = d/40 and t2 = d/60

Average speed is found by total distance over total time, so we get

Average_rate

Multiplying the numerator and denominator by 120/d we get 240/(3 + 2) = 48.

Example Question #41 : Proportion / Ratio / Rate

If an object takes 10 minutes to go 3 miles, how fast is the object going?

Possible Answers:

36 mph

18 mph

10/3 mph

3/10 mph

1/2 mph

Correct answer:

18 mph

Explanation:

First convert minutes to hours, so 10 minutes is 1/6 hours; then remember distance = rate * time, so distance/time = rate then 3/(1/6) = 18 mph

Example Question #41 : Proportion / Ratio / Rate

Mary travels at a constant speed to her friend Clara's house by walking directly east for 8 miles, and then walking directly north for 6 miles. The amount of time that it takes her to reach Clara's house is equal to t. If Mary had been able to travel directly to Clara's house in a straight line at the same speed, how much time would she have saved, in terms of t?

Possible Answers:

5t/7

3t/7

6t/7

2t/7

4t/7

Correct answer:

2t/7

Explanation:

Drt1

Drt2

Drt3

Example Question #21 : How To Find Rate

Sam earns d dollars per day. At this rate, how many days will it take Sam to earn q dollars?

Possible Answers:

10q

100d/q

d/q

q/d

dq

Correct answer:

q/d

Explanation:

q is the number of dollars to be earned, d is the amount earned each day, so you divide q by d to get the number of days.

Example Question #44 : Proportion / Ratio / Rate

Bob can build a house in 3 days. Gary can build a house in 5 days. How long does it take them to build a house together?

Possible Answers:

3/2 days

4 days

2 days

5/4 days

15/8 days

Correct answer:

15/8 days

Explanation:

DO NOT pick 4 days, which would be the middle number between Bob and Gary's rates of 3 and 5 days respectively. The middle rate is the answer that students always want to pick, so the SAT will provide it as an answer to trick you!

Let's think about this intuitively before we actually solve it, so hopefully you won't be tempted to pick a trick answer ever again! Bob can build the house in 3 days if he works by himself, so with someone else helping him, it has to take less than 3 days to build the house! This will always be true. Never pick the middle rate on a combined rates problem like this! 

Now let's look at the problem computationally. Bob can build a house in 3 days, so he builds 1/3 of a house in 1 day. Similarly, Gary can build a house in 5 days, so he builds 1/5 of a house in 1 day. Then together they build 1/3 + 1/5 = 5/15 + 3/15 = 8/15 of the house in 1 day.

Now, just as we did to see how much house Gary and Bob can build separately in one day, we can take the reciprocal of 8/15 to see how many days it takes them to build a house together. (When we took the reciprocal for Bob, 3 days/1 house = 1/3 house per day.) The reciprocal of 8/15 is 15/8, so they took 15/8 days to build the house together. 15/8 days is almost 2 days, which seems like a reasonable answer. Make sure your answer choices make sense when you are solving word problems!

Example Question #41 : Proportion / Ratio / Rate

Two brothers, Jake and Fred, have a pool in which 9 laps is 1 mile. Jake swims 2 laps in 1 minute, and Fred swims 4 laps in 1 minute. How far has Jake swum when Fred has finished swimming 2 miles?

Possible Answers:

2 miles

3/2 miles

3/4 miles

1 mile

9/2 miles

Correct answer:

1 mile

Explanation:

We can solve this with lots of calculations and conversions of laps to miles, etc., or we can look at what the question is really asking. We want to know how far Jake swims in the time it takes Fred to swim two miles. Instead of converting Fred's miles to laps and comparing to Jake's laps, let's just look at how fast the two brothers swim in relation to one another. Fred swims twice as fast as Jake, so in the same amount of time, he will swim twice as far as Jake. Therefore if Fred swims 2 miles, Jake swims 1 mile in the same amount of time.

Example Question #1411 : Sat Mathematics

Every 3 minutes, 4 liters of water are poured into a 2,000-liter tank. After 4 hours, what percent of the tank is full?

Possible Answers:

0.8\%

16\%

8\%

1.6\%

32\%

Correct answer:

16\%

Explanation:

60 minutes in an hour, 240 minutes in four hours. If 4 liters are poured every 3 minutes, then 4 liters are poured 80 times. That comes out to 320 liters. The tank holds 2,000 liters, so \frac{320}{2000} = 16\% of the tank is full.

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