1001_Math_Problems__LearningExpress_

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Set 48 (Answers begin on page 203.)

753. Divide:	6a2b ab2
	2c	÷	4c4

24ac

a.

b

12ac3

b.

b

24ac3

c.

b

d. 12abc3

754. Five oranges, when removed from a basket containing three more than seven times as many oranges, leaves how many in the basket? a. 21

b. 28 c. 33 d. 38

755. How many ounces of candy costing $1 per ounce must be mixed with 6 ounces of candy costing 70 cents per ounce to yield a mixture

costing 80 cents per ounce?

6

a. ounce

7

b. 3 ounces

c. 9 ounces

7

d. 20 ounces

10

756.Dave can wash and wax a car in 4 hours. Mark can do the same job in 3 hours. If both work together how long will it take to wash and wax the car?

a.1.7 hours

b.2.3 hours

c.3 hours

d.3.3 hours

757.How long will it take Sheri to walk to a store five miles away if she walks at a steady pace of 3 miles per hour?

a.0.60 hours

b.1.67 hours

c.3.33 hours

d.15 hours

758.Jeff was 10 minutes early for class. Dee came in four minutes after Mae, who was half as early as Jeff. How many minutes early was Dee?

a.1 minute

b.2 minutes

c.2.5 minutes

d.6 minutes

759.Jan loaned Ralph $45 expecting him to repay $50 in one month. What is the amount of annual simple interest on this loan? (R = the

annual rate of simple interest. Interest =

Principal × Rate × Time, or I = PRT.)

a.5%

b.33%

c.60%

d.133%

760.Twelve people entered a room. Three more than two-thirds of these people then left. How many people remain in the room?

a.0

b.1

c.2

d.7

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761. A 24-inch-tall picture is 20% as tall as the ceil-			766.	Rosa finds the average of her three most recent
ing is high. How high is the ceiling?				golf scores by using the following expression,
a.	4.8 feet						a + b + c
				where a, b, and c are the three scores: ×
b.								3
	10 feet			100. Which of the following would also deter-
c.	12 feet			mine the average of her scores?
d.	120 feet				a	b	c
				a. ( 3		+ 3	+ 3 ) × 100
					a + b + c
						3
762. Belinda is building a garden shed. When she				b.
					100
helped her neighbor build an identical shed it				c.	(a + b + c) × 3
						100
took them both 22 hours to complete the job.				d.	a × b × c		+ 100
If it would have taken her neighbor, working						3
alone, 38 hours to build the shed, how long will			767.				5	8
				Simplify the radical completely: 64x y .
it take Belinda, working alone, to build her				a. 8x2y4 x
shed?				b. 8x4y8 x
a.	33.75 hours			c. 64x2y4
b.	41.00 hours			d. 8x5y8
c.	41.25 hours
d.	52.25 hours		768.	While driving home from work, Sally runs
				over a nail causing a tire to start leaking. She
763. If nine candles are blown out on a birthday				estimates that her tire is leaking 1 pound per
cake containing seven times as many candles				square inch (psi) every 20 seconds. Assuming
altogether, how many candles are there in all?				that her tire leaks at a constant rate and her
a.	2			initial tire pressure was 36 psi, how long will
b.	16			it take her tire to completely deflate?
c.	63			a.	1.8 minutes
d.	72			b.	3.6 minutes
				c.	12 minutes
764. Simplify the radical:		81x2		d.	18 minutes
		2 .
	9x	y
a.
	y
b.	9x
c.	9xy
d.	9x2
	y
765. Which of the following linear equations has a
negative slope?
a.	6 = y – x
b.	y = 4x – 5
c.	–5x + y = 1
d.	6y + x = 7

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–ALGEBRA–

Set 49 (Answers begin on page 204.)

769.Mark needs to work five-sixths of a year to pay off his car loan. If Mark begins working on March 1st, at the end of what month will he first be able to pay off his loan?

a.June

b.August

c.October

d.December

770.Solve the equation for b: b – 4 = 5

a.1

b.9

c.21

d.29

2w 5w

771. Find the sum: z + z .

7w

a.

2z

7w

b.

z2

7w

c. z

d. 7w

772. Some birds are sitting in an oak tree. Ten more birds land. More birds arrive until there are a total of four times as many birds as the oak tree had after the ten landed. A nearby maple tree has sixteen fewer than twelve times as many birds as the oak tree had after the ten landed. If both trees now have the same number of birds, how many birds were originally in the oak tree before the first 10 landed?

a. 4

b. 7

c. 16

d. 24

773.A jar of coins totaling $4.58 contains 13 quarters and 5 nickels. There are twice as many pennies as there are dimes. How many dimes are there?

a.5

b.9

c.18

d.36

774.If a function is defined as f (x) = 5x2 – 3, what is the value of f (–2)?

a.–13

b.7

c.–23

d.17

775.A hiker walks from his car to a distant lake and back again. He walks on smooth terrain for 2 hours until he reaches a 5-mile-long, rocky trail. His pace along the 5-mile-long trail is 2 mph. If he walks steadily with no stops, how long will it take the hiker to complete the entire trip from his car to the lake and back again?

a.4.5 hours

b.9 hours

c.12 hours

d.16 hours

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776.The total pressure of a mix of gases in a container is equal to the sum of the partial pressures of each of the gases in the mixture. A mixture contains nitrogen, oxygen, and argon, and the pressure of nitrogen is twice the pressure of oxygen, which is three times the pressure of argon. If the partial pressure of nitrogen is 4 pounds per square inch (psi), what is the total pressure?

a.24 psi

b.16 psi

2

c. 14 psi

3

2

d. 6 psi

3

777.Suppose the amount of radiation that could be received from a microwave oven varies inversely as the square of the distance from it. How many feet away must you stand to reduce

1

your potential radiation exposure to the

16

amount you could receive standing 1 foot away?

a.16 feet

b.4 feet

c.32 feet

d.8 feet

778.Which of the following linear equations has undefined slope?

a.

y

x

b.

y

x

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c.		780.
	y
	x
		781.
d.
	y
	x	782.
779. Solve the equation for a: 2a + 6 – 4 = 6
a.	2
b.	17
c.	23
d.	47
		115

If Willie must pay an employment agency his first month’s salary as a placement fee, how much of his $28,000 first year’s salary will Willie end up with?

a.$2,333

b.$3,360

c.$24,343

d.$25,667

Jack went hiking in bad weather wearing a backpack filled with 60 pounds of supplies. A

couple of miles into his hike, he became tired

1

and discarded supplies equal to of the 60

3

pounds. A few miles later it started to snow,

2

and he discarded another of the original 60

5

pounds. How much did Jack discard altogether during his hike?

a.5 pounds

b.10 pounds

c.20 pounds

d.44 pounds

If a school buys three computers at a, b, and c dollars each, and the school gets a discount of 90%, which expression would determine the average price paid by the school?

0.9 × (a + b + c)

a.

3

(a b c)

b.

0.9

c. (a + b + c) × 0.9

(a + b + c)

d.

3

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783. Three apples and twice as many oranges add		784. Rudy forgot to replace his gas cap the last time
up to one-half the number of cherries in a fruit		he filled up his car with gas. The gas is evapo-
basket. How many cherries are there?		rating out of his 14-gallon tank at a constant
a.	11	rate of			1
					3 gallon per day. How much gas does
b.	18	Rudy lose in 1 week?
c.	21	a.	2 gallons
d.	24	b.	2	1	gallons
				3
		c.	4	2	gallons
				3
		d.	6 gallons

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	Set 50 (Answers begin on page 206.)					789. Pamela’s annual salary is six times as much as
						Adrienne’s, who earns five times more than
	785. Which ratio best expresses the following: five					Beverly, who earns $4,000. If Valerie earns one-
	hours is what percent of a day?					half as much as Pam, what is Valerie’s annual
	a.	5			x	salary?
				=
		100			24
	b.	5	=		24	a.	$25,000
		24			x	b.	$60,000
	c.	5	=		x
		24			100	c.	$90,000
	d.	x			24
		100		= 5
						d.	$110,000
	786. White flour and whole wheat flour are mixed					790. Yolanda and Gertrude are sisters. When one-
	together in a ratio of 5 parts white flour to 1
						fourth of Gertrude’s age is taken away from
	part whole wheat flour. How many pounds of
						Yolanda’s age, the result is twice Gertrude’s age.
	white flour are in 48 pounds of this mixture?
						If Yolanda is 9, how old is Gertrude?
	a.	8 pounds
						a.	2.25 years old
	b.	9.6 pounds
						b.	4 years old
	c.	40 pounds
						c.	4.5 years old
	d.	42 pounds
						d.	18 years old
	787. Timmy can sell 20 glasses of lemonade for 10					791. How many pounds of chocolates which cost
	cents per glass. If he raises the price to 25 cents
						$5.95 per pound must be mixed with 3 pounds
	per glass, Timmy estimates he can sell 7 glasses.
						of caramels costing $2.95 per pound to obtain
	If so, how much more money will Timmy
						a mixture that costs $3.95 per pound?
	make by charging 25 cents instead of 10 cents
						a.	1.5 pounds
	per glass?
						b.	3 pounds
	a.	−$0.25
						c.	4.5 pounds
	b.	$0
						d.	8 pounds
	c.	$0.10
	d.	$0.50				792. Kathy charges $7.50 per hour to mow a lawn.
	788. Bill lives five miles away from school. Tammy					Sharon charges 1.5 times as much to do the
						same job. How much does Sharon charge to
		1		as far away from school. Joe’s distance
	lives 2
						mow a lawn?
	from school is half way between Bill and
						a. $5.00 per hour
	Tammy’s. How far away from school does Joe
						b. $11.25 per hour
	live?
						c. $10.00 per hour
	a.	1.25 miles
						d. $9.00 per hour
	b.	3.75 miles
	c.	6.25 miles
	d.	7.5 miles

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793. Laura saves at three times the rate Hazel does.

1

If it takes Laura 1 years to save $1,000, how

2

long will it take Hazel to save this amount?

a.1 year

b.3.5 years

c.4.5 years

d.6 years

9 3w

794. Find the difference: –

2a 6a3

9a2 – w

a.

2a3

9 – 3w

b.

6a3

9a2 – w

c.

6a3

27a2 – w

d.

2a3

795. If a function is defined as g(x) = x 2 – 4x + 1, what is the value of g(1)?

a. –3 b. –2 c. –1 d. 1

796. Fire departments commonly use the following formula to find out how far from a wall to place the base of a ladder: (Length of ladder ÷ 5 feet) + 2 feet = distance from the wall. Using this formula, if the base of a ladder is placed 10 feet from a wall, how tall is the ladder?

a. 40 feet b. 48 feet c. 72 feet d. 100 feet

797.William has one-third as many toys as Tammy who has four times more toys than Edgar, who has 6. How many toys does Jane have if she has 5 more than William?

a.4 toys

b.13 toys

c.8 toys

d.9 toys

798.Susan and Janice are sign painters. Susan can paint a sign in 6 hours while Janice can paint the same sign in 5 hours. If both worked together, how long would it take them to paint this sign?

a.2.53 hours

b.2.73 hours

c.3.00 hours

d.3.23 hours

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799. Match the graph with the inequality:	c.
5y ≥ 10x – 15.		y
a.
y
		x
	x
	d.
		y
b.
y
		x
	x
	800. Solve the following system of equations alge-
	braically by substitution:
	y + 2x = 3
	x = 3y + 5
	a.	(2,–1)
	b.	(2,0)
	c.	(–1,–2)
	d.	(2,–2)
	119

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Set 51 (Answers begin on page 207.)

801.Which of the following systems contains two parallel lines?

a.x = 5 y = 5

b.y = −x

y = x – 1

c.x – y = 7 2 – y = –x

d.y = 3x + 4 2x + 4 = y

805.13 percent of a certain school’s students are A students, 15 percent are C students, and 20 percent make mostly Ds. If 16 percent of the students are B students, what percent are failing?

a.25%

b.36%

c.48%

d.64%

806.Which equation is represented by the graph below?

		y
802. How much simple interest is earned on $300
deposited for 30 months in a savings account
	3
paying 7 4 % simple interest annually? (Interest
Principal × Rate × Time, or I = PRT.)
a.	$5.81	x
b.	$19.76
c.	$23.25
d.	$58.13

803.Jason is six times as old as Kate. In two years, Jason will be twice as old as Kate is then. How old is Jason now?

a.6 months old

b.3 years old

c.6 years old

d.9 years old

804.Mike types three times as fast as Nick. Together they type 24 pages per hour. If Nick learns to type as fast as Mike, how much will they be able to type per hour?

a.18 pages

b.30 pages

c.36 pages

d.40 pages

a.y = x2 – 4

b.y = x2 – 2

c.y = x2

d.y = x2 + 4

2

807. A four-pound mixture of raisins and nuts is

3

raisins. How many pounds of nuts are there?

a.1.3 pounds

b.1.6 pounds

c.2.4 pounds

d.2.6 pounds

120