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Algebra

Description: Algebra Test - Free Online Algebra Test for Various Entrance Examination MBA Entrance, GRE, SAT, Bank PO, LAW, UPSC, Civil Services and Govt Jobs Preparation
Number of Questions: 25
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Tags: Algebra Quantitative Ability Arithmetic Linear Equations Word problems Time and Distance Percentages Letter JKL Synonyms
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Two cities n miles apart are located s inches apart on a certain map that is drawn to scale. What is the difference (in inches) on the map between two cities that are n + 1 miles apart?

  1. n/s

  2. (n + 1)/s

  3. s/(n + 1)

  4. s(n + 1)/n

  5. s(n - 1)/n


Correct Option: D
Explanation:

It is given that n miles are represented by s inches. So, 1 mile is represented by s/n inches. So, (n + 1) miles will be represented by s(n + 1)/n inches.

Carla has 2 more tapes than 3 times the number of tapes Julia has. If C represents the number of Carla's tapes and J represents the number of Julia's tapes, which of the following is a correct expression relating C and J?

  1. C = 2J + 3

  2. C = 2(J + 3)

  3. C = 3J - 2

  4. C = 3J + 2

  5. C = 3(J + 2)


Correct Option: D
Explanation:

Obviously, the given information can be translated as C = 3J + 2.

After Jenny deposited s dollars into her savings account, she had d dollars in the account. After that, if she withdrew (s - 70) dollars from this account, how many dollars did she have in her account?

  1. d - s - 70

  2. d - s + 70

  3. d + s - 70

  4. d - s

  5. d - 70


Correct Option: B
Explanation:

The first bit of information is in fact irrelevant. What the second bit says is that from an account which had d dollars, she withdrew (s - 70) dollars. So, what will be left behind is d - (s - 70) = d - s + 70 dollars.

The total weight of Bill and his son Tommy is 250 pounds. If Bill's weight is 10 pounds more than 3 times Tommy's, what is Tommy's weight in pounds?

  1. 40

  2. 50

  3. 60

  4. 70

  5. 80


Correct Option: C
Explanation:

lf Tommy's weight is x pounds, Bill's weight is 3x + 10. It is given that x + 3x + 10 = 250. So, 4x + 10 = 250, or 4x = 240, or x = 60.

If Jim receives m marbles in addition to the number of marbles he had originally, he will have t times as many as he had originally. In terms of m and t, how many marbles did Jim originally have?

  1. (t - m)

  2. (t + 1)/m

  3. m/(t + 1)

  4. m/(t - 1)

  5. (m- 1)/(t - 1)


Correct Option: D
Explanation:

If Jim had x marbles originally, it is given that x + m = tx.   So, m = tx - x = x(t - 1). So, x = m/(t - 1).

If a ball thrown straight up at a certain speed, at height h (in feet), after t seconds, is given by the formula h = 40t - 16t2. How many feet high will the ball be one second after it is thrown?

  1. 12

  2. 16

  3. 24

  4. 32

  5. 40


Correct Option: C
Explanation:

In the formula h = 40t - 16t2, h represents feet and t represents seconds. So, if t = 1, h = 40 - 16 = 24 feet.

The first third of a 75-mile trip took twice as long as the rest of the trip. If the first third took h hours, what was the average speed, in miles per hour, for the whole trip?

  1. 25/h

  2. 75/2h

  3. 50/h

  4. 125/2h

  5. 225/2h


Correct Option: C
Explanation:

The given information is that the whole of the trip of 75 miles was covered in h + h/2 hours, or 3h/2 hours. So, the average speed per hour was (distance/number of hours) = 75/(3h/2) = 150/3h = 50/h miles.

The Acme, Rent-a-car agency, charges $10.00 per day and $0.10 per mile to rent a car. The Super, Rent-a-car agency, charges $20.00 per day and $0.05 per mile to rent a car. If a car is rented for 1 day, at how many miles will the rental charges of the two agencies be equal?

  1. 50

  2. 100

  3. 150

  4. 200

  5. 20


Correct Option: D
Explanation:

If the total charges are equal for a travel of x miles, and we convert the dollars into cents, we get the equation 1000 + 10x = 2000 + 5x = 1000, or x = 200.

A postal clerk sold 75 stamps for a total of $10.85. Some of the stamps were 15-cent stamps and the remaining stamps were 13-cent stamps. How many of the stamps were 13-cent stamps?

  1. 15

  2. 20

  3. 25

  4. 30

  5. 35


Correct Option: B
Explanation:

If the numbers of 15 cents and 13 cents stamps were x and y respectively, we get the equation x + y = 75, and 15x + 13y = 1085. Multiplying the first equation by 15, we get 15x + 15y = 125. Subtracting the second equation from this, we get 2y = 40, or y = 20.

If the cost of x gallons of unleaded gasoline, priced at $1.24 per gallon, equals the cost of (x + 2) gallons of regular gasoline, priced at $1.16 per gallon, find the value of x.

  1. 29

  2. 24

  3. 16

  4. 14

  5. 12


Correct Option: A
Explanation:

It is given 124x = 116(x + 2). So, 8x = 232, or x = 29

The daily rate for a hotel room that sleeps 4 people is $39 for one person and x dollars for each additional person. If 3 people can take the room for one day and each pays $21 for the room, what is the value of x?

  1. $6

  2. $8

  3. $12

  4. $13

  5. $24


Correct Option: C
Explanation:

The charge for 3 people = 39 + 2x dollars. This is given to be equal to 63. So, 2x = 63 - 39 = 24, or x = 12.

At 9 a.m, train T left the station and two hours later train S left the same station on a parallel track. If train T averaged 60 kilometers per hour and train S averaged 75 kilometers per hour until S passed T, at what time did S pass T?

  1. 2 p.m

  2. 5 p.m

  3. 6 p.m

  4. 7 p.m

  5. 9 p.m


Correct Option: D
Explanation:

If the two trains met x hours after the first train left the station, we get the equation 60x = 75(X - 2). So, 15x = 150, or x = 10. So, the two trains would meet 10 hours after 9 a.m, or at 7 p.m.

Two tanks X and Y are filled to capacity with jet fuel. Tank X holds 600 gallons more than tank Y. If 100 gallons of fuel were to be pumped from each tank, tank X would then contain 3 times as much fuel as tank Y. What is the total amount of fuel in two full tanks (in gallons)?

  1. 1,400

  2. 1,200

  3. 1,000

  4. 900

  5. 800


Correct Option: A
Explanation:

If the capacities of the two tanks are x and y respectively, it is given x = y + 600, and (x -100) = 3(y - 100). Substituting the value of x in the second equation, we get y + 500 = 3y - 300. So, 2y = 800, or y = 400. So, x = 1000. So, the total number of gallons in two full tanks = 1400.

If the cost of an item is $8 and the sum of the cost and the profit is $11, then the profit (in dollars) is

  1. 2

  2. 3

  3. 4

  4. 19

  5. Cannot be determined


Correct Option: B
Explanation:

If the profit is y dollars, it is given that 8 + y = 11. So, y = 3.

A secretary typed 6 letters, each of which had either 1 or 2 pages. If the secretary typed 10 pages in all, how many of the letters had 2 pages?

  1. 1

  2. 2

  3. 3

  4. 4

  5. 5


Correct Option: D
Explanation:

If x letters had 1 page each and y letters had 2 pages each, it is given that x + y = 6, and x + 2y = 10. So, subtracting the first equation from the second, we get y = 4.

The price of ground coffee beans is 'd' dollars for 8 ounces and each ounce makes 'c' cups of brewed coffee. In terms of c and d, what is the cost (in dollars) of the ground coffee beans required to make 1 cup of brewed coffee?

  1. d/8c

  2. cd/8

  3. 8c/d

  4. 8d/c

  5. 8cd


Correct Option: A
Explanation:

The given information is 8c cups of coffee cost d dollars. So, 1 cup of coffee will cost d/8c dollars.

If a certain object has been moving at the constant rate of x meters per minute, how many metres has the object moved in the last y seconds?

  1. xy/60

  2. 60x/y

  3. x/60y

  4. 60/xy

  5. 60 xy


Correct Option: A
Explanation:

If the speed is x meters per minute, the speed per second is x/60 meters. So, the distance travelled in y seconds is xy/60 meters.

If 2/3 of the number of women attending a certain dance class is equal to 1/2 the number of men attending the class, what fraction of those attending the class are women?

  1. 2/5

  2. 3/7

  3. 5/7

  4. 3/4

  5. 5/6


Correct Option: B
Explanation:

Let the number of men and women be x and y respectively. It is given that x/2 = 2y/3. So, y = 3x/4. What is required is y/(x + y), which is equal to (3x/4) / (x + 3x/4) = 3x/7x = 3/7.  

The cost of sending a package by special delivery is x cents per ounce upto 10 ounces and y cents for each ounce in excess of 10 ounces. Which of the following represents the cost (in cents) of sending a package weighing w ounces (w > 10) by special delivery?

  1. x + (w - 10)y = 10

  2. x + (w - 10) + y

  3. 10x + 10(w - y)

  4. 10x + y(w - 10)

  5. 10x + wy


Correct Option: D
Explanation:

The cost for the first 10 ounces is 10x cents, and the cost for the next (w - 10) ounces is y(w - 10) cents. So, the total cost = 10x + y(w - 10) cents.

Sally buys a pen and a pencil for $1.45. If the pen costs $0.25 more than the pencil, how much does the pencil cost?

  1. $0.25

  2. $0.45

  3. $0.60

  4. $0.85

  5. $1.20


Correct Option: C
Explanation:

If the cost of the pencil is x cents, the cost of the pen is x + 25 cents. It is given x + x + 25 = 145.    So, 2x = 120, or x = 60 cents.

By weight, in a mixture of 5 grams, liquid A makes up 7 percent of solution I and 14.5 percent of solution II. If 3 grams of solution I is mixed with 2 grams of solution II, then liquid A accounts for what percent of the weight of the resultant solution?

  1. 6.09%

  2. 10%

  3. 10.75%

  4. 21.5%

  5. 50%


Correct Option: B
Explanation:

In the mixture of 5 grams, A makes up 7% of 3 grams and 14.5% of 2 grams, or  (21/100 + 29/100) grams or 50/100 grams, or 1/2 gram. So, its percentage in the mixture of 5 grams is (1/2)/5 × 100 =  1/10 × 100 = 10%

Mario bought equal numbers of 2-cent and 3-cent stamps. If the total cost of the stamps was $1.00, what was the total number of stamps bought?

  1. 25

  2. 34

  3. 40

  4. 46

  5. 48


Correct Option: C
Explanation:

Let the number of 2-cent and 3-cent stamps bought hex each.

It is given 2x + 3x = 100, or 5x = 100.

So, x = 20. So, the total number of stamps bought = 2x = 40.

What was the original price (in dollars) of an item if a discount of 20% reduced the price to $100?

  1. 80

  2. 120

  3. 125

  4. 150

  5. 250


Correct Option: C
Explanation:

If the original price is x dollars, then the reduced price = 80% of x = 4X/5. If this is equal to 100, then 4x = 500, and x = 125

The entry ticket per child in a certain amusement park is 7/12 of the admission price per adult. If the entry ticket for 4 adults and 6 children is $112.50, what is the entry ticket per adult?

  1. $15.00

  2. $13.50

  3. $12.75

  4. $11.25

  5. $10.75


Correct Option: A
Explanation:

If the admission price per adult is x dollars, it is given as 4x + (6 × 7x/12) = 112.50. So, 4x + 7x/2 = 112.50, or 15x/2 = 112.50. So, x = 225/15 = 15

Vishal lives in town A. He leaves his house for exactly 10 hours everyday to sell fruits. He purchases his fruits from either local Town A market or from any of the three neighbouring towns B, C or D. It takes him 1 hour to reach C and 1.5 hour to reach D from A. The time required for traveling from B to C, C to D or B to D is 1 hour. In 1 hour, he sells, exactly 1 kg of fruits. The rates of fruits in the four towns are as follows: A = Rs. 20/kg, B = Rs. 25/kg, C = Rs. 10/kg, D = Rs. 11/kg. He completes each day without any stock at the end. Assume that the buying and selling price are the same.

How many extra hours should Vishal put in, in order to earn Rs. 120?

  1. 4.5 hours

  2. 5 hours

  3. 6 hours

  4. 4 hours

  5. 5.5 hours


Correct Option: D
Explanation:

Correct Answer: 4 hours

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