MAT

Description: MAT Quiz: Test Your Mathematical Abilities
Number of Questions: 14
Created by:
Tags: mat mathematics quantitative aptitude reasoning
Attempted 0/14 Correct 0 Score 0

If 3x + 2y = 12 and 2x - 3y = 5, find the value of x and y.

  1. x = 2, y = 3

  2. x = 3, y = 2

  3. x = 4, y = 1

  4. x = 1, y = 4


Correct Option: A
Explanation:

Solving the given equations simultaneously, we get x = 2 and y = 3.

A train leaves a station at 10:00 AM and travels at a speed of 60 km/hr. Another train leaves the same station at 11:00 AM and travels in the same direction at a speed of 75 km/hr. At what time will the second train overtake the first train?

  1. 12:30 PM

  2. 1:00 PM

  3. 1:30 PM

  4. 2:00 PM


Correct Option: C
Explanation:

The relative speed of the second train with respect to the first train is 75 - 60 = 15 km/hr. Therefore, the second train will overtake the first train in 15/1 = 1 hour. Since the second train leaves at 11:00 AM, it will overtake the first train at 11:00 AM + 1 hour = 12:00 PM + 30 minutes = 1:30 PM.

A shopkeeper sells an article at a profit of 20%. If the selling price is (\$120), what is the cost price of the article?

  1. (\$100)

  2. (\$110)

  3. (\$120)

  4. (\$130)


Correct Option: A
Explanation:

Let the cost price of the article be (\$x). Then, the profit is (\$120 - \$x). Since the profit is 20% of the cost price, we have (\$120 - \$x) = 0.2 (\$x). Solving for (\$x), we get (\$x) = (\$100).

In a certain code, 'APPLE' is written as '51223'. How is 'ORANGE' written in the same code?

  1. 15021795

  2. 15902751

  3. 15027951

  4. 15920751


Correct Option: C
Explanation:

In the given code, each letter is assigned a number based on its position in the alphabet. For example, 'A' is assigned 1, 'P' is assigned 5, and so on. Therefore, 'ORANGE' is written as 15027951.

A rectangular garden has a length of 20 meters and a width of 15 meters. If a path of uniform width (\$x) meters is constructed around the garden, what is the area of the path?

  1. (\$2x(20 + 15))

  2. (\$2x(20 - 15))

  3. (\$(20 + 15)x^2)

  4. (\$(20 - 15)x^2)


Correct Option: A
Explanation:

The area of the path is equal to the area of the outer rectangle minus the area of the inner rectangle. The outer rectangle has a length of (\$(20 + 2x)) meters and a width of (\$(15 + 2x)) meters. Therefore, the area of the outer rectangle is (\$(20 + 2x)(15 + 2x)) square meters. The inner rectangle has a length of 20 meters and a width of 15 meters. Therefore, the area of the inner rectangle is (\$20 \times 15) square meters. Therefore, the area of the path is (\$(20 + 2x)(15 + 2x) - 20 \times 15) square meters = (\$2x(20 + 15)) square meters.

A train crosses a 100-meter long bridge in 10 seconds. If the speed of the train is 72 km/hr, what is the length of the train in meters?

  1. 150

  2. 200

  3. 250

  4. 300


Correct Option: B
Explanation:

First, convert the speed of the train from km/hr to m/s: (\$72 \times 5/18 = 20) m/s. Then, use the formula (\$distance = speed \times time) to find the length of the train: (\$100 = 20 \times 10). Therefore, the length of the train is 200 meters.

A sum of money doubles itself in 10 years at a certain rate of simple interest. In how many years will it triple itself at the same rate of interest?

  1. 15 years

  2. 20 years

  3. 25 years

  4. 30 years


Correct Option: A
Explanation:

Let the sum of money be (\$P) and the rate of interest be (\$r)%. Then, the amount after 10 years is (\$P + P \times r \times 10/100 = 2P). Therefore, (\$r = 10)%. Now, let the number of years required for the sum to triple itself be (\$n). Then, the amount after (\$n) years is (\$P + P \times r \times n/100 = 3P). Substituting (\$r = 10)%, we get (\$3P = P + P \times 10 \times n/100). Simplifying, we get (\$n = 15) years.

A shopkeeper sells two types of apples, variety A and variety B. Variety A apples cost (\$2) each and variety B apples cost (\$3) each. If the shopkeeper sells a total of 100 apples for (\$250), how many apples of each variety did he sell?

  1. 50 apples of variety A and 50 apples of variety B

  2. 60 apples of variety A and 40 apples of variety B

  3. 70 apples of variety A and 30 apples of variety B

  4. 80 apples of variety A and 20 apples of variety B


Correct Option: B
Explanation:

Let the number of apples of variety A sold be (\$x) and the number of apples of variety B sold be (\$y). Then, we have the following system of equations: (\$x + y = 100) and (\$2x + 3y = 250). Solving this system of equations, we get (\$x = 60) and (\$y = 40).

A company has 100 employees. If 60% of the employees are male and the rest are female, how many female employees does the company have?

  1. 30

  2. 40

  3. 50

  4. 60


Correct Option: B
Explanation:

The number of male employees is (\$100 \times 60/100 = 60). Therefore, the number of female employees is (\$100 - 60 = 40).

A train leaves a station at 10:00 AM and travels at a speed of 60 km/hr. Another train leaves the same station at 11:00 AM and travels in the same direction at a speed of 75 km/hr. At what time will the second train be 15 km ahead of the first train?

  1. 12:00 PM

  2. 12:30 PM

  3. 1:00 PM

  4. 1:30 PM


Correct Option: B
Explanation:

The relative speed of the second train with respect to the first train is (\$75 - 60 = 15) km/hr. Therefore, the second train will be 15 km ahead of the first train in (\$15/15 = 1) hour. Since the second train leaves at 11:00 AM, it will be 15 km ahead of the first train at 11:00 AM + 1 hour = 12:00 PM + 30 minutes = 12:30 PM.

A shopkeeper sells an article at a profit of 20%. If the selling price is (\$120), what is the cost price of the article?

  1. (\$100)

  2. (\$110)

  3. (\$120)

  4. (\$130)


Correct Option: A
Explanation:

Let the cost price of the article be (\$x). Then, the profit is (\$120 - \$x). Since the profit is 20% of the cost price, we have (\$120 - \$x) = 0.2 (\$x). Solving for (\$x), we get (\$x) = (\$100).

A rectangular garden has a length of 20 meters and a width of 15 meters. If a path of uniform width (\$x) meters is constructed around the garden, what is the area of the path?

  1. (\$2x(20 + 15))

  2. (\$2x(20 - 15))

  3. (\$(20 + 15)x^2)

  4. (\$(20 - 15)x^2)


Correct Option: A
Explanation:

The area of the path is equal to the area of the outer rectangle minus the area of the inner rectangle. The outer rectangle has a length of (\$(20 + 2x)) meters and a width of (\$(15 + 2x)) meters. Therefore, the area of the outer rectangle is (\$(20 + 2x)(15 + 2x)) square meters. The inner rectangle has a length of 20 meters and a width of 15 meters. Therefore, the area of the inner rectangle is (\$20 \times 15) square meters. Therefore, the area of the path is (\$(20 + 2x)(15 + 2x) - 20 \times 15) square meters = (\$2x(20 + 15)) square meters.

A train crosses a 100-meter long bridge in 10 seconds. If the speed of the train is 72 km/hr, what is the length of the train in meters?

  1. 150

  2. 200

  3. 250

  4. 300


Correct Option: B
Explanation:

First, convert the speed of the train from km/hr to m/s: (\$72 \times 5/18 = 20) m/s. Then, use the formula (\$distance = speed \times time) to find the length of the train: (\$100 = 20 \times 10). Therefore, the length of the train is 200 meters.

A sum of money doubles itself in 10 years at a certain rate of simple interest. In how many years will it triple itself at the same rate of interest?

  1. 15 years

  2. 20 years

  3. 25 years

  4. 30 years


Correct Option: A
Explanation:

Let the sum of money be (\$P) and the rate of interest be (\$r)%. Then, the amount after 10 years is (\$P + P \times r \times 10/100 = 2P). Therefore, (\$r = 10)%. Now, let the number of years required for the sum to triple itself be (\$n). Then, the amount after (\$n) years is (\$P + P \times r \times n/100 = 3P). Substituting (\$r = 10)%, we get (\$3P = P + P \times 10 \times n/100). Simplifying, we get (\$n = 15) years.

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