Common Admission Test (CAT) Questions and Answers with Explanation

Q:

Directions:

Four friends Raghu, Rajesh, Ramesh and Ravi complete their Graduation in different number of years. The one who took maximum time took eight years to complete his Graduation while the one who took least time took only three years to complete it.Ravi took more time only than Raghu and completed his Graduation in five years. Ramesh did not take longer time
than Rajesh to complete his Graduation.

Question:

Who took more years to complete his graduation among all ?

A) Ramesh	B) Raghu
C) Rajesh	D) Ravi

Answer & Explanation Answer: C) Rajesh

Explanation:

Rajesh - 8 years

Ramesh - 6 or 7 years

Ravi - 5 years

Raghu - 3 years

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Q:

The sides of a right-angled triangle are 12 cm, 16 cm, 20 cm respectively. A new right angle Δ is made by joining the midpoints of all the sides. This process continues for infinite then calculate the sum of the areas of all the triangles so made.

A) 312 sq.cm	B) 128 sq.cm
C) 412 sq.cm	D) 246 sq.cm

Answer & Explanation Answer: B) 128 sq.cm

Explanation:

Area = = 96

Sum of Area =

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Q:

Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 56, what will be the sum of the highest number and the lowest number?

A) 120	B) 160
C) 80	D) 60

Answer & Explanation Answer: A) 120

Explanation:

Let the three numbers be x, y, z.

From the gien data,

x = 2y ....(1)

x = z/2 => z = 2(2y) = 4y .....(From 1) ...........(2)

Given average of three numbers = 56

Then,

$\frac{x + y + z}{3} = 56 \frac{2 y + y + 4 y}{3} = 56 (From 1 & 2) 7 y = 56 x 3 y = 24$

Now,

x = 2y => x = 2 x 24 = 48

z = 4y = 4 x 24 = 96

Now, the highest number is z = 96 & smallest number is y = 24

Hence, required sum of highest number and smallest number

= z + y

= 96 + 24

= 120.

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Q:

The output quality of a printer is measured by

A) Dots per line	B) Dots printed per unit time
C) Dots per inch	D) All of the above

Answer & Explanation Answer: C) Dots per inch

Explanation:

DPI [Dots Per Inch] is a measurement of output quality of printer resolution. It represents number of ink dots the printer can place in an area of one square inch. The lesser the DPI the less sharper the image and vice versa.

Therefore, a printer that may have 400 DPI, a printer that can print 400 x 400 per square inch or 1,60,000 dots per inch.

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6 7245

Q:

The Largest Component of National Income is

A) Proprietors Income	B) Compensation of Employees
C) Corporate Profits	D) Rental Income

Answer & Explanation Answer: B) Compensation of Employees

Explanation:

National Income is the total income value of the goods and services produced by the residents of a country, usually during the period of one year.

National Income is categorized into 6 components. They are :

1. Compensation of Employees (Wages and Benefits)
2. Corporate Profits
3. Rental Income
4. Proprietors Income (Income of unincorporated business)
5. Net Interest

The Largest Component of National Income is Compensation of Employees.

The Largest component of National Income in India is Service Sector.

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Q:

For $x \in N, x > 1$ , and $p = \log_{x} (x + 1)$ , $q = \log_{x + 1} (x + 2)$ then which one of the following is correct?

A) p < q	B) p = q
C) p > q	D) can't be determined

Answer & Explanation Answer: C) p > q

Explanation:

$\frac{k}{l} > \frac{k + 1}{l + 1}$ for (k,l) > 0 and k > l

Let k = x+1 and l = x

Therefore, $\frac{x + 1}{x} > \frac{(x + 1) + 1}{(x) + 1}$

(x + 1) > x

Therefore, $\frac{\log (x + 1)}{\log (x)} > \frac{\log (x + 2)}{\log (x + 1)}$

$\Rightarrow \log_{x} (x + 1) > \log_{x + 1} (x + 2)$

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33 7219

Q:

Who of the following threw a bomb in the Central Legislative Assembly along with Bhagat Singh ?

A) B.K. Dutt	B) Sukhdev
C) Jatin Das	D) Rajguru

Answer & Explanation Answer: A) B.K. Dutt

Explanation:

Bhagat Singh and B.K. Dutt threw bombs in the Legislative Assembly as a protest against "Passage of public Safety bill".

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Q:

In a mixture of three varities of oils , the ratio of their weight is 4 : 5 : 8. If 5 kg of oils of the first variety, 10 kg of the second variety and some quantity of oils of the third variety are added to the mixture, the ratio of the weights of three varieties of oils becomes as 5 : 7 : 9 in the final mixture, find the quantity of third variety of oil was ?

A) 15 kg	B) 25 kg
C) 35 kg	D) 45 kg

Answer & Explanation Answer: D) 45 kg

Explanation:

Let the ratio of initial quantity of oils be 'x' => 4x, 5x & 8x.
Let k be the quantity of third variety of oil in the final mixture.
Let the ratio of initial quantity of oils be 'y'
From given details,
4x + 5 = 5y ..... (1)
5x + 10 = 7y .....(2)
8x + k = 9y ......(3)

By solving (1) & (2), we get
x = 5 & y = 5

From (3) => k = 5

Therefore, quantity of third variety of oil was 9y = 9(5) = 45kg.

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