CAT Questions

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Volume of cuboid = (24 x 9 x 8) cm = 1728 cu.cm
Volume of small cube = (3 x 3 x 3) cm = 27 cu.cm

So, No. of small cubes formed = 1728/27 = 64.

Let the required number of minutes = M
Total minutes between 3o'clock and 6o' clock = 180 minutes
M + 50 + 4M = 180
5M + 50 = 180
5M = 130
M = 26 minutes.

Let the cost price of the item = Rs. 50

Sold at 10% loss => for Rs. 50 loss  S.P = Rs. 45

From the  given data,

25/2 % gain if it is sold at Rs. 9 more

56.25 - 45 = 9

=> 11.25 = 9

=> 22.5 = 18

=> 45 = 36

=> 50 = ?

=> C.P = 50 x 3645 = 40

Hence, the Cost price of the item = Rs. 40.

The Gulf of Mexico is the largest among all the gulfs in the world.

A gulf is nothing but a large inlet from the ocean into the landmass, typically with a narrower opening than a bay.

The Gulf of Mexico is an ocean basin mostly surrounded by the North American continent. It is a unique, semi-enclosed sea located between the Yucatan and Florida peninsulas, at the southeast shores of the United States.

Let the number of students in classes A, B and C be P, Q and R respectively.
Then, total score of A = 83P, total score of B = 76Q, total score of C = 85R.
Also given that,
(83P + 76Q) / (P + Q) = 79
=>4P = 3Q.
(76Q + 85R)/(Q + R) = 81
=>4R = 5Q,
=>Q = 4P/3 and R = 5P/3
Therefore, average score of A, B, C = ( 83P + 76Q + 85R ) / (P + Q + R) = 978/12 = 81.5

False. The ankle is not the third-class lever in the body.

Levers are typically labeled as first class, second class, or third class. All three types are found in the body, but most levers in the human body are third class.

First-class levers in the human body are rare and have the axis (fulcrum) located between the weight (resistance) and the force. One example is the joint between the head and the first vertebra.

In a second-class lever, the weight (resistance) is located between the axis (fulcrum) and the force. An example of a second-class lever in the human body is found in the lower leg when someone stands on tiptoes

In a third-class lever, the most common in the human body, force is applied between the resistance (weight) and the axis (fulcrum). There are numerous third-class levers in the human body; one example can be illustrated in the elbow joint.

Let the present ages of Arun and Harish be 4x and 3x years respectively.

Then, 4x + 6 = 26 => x = 5

Harish's age = 3x = 15 years.

Given numbers are 1, 2 and 3

Factors of 1 = 1

Factors of 2 = 1, 2

Factors of 3 = 1, 2 and 3

Common factors = 1

Hence, the HCF of 1, 2 and 3 = 1.