CAT Questions

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Let the two no's be a and b;
Given product of the no's is p = ab;
If the each nos is increased by 2 then the new product will be
(a+2)(b+2) = ab + 2a + 2b + 4
= ab + 2(a+b) + 4
= p + 2(a+b) + 4
Hence the new product is (p+4) times greater than twice the sum of the two original numbers.

Let us assume Amount be 100 Rs and we calculate in CI

 First year 60% of 100 = 60 amount (100+60) is 160

 Second year 60% of 160 = 96 amount (160+96) is 256

 Third year 60% of 256 =153.6 amount (256+153.6) is 409.6

 Here the Amount of 100 Rs is quadrapled in 3 years.

 One year contains 2 half years

 Three year has 6 half years.

 Therefore,  It takes 6 half 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.

The Lami's theorem states that " If three forces coplanar and concurrent forces acting on a particle keep it in equilibrium, then each force is proportional to the sine of the angle between the other two and the constant of proportionality is the same." This theorem is derived from the Sine rule of triangles.

Given speed of the first train = 60 km/hr = 60 x 5/18 = 50/3 m/s

Let the speed of the second train = x m/s

Then, the difference in the speed is given by

503 - x = 12018

=> x = 10 m/s

=> 10 x 18/5 = 36 km/hr

ALPHABET is the only has the most letters in it.

Alphabet has all the 26 letters from A - Z. 

Hence, ALPHABET is one word that has the most letters in it.

The letters at odd positions are each moved two steps backward and those at even positions are each moved two steps forward and the obtained code is reversed to get the corresponding letters of the code.