CAT Question Bank (Quant)  Gaurav Sharma  Set 1

Q6) If a + b + c = 1 ,
a^2 + b^2 + c^2 = 2,
a^3 + b^3 + c^3 = 3
then a^4+b^4+c^4=.......?

Method 1:
1 step in 1 way
2 steps in 1 way
3 steps in 2 ways
4 steps in 3 ways
5 steps in 4 ways
6 steps in 6 ways
7 steps in 9 ways
8 steps in 13 ways
9 steps in 19 ways
10 steps in 28 ways
So 28 should be the answerMethod 2:
Fibonacci with a gap of 1
1,1,2,3,4,6,9,13,19,28Method 3:
Solve by x + 3y = 10

Q7) (1! * 2! * 3! ... 1000!)/n! Is a perfect square for some natural number 'n'. Find n

Q8) How many Obtuse angled triangle with integral sides are there whose longest side has length of 13 units

Q9) In how many ways letters of word PERMUTATIONS be arranged so that there are always 4 letters between P and S ?

Q10) A, B, C are 3 friends, B takes 2 days more than C to complete the work. If A started a work and 3 days later B joins him, then the work gets completed in 3 more days. Working together A, B, C can complete thrice the original work in 6days. In how many days B can complete twice the original work with double the efficiency working alone

Q11) Find the least number which can be written as product of 2 numbers in 11 ways

Q12) In how many ways letters of word PERMUTATIONS be arranged so that there are always 4 letters between P and S ?

Q13) Pipe A takes 3/4 of the times required by pipe B to fill the empty tank individually. When an outlet pipe C also opened simultaneously with pipe A and pipe B it takes 3/4 more time to fill the empty tank than it takes when only pipe A and pipe B are opened together. if it takes to fill 33hrs when all the 3 pipes are opened simultaneously, then in what time pipe C can empty the full tank by operating alone.

Q14) How many positive even integers less than 200 can be written as the sum of three consecutive integers?
a. 33
b. 20
c. 15
d. 35
e. 51

Q15) Which is greater?
99^50 + 100^50 or 101^50

Q16) The length of the minute hand of a clock is 10 cm. What is the area (in cm^2) that it covers between crossing the hour hand after 4 a.m. and the clock showing 5 a.m. on the same day?
(1) 200
(2) 180
(3) 180π
(4) 250
(5) 200π

Q17) In how many ways, we can choose a black and a white square on a chess board such that the two are not in the same row or column?
a) 32
b) 96
c) 24
d) None of these

Q18) In a hostel, more than 75% of the inmates drink tea and more than 55% of the inmates drink coffee and less than 40% of the inmates drink both. Which of the following cannot be the percentage of the inmates drinking neither tea nor coffee?
(1) 1%
(2) 5%
(3) 7%
(4) 8%
(5) 10%

Q19) Ashok travels same distance at 2 kmph on the first day, 4 kmph on second day, 8 kmph on third day and so on. Find Ashok’s average at the end of the 5th day.
a) 5 kmph
b) 5.16 kmph
c) 5.32 kmph
d) 5.64 kmph
e) 6.28 kmph

Q20) For the ninedigit number 2982a7645,following operation is performed:
2 – 9 + 9 – 8  + …+ 6 – 4 + 4 – 5.
For which of the following values of ‘a’ will the above summation be maximum? (  represents the modulus function)
A. 0
B. 2
C. 8
D. 9
E. Both (A) and (D

Q21) Ram said to Rahim, “The unit’s digit of the product of my age and your age is one or the other of three values 2, 4 and 8”. If the age (in years) of Ram and Rahim is R1 and R2 respectively, then find the total number of possible pairs (R1, R2).(Given that R1 and R2 are natural numbers less than 20.)
A. 108
B. 184
C. 128
D. 96
E. 144

Q22) Total number of integer pairs satisfying x + y = xy is ?

Q23) A cube of white chalk is painted red, and then cut parallel to the sides to form two rectangular solids of equal volume. What percent of the surface area of each of the new solids is not painted red?
(A) 20%
(B) 16 2/3 %
(C) 15%
(D) 25%

Q24) when a number "N" is divided by a proper divisor "d" then it leaves a remainder of 14 and if thrice of that number ie "3N",is divided by same divisor d,the reaminder comes out to be 8.again if 4 times of the same number ie "4N", is divided by d remainder will be?