CAT Question Bank (Quant)  Gaurav Sharma  Set 1

Number of questions : 100
Answer Key Available  No
Topic : Quant Mixed Bag
Source  Genius Tutorials CAT preparation forum

Q1) Ratio of AM and GM between two numbers is 5:3. Find ratio of two numbers

Q2) What is the number of noncongruent Rectangles in a chess board?

Q3) How many times does the graph of y = 4^x  2^x  2 intersect the x  axis?

Q4) How many acute angle triangles can be formed two of whose sides are 14cm and 9cm ?

Q5) There is a frog who could climb either 1 stair or 3 stairs in one shot. In how many ways he could reach at 10th stair ?

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%