CAT Question Bank (Quant)  Gaurav Sharma  Set 1

gaurav_sharma last edited by gaurav_sharma
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Number of questions : 100
Answer Key Available  No
Topic : Quant Mixed Bag
Source  Genius Tutorials CAT preparation forum

gaurav_sharma last edited by gaurav_sharma
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q1) Ratio of AM and GM between two numbers is 5:3. Find ratio of two numbers

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q2) What is the number of noncongruent Rectangles in a chess board?

gaurav_sharma last edited by gaurav_sharma
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q3) How many times does the graph of y = 4^x  2^x  2 intersect the x  axis?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q4) How many acute angle triangles can be formed two of whose sides are 14cm and 9cm ?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
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 ?

gaurav_sharma last edited by gaurav_sharma
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
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=.......?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
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

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q7) (1! * 2! * 3! ... 1000!)/n! Is a perfect square for some natural number 'n'. Find n

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q8) How many Obtuse angled triangle with integral sides are there whose longest side has length of 13 units

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q9) In how many ways letters of word PERMUTATIONS be arranged so that there are always 4 letters between P and S ?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
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

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q11) Find the least number which can be written as product of 2 numbers in 11 ways

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q12) In how many ways letters of word PERMUTATIONS be arranged so that there are always 4 letters between P and S ?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
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.

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
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

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q15) Which is greater?
99^50 + 100^50 or 101^50

gaurav_sharma last edited by gaurav_sharma
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
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

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
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

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
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%