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 non-congruent 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 answer

    Method 2:
    Fibonacci with a gap of 1

    Method 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

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