CAT Question Bank (Quant) - Gaurav Sharma - Set 1
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Number of questions : 100
Answer Key Available - No
Topic : Quant Mixed Bag
Source - Genius Tutorials CAT preparation forum
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Q1) Ratio of AM and GM between two numbers is 5:3. Find ratio of two numbers
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Q2) What is the number of non-congruent Rectangles in a chess board?
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Q3) How many times does the graph of y = 4^x - 2^x - 2 intersect the x - axis?
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Q4) How many acute angle triangles can be formed two of whose sides are 14cm and 9cm ?
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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 ?
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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=.......?
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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
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Q7) (1! * 2! * 3! ... 1000!)/n! Is a perfect square for some natural number 'n'. Find n
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Q8) How many Obtuse angled triangle with integral sides are there whose longest side has length of 13 units
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Q9) In how many ways letters of word PERMUTATIONS be arranged so that there are always 4 letters between P and S ?
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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
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Q11) Find the least number which can be written as product of 2 numbers in 11 ways
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Q12) In how many ways letters of word PERMUTATIONS be arranged so that there are always 4 letters between P and S ?
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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.
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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
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Q15) Which is greater?
99^50 + 100^50 or 101^50
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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
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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
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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%
