Quant Boosters  Hemant Yadav  Set 4

Number of Questions  30
Topic  Quant Mixed Bag
Solved ? : Yes
Source : Collection of solved questions from Hemant Yadav, Math faculty  FIITJEE

Q1) Find the minimum possible positive value of A = 224x + 140y + 531, where x and y are integers
[OA : 27]

Q2) Find the largest value of n for which 6^101 + 10^101 is divisible by 2^n

Q3) For every 5 element subset of the set {1, 2, . . . , 2014}, Amar writes down the smallest of the five numbers. The largest number he writes down is
(a) 5
(b) 2009
(c) 2010
(d) 2014
(e) none of these[OA : 2010]

Q4) A subset B of the set of first 100 positive integers has the property that no two elements of B sum to 125. What is the maximum possible number of elements in B?
[OA : 62]

Q5) A round table with 5 chairs is to be decorated. Each chair can be painted with one of 5 colors available. In how many different ways the chairs can be painted?

Q6) At a party of 11 people, find the probability that every person has shook hands with exactly 5 other people.
[OA : 0]

Q7) What will be the probability that out of 10 persons odd number of persons will have odd number of friends (among these 10 persons only) ?
[OA : 0]

Q8) If it is known that log2 = 0.3010, then find the smallest possible positive integral value of n such that 2^(10n) does not begin with 1

Q9) The lattice points (points having integral coordinates) lying on a circle centered at origin having radius 5 forms a polygon. Find the area of the polygon.

4 * {area of quad. with vertices (5,0),(3,4),(4,3),(0,5) + triangle with vertices (0,0,), (0,5), (5,0) }
= 4 * (6 + 25/2) = 4 * 37/2 = 74

Q10) A faulty 12 hour digital clock displays 9 whenever it is supposed to display 1. For example when it is 1:21, the clock incorrectly shows 9:29. For what fraction of the day will the clock show the right time?
a) 1/2
b) 2/3
c) 3/4
d) 5/6

Q11) Two sides of a triangle are 12.5 and 15.5. How many different integral values can the third side take?
[OA : 24]

Q12) An acute triangle has sides as 12, 16 and ‘n’. How many different integral values ‘n’ can take?

Case i) when n is the largest side
=> n² < 12² + 16² = 20²
=> n < 20Case ii) When 16 is the largest side
=> 16² < n² + 12²
=> n² > 112
=> n > 10So, 11 to 19
Hence 9 values!!

Q13) If perimeter of a right angle triangle is 12 + 8√3 and sum of squares of the sides is 294, then find the area of the triangle.

Q14) How many ordered triplets of natural numbers (a, b, c) are there such that GCD(a, b, c) = 1 and all a, b, c are factors of 2310 ?

Q15) How many positive integral solutions does the following equation has : x + y + z + w = xyzw

Q16) If x and y are integers with (y − 1)^(x + y) = 4^3, then the number of possible values for x is

Q17) Dolly, Molly and Polly each can walk at 6 km/h. They have one motorcycle, which travels at 90 km/h, which can accommodate at most two of them at once (and cannot drive by itself!). Let t hours be the time taken for all three of them to reach a point 135 km away. Ignoring the time required to start, stop or change directions, what is true about the smallest possible value of t ?