# 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 < 20

Case ii) When 16 is the largest side
=> 16² < n² + 12²
=> n² > 112
=> n > 10

So, 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 ?

62

107

61

65

63

31

61

61