# Quant Boosters - Gaurav Sharma - Set 6

• Number of Questions - 30
Solved ? - Not yet
Topic - Quant Mixed Bag
Source - Genius Tutorial Preparation Forum

• Q1) Max no of intersection of diagonals of polygon of side 8 is

[OA : 70]

• Q2) Find x,y all positive integers such that x^y + y^x + x^y * y^x = 5329

• Q3) If x^2 + y^2 = 10x + 6y - 17, find minimum value of 2x + 7y

• Q4) How many 4 digit numbers consist of max. only 2 distinct digits?

[OA : 576]

• Q5) Two person A and B start moving towards each other from point P and Q respectively which are 1400 km apart. Speed of A is 50 km/hr and that of B is 20km/hr. How far is A from Q when he meets B for 22nd time?

• For 1st meeting they need to travel 1400 km and for rest 21 round they will cover 2800 km
So total 2800 x 21 + 1400= 60200km
A will travel 5/7 x 60200= 43000 km
For 42000 km he needs 30 rounds
In the last round he will cover 1000km from P
So he is at 1400-1000= 400km from Q

• Q6) A die is rolled three times, the probability of getting a larger number than the previous number is
(a) 1/54
(b) 5/54
(c) 5/108
(d) 13/108

• Q7) A mixture contains alcohol and water in the ratio 4 : 3. If 7 litres of water is added to the mixture, the ratio of alcohol and water becomes 3 : 4. The quantity of alcohol in the mixture is
(a) 10 litres
(b) 12 litres
(c) 32 litres
(d) 48 litres

• Q8) The points (0, 8/3), (1, 3) and (82, 30)
(a) form an obtuse angled triangle.
(b) form an acute angled triangle.
(c) form a right angled triangle.
(d) lie on a straight line.

• Slope of AB = slope of BC
So striaght line

• Q9) Sum of digits of a 5-digit number is 41.The probability that such a number is divisible by 11 is k/ 35 where k =

• The 5-digit combination whose sum = 41 are
● 99995 : No. of arrangements = 5
● 99986 : No. of arrangements = 20
● 99977 : No. of arrangements = 10
● 99887 : No. of arrangements = 30
● 98888 : No. of arrangements = 5
Total = 70

Now, for a number (abcde) to be divisible by 11, we should have (a + c + e) – (b + d) = 11
and (a + c + e) + (b + d) = 41
So, a + c + e = 26, b + d = 15
Thus (a, c, e) = (9, 9, 8 ) and (b, d) = (7, 8 ) or (6, 9)
Hence total 12 cases

Probability = 12/70 = 6/35
k = 6

• Q10) 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 ?

• Fibonacci with a gap of 1 : 1, 1, 2, 3, 4, 6, 9, 13, 19, 28

Method 2 :
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 3 :

x + 3y = 10
(1 , 3 ) -> 4
(4 , 2 ) -> 6!/4!2! = 15
(7 , 1) -> 8!/7! = 8
(10 , 0) -> 1
TOTAL = 15 + 4 + 8 + 1 = 28

• Q11) If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?

[OA : 5/8]

• Q12) If March 1, 2006 was a Wednesday, which day was it on March 1, 2002?

• Q13) N is a natural number of at least 5 digits and its leftmost digit is 6. When this 6 is removed from N, the number thus obtained is found to be 1/25 times of N. What is the sum of the digits of N?

• Q14) Number of terms in the expansion of (a + b + c)^10
a) 11
b) 21
c) 55
d) 66

• Q15) The product of all the factors of a number is equal to the tenth power of the number. N cannot be exactly divisible by which of the following?
a. 90
b.200
c. 210
d. 126

61

61

61

64

61

54

61

61