Quant Boosters  Gaurav Sharma  Set 6

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 14001000= 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 5digit number is 41.The probability that such a number is divisible by 11 is k/ 35 where k =

The 5digit 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 = 70Now, 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 casesProbability = 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
Answer : 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 answerMethod 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

Q16) 2n has 28 factors 3n has 30 factors How many factors will 6n have ?

N = 2^a × 3^b
Factors of 2N = ( a + 2) ( b + 1)=28
Factors of 3N = ( a + 1 )( b + 2 )=30
So a = 5 and b = 3
So N = 2^5 × 3^3
Now Factors of 6N ( 2^6 × 3^4 )
will be 7 × 5 = 35