Quant Boosters  Gaurav Sharma  Set 6

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
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 ?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
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

gaurav_sharma last edited by gaurav_sharma
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
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]

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q12) If March 1, 2006 was a Wednesday, which day was it on March 1, 2002?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
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?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q14) Number of terms in the expansion of (a + b + c)^10
a) 11
b) 21
c) 55
d) 66

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
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

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q16) 2n has 28 factors 3n has 30 factors How many factors will 6n have ?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
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

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q17) If a three digit number ‘abc’ has 3 factors, how many factors does the 6digit number ‘abcabc’ have?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q18) Let N = 2^15 * 3^12. How many factors of N^2 are less than N but do not divide N?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q19) If 2n has 28 factors, 3n has 30 factors, how many factors does 5n have ?

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q20) The sum of the factors of a number is 124. What is the number?
a) Number lies between 40 and 50
b) Number lies between 50 and 60
c) Number lies between 60 and 80
d) More than one such number exists

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q21) If coordinates of the vertices of a triangle are (2, 0), (6, 0) and (1, 5) then distance between its orthocentre and circumcentre is
(a) 4
(b) 6
(c) 5
(d) none of these

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q22) Let (a1, a2, a3, ….) be a sequence such that a1 = 2 and an – an1 = 2n for all n ≥ 2. Then a1 + a2 + …. + a20 is
(a) 420
(b) 1750
(c) 3080
(d) 3500

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q23) In a class comprising 60 boys and some girls, the average age of boys is 14.8 years and that of girls is 14.1 years. If the average age of the class is 14.7 years, then how many girls are there in the class?
a) 10
b) 15
c) 20
d) 25

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q24) N is a natural number which has 4 factors. If 10 ≤ N ≤ 70, then how many values are possible for N?
(a) 19
(b) 20
(c) 21
(d) 22

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q25) The two sequences of numbers {1, 4, 16, 64, ….} and {3, 12, 48, 192, ….} are mixed as follows : {1, 3, 4, 12, 16, 48, 64, 192, ….}. One of the numbers in the mixed series is 1048576. Then the number immediately preceding it is
(a) 786432
(b) 262144
(c) 814572
(d) 786516

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q26) A, B and C individually can finish a work in 6, 8 and 15 hours respectively. They started the work together and after completing the work got Rs.94.60 in all. When they divide the money among themselves, A, B and C will respectively get (in Rs.)
(a) 44, 33, 17.60
(b) 43, 27.20, 24.40
(c) 45, 30, 19.60
(d) 42, 28, 24.60

gaurav_sharma last edited by
Director, Genius Tutorials, Karnal ( Haryana ) & Delhi  MSc (Mathematics)
Q27) Two trains are traveling in opposite direction at uniform speed 60 and 50 km per hour respectively. They take 5 seconds to cross each other. If the two trains had traveled in the same direction, then a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds. What are the lengths of trains (in metres)?
(a) 112, 78
(b) 97.78, 55
(c) 102.78, 50
(d) 102.78, 55