Quant Boosters - Gaurav Sharma - Set 4
Method 1 :
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 2 :
Fibonacci with a gap of 1
1, 1, 2, 3, 4, 6, 9, 13, 19, 28
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
Q16) In how many ways you can climb up 8 steps if minimum and maximum numbers of steps you can take at a time are 1 and 6 respectively?
gaurav_sharma last edited by gaurav_sharma
Minimum steps required is 8, which can be written as a + b + c + d + e + f + g + h = 8, only 1 way.
If we complete in 7 steps, then positive integral solution of a + b + c + d + e + f + g = 8 i.e. 7C6 ways
If we complete in 6 steps, then positive integral solution of a + b + c + d + e + f = 8 i.e 7C5 ways
and so on upto 7C1
But these solutions contains two cases where a or b is more than 6 so eliminate those cases
Final answer is
( 7C7 + 7C6 + 7C5 + 7C4 + 7C3 + 7C2 + 7C1 ) - 2 = 2^7 - 7C0 - 2 = 125
Q17) Rs. 4,500 was distributed among Aman, Baman and Chaman. From the amount that they received Aman, Baman and Chaman spent Rs.110, Rs.120 and Rs.140 respectively. The amounts then left with Aman and Baman were in the ratio 3 : 4 and with Baman and Chaman were in the ratio 5 : 6. What amount (in Rs.) did Baman receive?
Q18) If the nth day of August lies on the same day as the 2nd day of October, then how many values of n are possible?
Q19) A two digit number is divided by the sum of its digits. What is the maximum possible remainder?
Q20) Ashu and Manoj start running simultaneously from the ends A and B respectively, of a straight track of length 800 m, with speeds that are in the ratio 5 : 3. Whenever Ashu reaches either of the ends, he turns around and continues running at the same speed. Whenever Manoj meets Ashu, he turns around and continues running at the same speed. When Ashu comes back at A for the first time, how far (in meters) is Manoj from B?
d) None of these
Q21) The sum of thirty-two consecutive natural numbers is a perfect square.What is the least possible sum of the smallest and largest of thirty -two numbers?
Q22) A sequence 'S' is formed from the set of first 'N' natural numbers by deleting all the perfect squares and all the perfect cubes. If the elements are arranged in an ascending order then, what is the 240th term of the sequence 'S' ?
Q23) A packet of toffees is distributed in a class. A child who receives one-eighth of the total number of toffees gets five times the average number of toffees received by the remaining children in the class. What is the strength of the class?
d) Cannot be determined
Q24) Find the smallest prime that is the fifth term of an increasing arithmetic sequence, all four preceding terms also being prime.
Q25) A farmer has 88 m of barbed wire fencing. With this he encloses a field of area X sq. m. What can be said about the maximum possible value of X?
Q26) If a, b, c, d, e and f are non negative real numbers such that a + b + c + d + e + f = 1, then the maximum value of (ab + bc + cd + de + ef) is
Q27) How many 4 digit numbers can be formed using only 3 and 9, which is a multiple of 9
Q28) There are k candidates (where k is an odd number) for the Bookie Prize. The rules of the Bookie Prize say that at least 1 but not more than 50% of the candidates must be awarded a prize. If the number of possible ways of selecting the awardees is 63, find k.
Q29) A bus travels at a speed of 50 km/hr if it does not carry any passenger. Its speed decreases by a quantity directly proportional to the square of the number of passengers. If the bus carries 10 passengers, its speed is 45 km/hr. What will be its speed (in km/hr) if it carries 20 passengers?
Q30) Find the sum of all positive integral values of n such that 1001 + n^2 is a perfect square
how gap of 1 ?