# Quant Boosters - Hemant Malhotra - Set 14

• Q11) a1, a2, ...., a40 are 40 natural numbers such that 0 < a1 < a2 < ... < a40 < 100, then find the difference between the maximum and minimum possible sum of all the differences di, where di = a(i + 1) - a(i)

• Q12) A function f(k) is defined on natural numbers as follows
f(k) = 2k if k is odd
= k/2 if k is even.
if f(f(f(k))) = 22 then find the sum of all possible values of k.

• f(f(f(k))=22
f((f(k))=11 or 44 (( 11 odd so we will get 22 or 44 even so we will get 44/2=22
case= f(f(k)=11
then f(k)=22 (K if even then k/2 ,)
when f(k)=22
then k=44 or 11
When f(f(k)=44
then f(k)=88 or 22
when f(k)=22 then k=44 or 11
f(k)=88 then k=44 or 176
so k=11,44,176
so sum 11+44+176=231

• Q13) If [ x ] + [ 2x ] + [ 3x ] = n, where [ x ] is the greatest integer less than or equal to x, then how many different values n can take if 1 ≤ n ≤ 2007 ?

• Q14) Given that log 3 = 0.477, log 7 = 0.845, log 2 = 0.301. Find the number of digits in y if y = 252^10

• Q15) For what values of k does the equation log(kx) = 2 log(x + 1) have only one real root?

• Q16) A loan of Rs. 48,000 is borrowed at an interest rate of 10% per annum compounded annually and repaid in 3 equal yearly installments of Rs. X starting after one year. What is the approximate value of X?
a) Rs. 19300.50
b) Rs. 19300.75
c) Rs. 19301
d) Rs. 19301.25
e) Rs. 19301.50

• Q17) What is the units digit of 1^1 + 2^2 + 3^3 + … + 2008^2008?

• Q18) 10 students are going to perform 10 different items in school’s annual program. What is the number of ways in which these 10 items can be arranged, if Amar will perform before Bindu, Bindu will perform before Chetan, and Chetan will perform before David?

• Q19) Four friends P, Q, R and S have Rs. 200 among them. They made the following statements about the money with them.

P: Q has Rs. 60 and if I give Rs. 10 to R, then Q and R will have equal amounts of money.
Q: I have more money than R and two people have the same amount of money
R: The person(s) with the lowest amount has (ve) Rs. 30 and S does not have the highest amount.
S: Q and I have the same amount of money and if R gives Rs. 10 to Q, he would have Rs. 5 less than Q.

Only one of the statements is completely incorrect.
How much money does S have?

a) Rs. 50
b) Rs. 60
c) Rs. 20
d) Rs. 30
e) Cannot be determined

• Q20) 5 boys and 5 girls sit in a row. Which of the following is true?

A) The probability that all the boys do not sit together is 41/42
B) The probability that boys and girls sit alternate to each other is (5! × 4!)/9!
C) The probability that one of the boys Aman sits with one of the girls Tanushree is 1/5
D) The probability that all the boys sit together and all the girls sit together is 2/10!

a) A and B
b) A, B and C
c) B, C and D
d) C and D
e) D

• Q21) If a, b, c are whole numbers, and a^b + b^c + c^a = 17 and a^c + c^a = 17, what could be the possible sum of a and c?
a) 17
b) 18
c) 0
d) 11
e) None of these

• Q22) What is the probability of forming word from the letters of word “IMPEACH” such that all vowels come together?

• Q23) What is the remainder when sum of square of any 20 consecutive odd numbers is divided by 40 ?

• Q24) Doodhnath, a milkman, has 100 litres of milk and water solution that contains 70% milk. What quantity of water (in litres) should he add to the solution to bring down the concentration of milk to 40%?
(a) 65
(b) 75
(c) 40
(d) 85

• Q25) Let S be the set of the first six natural numbers. If five numbers are picked randomly from S, what is the probability that the sum of the five numbers is divisible by 3?

• Q26) A teacher asks one of her students to divide a 30-digit number by 11. The number consists of six consecutive 1’s, then six consecutive 2’s, and likewise six 3’s, six 4’s and six 7’s in that order from left to right. The student inserts a three-digit number between the last 4 and the first 7 by mistake and finds the resulting number to be divisible by 11. Find the number of possible values of the three-digit number

• Q27) In how many ways can you climb up 8 steps if the minimum and maximum steps you can take at a time are 1 and 6 respectively?

• 1step = 1 way =2^0
2 step = (1,1) , (2,0) = 2^1 way
3 step = (1,1,1) , (2,1) ,(1,2) ,(3)=2^2=4 way
4 step = 2^3= 8 way
5 step = 2^4 = 16 way
6 step = 2^5 = 32 way
now step 7th step will be sum of previous 6 steps= 63
8th step = sum of previous 6 step = 125

• Q28) How many arrangements can be made in a round table of 8 chairs if 2 of them like to sit opposite to each other ?

61

61

61

63

105

63

61

1