# Quant Boosters - Hemant Malhotra - Set 14

• 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 ?

• Q29) In a group of four boys, each of them has a certain number of Re. 1 coins with him. Every boy has an amount that is an integral multiple of the amount possessed by every other boy who has an amount less than him. If the total amount with the four boys put together is Rs. 70, and no two boys have the same amount, what is the minimum possible amount (in Rs.) with the boy who has the maximum number of Rs. 1 coins with him?

• let A,B,C,D
let A got a rs
B got a * b rupees
C got a * b * c rupees
D got a * b * c * d rupees
a(1+b+bc+bcd)=70
a * (1+b+bc+bcd) = 2 * 35
this will be minimum when all values are as close as possible
1+b+bc+bcd=35
b(1+c+cd)=34
so b=2
1+c+cd=17
so c(1+d)=16
so c=4 and d=3
so a=2,b=2,c=4,d=3
so 2,4,16,48 these are values

• Q30) 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.

• @hemant_malhotra Approach?sir

• @hemant_malhotra -1/5?.............................................................

• @hemant_malhotra 22?.......................................................................

• @hemant_malhotra None of the above?.....................

• @hemant_malhotra 20???........................................

• @hemant_malhotra 4&0???????????????????????????????????????????????????????

63

48

58

54

33

61

64