Quant Boosters  Hemant Malhotra  Set 13

Q4) How many fourdigit even numbers are there which have 0 and 1 as two of the digits and the remaining two are distinct digits among 2, 4 and 6?

Q5) Find the remainder when 87^24  13^24 is divided by 37?
[OA : 0]

Q6) Eight balls of different colours need to be placed in three boxes of different sizes. Each box can hold all the eight balls. In how many ways can the balls be placed in the boxes so that no box remains empty ?
[OA : 5796]

Q7) A king gave each of his sons a few gold coins such that no pair of sons has the same total number of gold coins as any other pair of sons.
a) If the king had 6 sons what is the minimum number of gold coins that king could have given his sons?
b) If the king gave less than 100 coins on the whole to his sons, what is the maximum number of sons he could have had?

a) 1 + 2 + 3 + 5 + 8 + 13 = 32 (Fibonacci summation)
b) 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 so 8 sons

Q8) 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?
[OA : 125]

Q9) Sum of two number is 840 and their HCF is 7. Find the number of pairs?
[OA : 16]

Q10) What is the sum of all the numbers less than 100, that can be written as the sum of 9 consecutive positive integers?
[OA : 504]

Q11) In how many ways can 73 identical chocolates be stuffed into three boxes – B1, B2 and B3 – such that B1 contains more chocolates that B2 and B2 contains more chocolates than B3?
[OA : 444]

Q12) Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. The number of ways in which we can place the balls in the boxes so that no box remains empty is
[OA : 150]

Q13) Four identical bags are distributed among four boys. If each boy can get any number of bags then what is the probability that no boy gets more than two bags?
[OA : 19/35]

Q15) Find the number of positive integral solutions of a * b * c = 210

Q16) The product of the digits of a 5–digit number is 1800. How many such numbers are possible?
[OA : 240]

Q17) When different buttons are pressed, a robot may move forward by 1 cm, 3 cm, 5 cm. If buttons are pressed six times, how many different distance a robot may move
[OA : 13]

The minimum distance the robot may move is 1+1+1+1+1+1 = 6.
The maximum distance is 5+5+5+5+5+5 = 30.
and 1,3,5 odd so sum of odd+odd+odd+odd+odd+odd=even so sum will alwys be even
so 6,8,10,12.......30 possible
so 30 = 6 + (n  1) * 2
so n=13 different possible

Q18) In a class of 10 students, Vishal was the topper in English, who scored minimum 70 marks while each of the remaining 9 students scored minimum 30 marks. If the sum of total marks scored by the group was 360, in how many different ways could the marks be scored by the 10 students?
[OA : 29C9]

Q19) There are 35 employees in an office. 49 diaries, each having either a pink cover, blue cover or a red cover are distributed in a way, such that employees get atleast one diary. The number of employees who get only one diary with either red, blue or pink cover are 21, of which, less than 5 employees got only one diary each with a blue cover, more than 4 employees got only one diary each with a red cover and more than 8 employees got only one diary each with a pink cover. The number of employees who got both red and blue covered diaries but not a pink covered one is one more than those who got only red covered diaries . Employees who got blue and pink covered diaries but not a red covered one are 4 less then the employees who got only pink covered diary. Nobody got all the three diaries. The number of employees who got only red covered diaries is not less than those who got both blue and pink covered diaries but not a red covered one. Nobody got both red and pink covered diaries.
Q1) What is the minimum possible number of red covered diaries?
a) 15
b) 17
c) 18
d) 19Q2) If the total number of diaries is 52, find the minimum number of pink covered diaries that would be required?
a) 14
b) 15
c) 16
d) 19

Q20) Zada has 15 choclates which she has to distribute among her children Sana, Ada, Jiya, Amir and Farhan.
She has to make sure that Sana gets at least 3 and at most 6 chocolates. In how many ways can this be done?

Method 1 :
a + b + c + d + e = 15
where 3 < = a < = 6
so (3 + a') + b + c + d + e = 15 where a' < = 3
so a' + b + c + d + e = 12
so (12 + 5  1)C(5  1) = 16c4
now this will include case where a1' > 3
so put a' = 4 + a''
4 + a'' + b + c + d + e = 12
a'' + b + c + d + e = 8
so (8 + 5  1)C(5  1) = 12C4
so 16C4  12C4 = 1325Method 2 :
3 + a + b + c + d = 15
so a + b + c + d = 12
so (12 + 4  1)C(4  1) = 15C3
4 + a + b + c + d = 15
so a + b + c + d = 11
so 14c3
15c3 + 14c3 + 13c3 + 12c3 = 1325

Q21) I have x cards with me. If I distribute them among 7 boys equally, then I'll have 2 cards left with me. Similarly, if I distribute them among 8, then I'll have 6 left and if I distribute among 9, I'll have 3 left. What is the minimum number of cards that I have in hand if no card is left after I distribute them among 3 boys or 5 boys?
[OA : 30]