Quant Boosters  Hemant Malhotra  Set 13

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]

Q22) A woman and a girl went to a fruit market. The woman bought 5 apples, 3 mangoes and 7 oranges for Rs.51. The girl bought 10 apples, 5 mangoes and 14 oranges for Rs.98. Find the cost of each mango.

Q23) In how many ways 20 similar mangoes can be distributed among 4 men such that no one can get more than 10 and each one can get atleast one mango.
OA : 19C3  4(9C3)

Q24) Find number of ways in which sum on 3 dice rolled is 15

Q25) What will be the last digit of 2^3^4^5  2^3^5^4?

Q26) ABC is a 3 digit number such that ABC = 5 * (AB + BC + CA)
Find total number of possible values for ABC

100A + 10B + C = 5 * (10A + B + 10B + C + 10C + A)
100A + 10B + C = 55 * (A + B + C)
45(A  B) = 54C
so A  B = 6/5 * C
so C = 0 then A  B = 0 then A will vary from 1 to 9 so 9 values
when C = 5 then A  B = 6 then A will vary from 6 to 9 so 4 values
so 9 + 4 = 13 values

Q27) Find number coprimes to 300 which are greater than 200 but less than 300

Q28) Find number of triangles with integral sides if perimeter is 50
[OA : 52]

Q29) Find the number of trailing zeros if 75^25 is written in base 25

Q30) Find the number of non negative integral solutions to the equation a + b + c = 13, such that a, b and c are distinct