Quant Boosters  Hemant Malhotra  Set 13

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