Quant Boosters  Hemant Malhotra  Set 13

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