Quant Boosters - Hemant Malhotra - Set 13


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    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?


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    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 = 1325

    Method 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


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    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]


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    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.


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    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 at-least one mango.

    OA : 19C3 - 4(9C3)


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


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


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


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


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


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


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    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


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q27) Find number co-primes to 300 which are greater than 200 but less than 300


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q28) Find number of triangles with integral sides if perimeter is 50

    [OA : 52]


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


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


  • Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


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


 

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