Quant Boosters - Hemant Malhotra - Set 13
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hemant_malhotra last edited by
Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975
Q9) Sum of two number is 840 and their HCF is 7. Find the number of pairs?
[OA : 16]
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hemant_malhotra last edited by
Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975
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]
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hemant_malhotra last edited by hemant_malhotra
Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975
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]
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hemant_malhotra last edited by
Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975
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]
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hemant_malhotra last edited by
Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975
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]
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hemant_malhotra last edited by hemant_malhotra
Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975
Q15) Find the number of positive integral solutions of a * b * c = 210
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hemant_malhotra last edited by
Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975
Q16) The product of the digits of a 5–digit number is 1800. How many such numbers are possible?
[OA : 240]
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hemant_malhotra last edited by
Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975
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]
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hemant_malhotra last edited by
Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975
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
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hemant_malhotra last edited by hemant_malhotra
Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975
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]
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hemant_malhotra last edited by
Director at ElitesGrid | CAT 2017 - QA 100 Percentile / CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975
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
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hemant_malhotra last edited by
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?
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hemant_malhotra last edited by hemant_malhotra
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 = 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
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hemant_malhotra last edited by hemant_malhotra
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]
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hemant_malhotra last edited by
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.
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hemant_malhotra last edited by
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)
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hemant_malhotra last edited by
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
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hemant_malhotra last edited by
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?
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hemant_malhotra last edited by
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
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hemant_malhotra last edited by
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
