Quant Boosters  Hemant Malhotra  Set 13

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Number of Questions  30
Solved ? 
Topic  Quant Mixed Bag
Source  Elite's Grid CAT Preparation Forum

hemant_malhotra last edited by hemant_malhotra
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q1) LCM of 3 natural numbers = 150. how many ordered pairs of 3 numbers are possible
[OA : 931]

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q2) In how many ways can 6 letters A, B, C, D, E and F be arranged in a row such that D is always somewhere between A and B?
[OA : 240]

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q3) In how many ways can the letters of the word MELANCHOLY be arranged such that E appears before A and A appears before O?

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q4) How many fourdigit even numbers are there which have 0 and 1 as two of the digits and the remaining two are distinct digits among 2, 4 and 6?

hemant_malhotra last edited by hemant_malhotra
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q5) Find the remainder when 87^24  13^24 is divided by 37?
[OA : 0]

hemant_malhotra last edited by hemant_malhotra
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q6) Eight balls of different colours need to be placed in three boxes of different sizes. Each box can hold all the eight balls. In how many ways can the balls be placed in the boxes so that no box remains empty ?
[OA : 5796]

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q7) A king gave each of his sons a few gold coins such that no pair of sons has the same total number of gold coins as any other pair of sons.
a) If the king had 6 sons what is the minimum number of gold coins that king could have given his sons?
b) If the king gave less than 100 coins on the whole to his sons, what is the maximum number of sons he could have had?

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
a) 1 + 2 + 3 + 5 + 8 + 13 = 32 (Fibonacci summation)
b) 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 so 8 sons

hemant_malhotra last edited by hemant_malhotra
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q8) In how many ways you can climb up 8 steps if minimum and maximum numbers of steps you can take at a time are 1 and 6 respectively?
[OA : 125]

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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]

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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]

hemant_malhotra last edited by hemant_malhotra
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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]

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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]

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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]

hemant_malhotra last edited by hemant_malhotra
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q15) Find the number of positive integral solutions of a * b * c = 210

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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]

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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]

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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

hemant_malhotra last edited by hemant_malhotra
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  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]