Quant Boosters  Hemant Malhotra  Set 14

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) If a = 3^x, b = 3^y , c = 3^z , and d = 3^w and if x, y, z, and w are positive integers, determine the smallest value of x + y + z + w such that a^2 + b^3 + c^5 = d^7
a) 17
b) 31
c) 106
d) 247
e) 353

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
If you know basic base rule think of base 3
If 3^m + 3^n + 3^p = 3^q, then
m = n = p is the only possibility
3^(2x)+3^(3y)+(3^5z)=3^7z
2x=3y=5z
3^(2x+1)=3^7z
so 2x=7z1
2x=3y=5z=7z1=k
so x=k/2 , y=k/3 , z=k/5 , z=(k+1)/7
k=90
so x+y+z+w=106

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
Q5) In a group of people, there are 13 who like apples, 9 who like blueberries, 15 who like cantaloupe,and 6 who like dates. (A person can like more than 1 kind of fruit.) Each person who likes blueberries also likes exactly one of apples and cantaloupe. Each person who likes cantaloupe also likes exactly one of blueberries and dates. Find the minimum possible number of people in the group.

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
Q6) f(x) = min(1  3x, 2x  1), find the maximum value of f(x)

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) What will be the minimum value of n for which 48!/12ⁿ is not divisible by 12 ?
a) 44
b) 43
c) 23
d) 22
e) 5

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
Q8) When a certain number 'x' is multiplied by 18 the product 'y' has all of its digits as 4. What is the minimum number of digits 'x' can have ?

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
OA=8 , 18 = 2 * 9
for a number consisting of 4s to be divisible by 9
the 444.... has to have 9 4s
so 444444444 / 18 = 24691358= 8 digits

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) Find the minimum value of the expression: √((x + 2)^2 + 16) + √((x  14)^2 + 64)

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) The sum of the squares of three numbers, x, y and z is 138, while the sum of their products taken two at a time is 131. Their sum is:
a) 30
b) 40
c) 50
d) None of the above

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
Q11) a1, a2, ...., a40 are 40 natural numbers such that 0 < a1 < a2 < ... < a40 < 100, then find the difference between the maximum and minimum possible sum of all the differences di, where di = a(i + 1)  a(i)

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) A function f(k) is defined on natural numbers as follows
f(k) = 2k if k is odd
= k/2 if k is even.
if f(f(f(k))) = 22 then find the sum of all possible values of k.

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
f(f(f(k))=22
f((f(k))=11 or 44 (( 11 odd so we will get 22 or 44 even so we will get 44/2=22
case= f(f(k)=11
then f(k)=22 (K if even then k/2 ,)
when f(k)=22
then k=44 or 11
When f(f(k)=44
then f(k)=88 or 22
when f(k)=22 then k=44 or 11
f(k)=88 then k=44 or 176
so k=11,44,176
so sum 11+44+176=231

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) If [ x ] + [ 2x ] + [ 3x ] = n, where [ x ] is the greatest integer less than or equal to x, then how many different values n can take if 1 ≤ n ≤ 2007 ?

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
Q14) Given that log 3 = 0.477, log 7 = 0.845, log 2 = 0.301. Find the number of digits in y if y = 252^10

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
Q15) For what values of k does the equation log(kx) = 2 log(x + 1) have only one real root?

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) A loan of Rs. 48,000 is borrowed at an interest rate of 10% per annum compounded annually and repaid in 3 equal yearly installments of Rs. X starting after one year. What is the approximate value of X?
a) Rs. 19300.50
b) Rs. 19300.75
c) Rs. 19301
d) Rs. 19301.25
e) Rs. 19301.50

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) What is the units digit of 1^1 + 2^2 + 3^3 + … + 2008^2008?

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
Q18) 10 students are going to perform 10 different items in school’s annual program. What is the number of ways in which these 10 items can be arranged, if Amar will perform before Bindu, Bindu will perform before Chetan, and Chetan will perform before David?

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
Q19) Four friends P, Q, R and S have Rs. 200 among them. They made the following statements about the money with them.
P: Q has Rs. 60 and if I give Rs. 10 to R, then Q and R will have equal amounts of money.
Q: I have more money than R and two people have the same amount of money
R: The person(s) with the lowest amount has (ve) Rs. 30 and S does not have the highest amount.
S: Q and I have the same amount of money and if R gives Rs. 10 to Q, he would have Rs. 5 less than Q.Only one of the statements is completely incorrect.
How much money does S have?a) Rs. 50
b) Rs. 60
c) Rs. 20
d) Rs. 30
e) Cannot be determined

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
Q20) 5 boys and 5 girls sit in a row. Which of the following is true?
A) The probability that all the boys do not sit together is 41/42
B) The probability that boys and girls sit alternate to each other is (5! × 4!)/9!
C) The probability that one of the boys Aman sits with one of the girls Tanushree is 1/5
D) The probability that all the boys sit together and all the girls sit together is 2/10!a) A and B
b) A, B and C
c) B, C and D
d) C and D
e) D