Question Bank (3)  Quant Mixed Bag  Shashank Prabhu, CAT 100 Percentiler

Number of Questions  100
Topic  Quant Mixed Bag
Answer Key Available ? : Yes
Source : Learningroots forum

Q1) The function f is defined for all positive integers n by the following rule: f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is prime, then f(p) = ?
a) P1
b) P2
c) (P+1)/2
d) (P1)/2[OA: Option a]

Q2) For the past k days the average (arithmetic mean) cupcakes per day that Liv baked was 55. Today Bibi joined and together with Liv they baked 100 cupcakes, which raises the average to 60 cupcakes per day. What is the value of k?
[OA: 8]

Q3)
[OA: Option D]

Q4) Of the applicants passes a certain test, 15 applied to both college X and Y. If 20 % of the applicants who applied college X and 25% of the applicants who applied college Y applied both college X and Y, how many applicants applied only college X or college Y?
[OA: 105]

Q5) A committee of 6 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed if two of the men refuse to serve together?
[OA: 635]

Q6) What is the probability that a 3digit positive integer picked at random will have one or more 7s in its digits?
[OA: 252/900]

Negation would work better I suppose. No 7s will be 8 * 9 * 9 = 648 out of 900.
Negation will be 252/900 or 7/25

Q7) A family consisting of one mother, one father, two daughters and a son is taking a road trip in a sedan. The sedan has two front seats and three back seats. If one of the parents must drive and the two daughters refuse to sit next to each other, how many possible seating arrangements are there?
[OA: 32]

Q8) Gringotts Wizarding Bank has 4 shareholders: Dobby, Hokey, Winky and Kreacher. Number of shares that Dobby owns is 2/3rd of number of the shares of the other three shareholders, number of the shares that Hokey owns is 3/7th of number of the shares of the other three shareholders and number of the shares that Winky owns is 4/11th of number of the shares of the other three shareholders. If dividends of 3,600,000 Galleons were distributed among the 4 shareholders, how much of this amount did Kreacher receive?

Q9) The Nemo fish is known to eat its eggs before they hatch. At one time the Nemo fish lays 32 eggs. Each of these eggs after becoming Nemos lays 32 eggs and so on. However, only 12.5 % are able to survive because the mother fish eats them up after which she moves out of the colony. If the number of Nemo fishes after 6 such processes is 12,288, then how many fishes were there at the beginning?
[OA: 3]

Q10)
[OA: 30]

Q11) Three friends X, Y and Z have to complete an assignment. Initially, X and Y start working on it. X types at the rate of 4 pages/hr and Y at the rate of 2 pages/hr. When 50 % of the work was done, Z joins in. When the assignment was completed, 80 % of the work was done by X and Z. Find the ratio of work done by X and Z to that by Y when only 80 % of the assignment was completed?
[OA: 184/56]

Take some number and do it. Say 300 units. 150 done, 150 to go. Y did 20 percent of the total work so 60 units. Before z joined x and y did 150. So after z joined y did 10. In the same time period, x would have done 20. So z did 120. When 150 were done, x would be 100, y would be 50. For 90 more units, the split will be 12, 6, 72. So 184/56

Q12)
[OA: Option 4]

Q13) N is an eight digit number and S(N) is the sum of the digits of N. If N + S(N) = 100,000,000 what would be N?
[OA: 99999941]

By observation, we can figure out that it will be the last two digits that will contribute (99999999 will have 72 as the sum of digits and so, the max possible sum would be 100000072). Let the last 2 digits be x and y.
So, 999999xy + 54 + x + y = 100000000
11x + 2y = 46, x = 4, y = 1.

Q14) The average marks scored by two groups X and Y of students are 70 and 75 respectively. Four students are moved from group Y to group X, thereby interchanging the average marks of the two groups. Find the total number of students in two groups put together, if the average marks scored by the four students who moved are 85.
[OA: 20]

Q15) If g(y) = g(y – 1) + g(y + 1), where g(15) = 7 and g(20) = 2g(21), then g(21) = ?
[OA : 7]

Q16)
[OA: Option 1]