Question Bank (4)  Quant Mixed Bag  Shashank Prabhu, CAT 100 Percentiler

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

Q1) In the rectangular coordinate system, points (4, 0) and (– 4, 0) both lie on circle C. What is the maximum possible value of the radius of C ?
(A) 2
(B) 4
(C) 8
(D) 16
(E) None of the above[OA: Option E]

The answer is not B. You can draw a circle of any dimension and join 2 points on the circumference that are separated by 8. So, the max possible is infinite.

Q2) A, B, C and D are four friends each of whom weighs less than 100 kg. From among them they form a group and find the total weight of that group. If the sum of the total weights of all possible distinct groups, each having the same number of members as in the first is 882 kg, then the average weight of the four friends is
(1) 41.75 kg
(2) 63.5 kg
(3) 73.5 kg
(4) Cannot be determined[OA: Option 3]

We can all possible groups of 1 per person each OR all possible groups of 2 persons each OR all possible groups of 3 persons each OR all possible groups of 4 persons each. These will be 4c1, 4c2, 4c3 and 4c4 respectively. If the weights of the four friends are a, b, c and d respectively, and if we consider one person at a time, the total weight of all possible combinations will be a+b+c+d. For combinations of groups of 2 people each, it will be (a+b)+(a+c)+(a+d)+(b+c)+(b+d)+(c+d). For all groups of 3 people it will be (a+b+c)+(a+b+d)+(a+c+d)+(b+c+d). For four people it will be a+b+c+d. As the weight of each person is less than 100, exactly one person groups and exactly four persons groups are out as the total will be less than 400. For all possible groups with exactly 2 people, we get 3a+3b+3c+3d=882 which is possible and so, average as 73.5. For all possible groups with exactly 3 people we again get 3a+3b+3c+3d=882 and the average as 73.5.

Q3) Tarun invited 750 people to a party. Everyone who came to the party, came by a car. Three cars carried 6 people each and rest of the cars carried 7 people each. Only those people came to the party who were invited by Tarun. At the party, when every person including Tarun was seated in groups of eleven, one group fell short by four people. If maximum possible number of people came to the party, then out of the people who were invited by Tarun, how many people did not come to the party?
[OA: 18]

Should be 7n + 4 = 11m + 6, 39 is the remainder when divided by 77.
So 77k + 39. 732 is the highest value less than 750.
So 18 didn't attend.

Q4) Each of Amit, Bosco, Chris and Deepak bought 56 pencils out of which a total of 64 pencils were found to be broken. If the number of unbroken pencils with Chris is 60% and 75% more than Amit and Bosco respectively, then find the number of broken pencils with Deepak.
[OA: 19]

Q5) Which of the following cannot be expressed as the sum of three distinct composite numbers?
(1) 21
(2) 23
(3) 16
(4) 18[OA: Option 3]

Q6) Three students try to solve a problem independently with a probability of solving it as 1/3, 2/5, 5/12 respectively. What is the probability that the problem is solved ?
[OA: 23/30]

Q7) What is the sum of all roots of the equation ( x + 4 )^2  10 x + 4 = 24
[OA: 8]

Q8) A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn?
[OA: 4/27]

Q9) There are 49 zeros, 51 ones and 53 twos written on the board randomly. A student is blindfolded and then asked by his teacher to touch any two numbers on the board arbitrarily. The teacher deleted those two numbers and replaced them by a single number in the following manner:
The pair is replaced by
(0, 0) → 0
(1, 1) → 0
(2, 2) → 2
(1, 2) → 1
(0, 1) → 1
(0, 2) → 0If they continued this process what was the number left on the board in the end?
(a) 0
(b) 1
(c) 2
(d) Cannot be determined[OA: Option B]

Q10) What is the least possible distance between a point on the circle x^2 + y^2 = 1 and a point on the line y = (3x/4)  3?
A) 1.4
B) sqrt (2)
C) 1.7
D) sqrt (3)

Q11) The average of temperatures at noontime from Monday to Friday is 50; the lowest one is 45, what is the maximum possible range of the temperatures?
[OA: 25]

Q12) If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all values for k such that f(k+2) = g(2k)?
[OA: 4]

Q13) In an ensemble of gongs, all gongs have a diameter of either ten inches, or twelve inches or fifteen inches. In the collection there are 18 ten inch gongs. Half of the gongs in the collection are Tiger gongs. Of the Tiger gongs, there are equal numbers of ten inch, twelve inch and fifteen inch gongs. Half of the twelve inch gongs are not Tiger gongs, and half of all gongs are fifteen inches in diameter. How many gongs are there in the collection?
[OA: 108]

Q14) A and B ran, at their respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B’s speed in m/s?
[OA: 12 m/s]

Q15) If n is an integer from 1 to 96 (inclusive), what is the probability for n*(n+1)*(n+2) being divisible by 8?
a. 25%
b. 50%
c. 62.5%
d. 75%[OA: Option c]

Q16) A container has 3L of pure wine. 1L from the container is taken out and 2L water is added.The process is repeated several times. After 19 such operations, quantity of wine in mixture is
A. 2/7 L
B. 3/7 L
C. 6/19 L
D. None of these[OA: Option A]