Quant Boosters  Maneesh  Set 4

It depends on a, b, c
answer will be smallest of √{a² + (b + c)²}, √{b² + (a + c)²} and √{c² + (a + b)²}
(solution by hemant yadav sir)

Q5) Two consecutive numbers are removed from a list of first ‘n’ natural numbers. The average of the
remaining numbers is 21 (1/3). What is the product of the two numbers that have been removed?

Average of first n natural numbers used to be a value near to middle number
considrng 21 as middle number > so n can be (39 + 2), (42 + 2), (45 + 2)....
when n = 41 > sum = 832 + x + x + 1 = 833 + 2x
sum of first 41 natural numbers = 41 * 21 = 861
2x = 28
x = 14
two missd numbers 14 and 15
product = 14 * 15 = 210

Q6) A train after travelling 50 KM from A meets with an accident and proceeds at (4/5)th of the former speed and reaches B 45 min late. Had the accident happened 20 KM further on it would have arrived 12 min sooner. Find the original speed and distance.

Let original speed of train is S
20/(4S/5) – 20/S = 12/60 = 1/5
10080 = 4S/5
4S = 100
S = 25 KM/HR
Let the original distance is D
D50/20  D50/25 = 3/4
5D2504D+200 = 75
D = 125 KM

Q7) I have six identical oranges and six distinct apples. In how many ways can I have a basket of five fruits containing at least one apple and at least one orange?

1 orange 4 apple > 6c4
2 orange 3 apple > 6c3
3 orange 2 apple > 6c2
4 orange 1 apple > 6c1
15 + 20 + 15 + 6 = 56

Q8) A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of the three popular options, air conditioning, radio and power windows were already installed.
The survey found:
15 had air conditioning
2 had air conditioning and power windows but no radios
12 had radio
6 had air conditioning and radio but no power windows
11 had power windows
4 had radio and power windows
3 had all three options.What is the number of cars that had none of the options?
a. 4
b. 3
c. 1
d. 2

N(AURUP) = N(A)+N(R)+N(P)N(AnR)  N(AnP)  N(PnR) + N(AnPnR)  car with no options
25 = 15 + 12 + 11  6  2  4 + 3  car with no options
25 = 29  car with no options
car with no options = 4

Q9) A Father is willing his estates like this. If a boy is born, wife has 1/3 part and remaining for boy. If a girl is born, Wife has 2/3 and remaining for the girl. But twins (Boy + Girl) are born. What is the share that the daughter would get?

M : B = 1 : 2
M : G = 2 : 1
M : B : G = 2 : 4 : 1
daughter's share = 1/7

Q10) 70% of the students who joined XLRI last year play football, 75% play cricket, 80% play basketball and 85% play carrom. The minimum percentage of people who play all games is:
a) 5%
b) 10%
c) 15%
d) 20%
e) None of the above

100  (30 + 25 + 20 + 15) = 10

Q11) N is a fourdigit number in which each of the digits used appears at least two times. The number of different values that N can assume is

let first digit is 1 then other 3 digits can be 1 itself > 1 way
one of them can be 1 and other two any of (0,2,3....9) > 3 * 9 = 27
total 27 + 1 = 28similarly when first digit is 2,3,4...9 > 9 * 28 = 252

Q12) There are 2 bags, one consists of 3 red and 4 black balls and the other consists of 4 red and 2 black balls. One bag is selected at random and from a selected bag a ball is drawn. Let E be an event that first bag is selected, F be an event that second bag is selected, G be an event that a ball drawn is red. Find P(G/E).

P(G/E) = P(GnE)/P(E)
P(GnE) = 1/2 * 3/7 = 3/14
P(E) = 1/2
P(G/E) = 3 * 2/14 = 3/7

Q13) The average age of A ,B ,C ,D five years ago was 45 years. By including X, the present average age of all the five is 49 years.The present age of X is
a) 64 years
b) 48 years
c) 45 years
d) 40 years

Total Age 5 years ago = 180
Total age now = 180 + 20 = 200
X included,total age = 5 * 49 = 245
Age of X = 45

Q14) There are 42 students in a hostel. Due to admission of 13 new students, the expenses of mess increase by Rs 31 per day while the average expenditure per head diminished by Rs 3. What was the original expenditure of the mess ?