RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Two employees A and B are paid a total of Rs. 560 per week by their employer. If A is paid 150 percent of the sum paid to B, how much is B paid per week?
A.s.130
B.s.140
C.s.150
D.s.224
Answer: D.s.224
Explanation: Let the amount paid to A per week = x
and the amount paid to B per week = y
Then x + y = 560
But x = 150% of y = 150y/100 = 15y/10
∴15y/10 + y = 560
⇒ y[15/10 + 1] = 560
⇒ 25y/10 = 560
⇒ 25y = 5600
⇒ y = 5600/25 =Rs.224
D)
Question: A bag contains 20 red and 30 white balls. One ball is drawn at random. What is the probability that the ball drawn is red?
A.11/5
B.2/5
C.3/5
D.4/5
Answer: B.2/5
Explanation: Total number of balls = 20+30 = 50
number of red balls = 20
Probability = 20/50 = 2/5
Answer is B
Question: A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?
A.128
B.144
C.176
D.186
Answer: B.144
Explanation: Explanation:
Given that SP = Rs. 102 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.
To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = Rs. 144
Answer:B
Question: Total 60 cows 20 cow gives each 2 liter milk 20 cow gives each 3/4 liter milk 20 cow gives each 1/4 liter milk this is split into 3 son per each 20 cows & 20 liter milk how?
A.20
B.10
C.15
D.16
Answer: A.20
Explanation: 20 cow 2 liter each =40 liter
20cow 3/4 liter each= 3/4=0.75*20=15
20 cow 1/4 liter each = 1/4=0.25*20=5
add 40+15+5=60
milk split into 3 son each 20 liter then 60/3=20
ANSWER:A
Question: Two trains of length 120 m and 210 m are 80 m apart. They start moving towards each other on parallel tracks, at speeds 69 kmph and 82 kmph. After how much time will the trains meet?
A.15/10
B.19/10
C.20/19
D.16/10
Answer: B.19/10
Explanation: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (69 + 82)*5/18 =41.9 mps.
The time required = d/s = 80/41.9 = 19/10 sec.
Answer:B
Question: There are 57 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs?
A.1) 4
B.2) 7
C.3) 17
D.4) 21
Answer: D.4) 21
Explanation: x -> Golf Club
2x -> Tennis Club
y -> both
x+2x-y = 51
3x - y =51
multiples of 3 greater than 51
60
63
66
69
72 - 21 = 51
IMO (D)
Question: The size of the wooden block is 5 x 10 x 20 cm .How many such blocks will be required to construct a solid wooden cube of minimum size?
A.6
B.8
C.12
D.16
Answer: B.8
Explanation: Side of smallest cube = L.C.M of 5,10,20 = 20cm
Volume of the cube = (20x20x20)= 8000 cm3
Volume of the block= (5x10x20cm3 = 1000cm3
Number of blocks = (8000/1000) = 8 Answer: B
Question: If the charge of staying in a student youth hostel $18.00/day for the first week, and $13.00/day for each additional week, How much does it cost to stay for 23 days?
A.$160
B.$289
C.$334
D.$274
Answer: C.$334
Explanation: Total number of days of stay = 23
Charge of staying in first week = 18*7 = 126 $
Charge of staying for additional days =(23-7)*13 = 16*13 = 208 $
Total charge =126 +208 = 334$
Answer C
Question: If 'Pink' is called 'Orange', 'Orange' is called 'Blue', 'Blue' is called 'Red', 'Red' is called 'Green', 'Green' is called 'Black' and 'Black' is called 'white', what would be the color of human blood ?
A.Green
B.BLUE
C.PINK
D.ORANCE
Answer: A.Green
Explanation: Explanation:
Pink → Orange
Orange → Blue
Blue → Red
Red → Green
Green → Black
Black → White
The color of human blood is 'Red' but in coding language, 'Red' is called 'Green'. So, the color of human blood is 'Green'.
ANSWER: A
Question: The markup on a necklace is 80 percent of the cost. The markup is what percent of the selling price?
(markup = selling price - cost)
A. 8%
B. 10%
C. 44.44%
D. 55%
Answer: C. 44.44%
Explanation: MP = 0.8 CP
SP = CP + 0.8 CP = 1.8 CP
hence MP = 0.8/1.8 SP = 4/9 SP. Hence MP is 44.44% of SP
Answer C
Question: Shawn has $150 to buy a new guitar. he found a guitar strap for $20, a guitar amplifier
for $80, and some guitar picks for $8. How much does he have left to buy the guitar?
A.$52
B.$42
C.$32
D.$22
Answer: A.$52
Explanation: we know that shawn had 150 dollars
then we have
$150all-$20strap-$80 amplifier-$8picks
we take
$52 dollars
correct answer A
Question: How many even number in the range between 10 to 120 inclusive are not divisible by 3
A.15
B.30
C.31
D.37
Answer: D.37
Explanation: We have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)
For 2,
10,12,14...120
using AP formula, we can say 120 = 10 + (n-1) *2
or n=56.
For 6,
12,18,...120
using AP formula, we can say 120 = 12 + (n-1) *6
or n=19.
Hence, only divisible by 2 but not 3 =56-19 = 37. hence, Answer D
Question: In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1:2:3. If there are Rs. 30 in all, how many 5 p coins are there?
A.165
B.716
C.150
D.143
Answer: C.150
Explanation: Let the number of 25 p, 10 p and 5 p coins be x, 2x and 3x respectively.
Then, sum of their values = [25x/100 + (10 * 2x)/100 + (5 * 3x)/100] = Rs. 60x/100
60x/100 = 30 => x = 50.
Hence, the number of 5 p coins = 3 * 50 = 150.
Answer:C
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
A.250
B.256
C.259
D.255
Answer: A.250
Explanation: CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => Rs.250
Answer: A
Question: How many positive number less than 1000 have sum of there digit 17?
A.43
B.53
C.63
D.75
Answer: C.63
Explanation: digits between 1-100 sum 17 =only 2 (89,98)
digits between 101-200 sum 17 =3 (188,179,197)
digits between 201-300 sum 17 = 4 (296,287,278,269)
and so on.....
digits between 301-400 sum 17 =5
digits between 401-500 sum 17 =6
digits between 501-600 sum 17 =7
digits between 601-700 sum 17 =8
digits between 701-800 sum 17 =9
digits between 801-900 sum 17 =10
but in
digits between 901-999 sum 17 =9 (980,971,962,953,944,935,926,917,908)
so total number is
2+3+4+5+6+7+8+9+10+9=63
ANSWER:C
Question: Solve 7x – 2(x+5) = 4x + 11
A.16
B.25
C.21
D.15
Answer: C.21
Explanation: Sol.
7x – 2(x+5) = 4x + 11
7x - 2x -10 = 4x + 11
=> 7x – 2x - 4x = 11 + 10
=> x = 21
Answer C
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
A.298
B.268
C.800
D.266
Answer: C.800
Explanation: 25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800
Answer:C
Question: If |5x-5| = 100, then find the sum of the values of x?
A.1
B.-2
C.2
D.-3
Answer: C.2
Explanation: |5x-5| = 100
5x-5 = 100 or 5x-5 = -100
5x = 105 or 5x = -95
x = 21 or x = -19
sum = 21-19 = 2
Answer is C
Question: Bob finishes the first half of an exam in four sixth the time it takes him to finish the second half. If the whole exam takes him an hour, how many minutes does he spend on the first half of the exam?
A.12
B.24
C.27
D.36
Answer: A.12
Explanation: Many times, it is easiest to think of problems like this conceptually (as opposed to formulaically). Conceptually, if the first half of the exam takes 4/6's the time of the second half (6/6's), we can see that the hour the entire exam took to finish can be broken down into tenth's. (Another way to look at this problem is via ratio's - first half is 4:10 and the second half is 6:10). With each tenth of an hour being 6 minutes (60/10), the first half of the exam would have taken 12 minutes. Correct answer is A.
Question: Excluding stoppages, the speed of a bus is 54 km/hr and including stoppages, it is 45 km/hr. For how many minutes does the bus stop per hour?
A.11 min
B.10 min
C.37 min
D.17 min
Answer: B.10 min
Explanation: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km
= 9/54 * 60 = 10 min.
Answer: B
Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
A.4
B.5
C.6
D.7
Answer: A.4
Explanation: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
Age of the youngest child = x = 4 years.
Answer:A
Question: A is thrice as efficient as B and is, therefore, able to finish a piece of work 10 days earlier than B. In how many days A and B will finish it together?
A.6
B.7
C.87
D.5
Answer: D.5
Explanation: WC = 3:1
WT = 1:3
x 3x
1/x – 1/3x = 1/10
x = 20/3
3/20 + 1/20 = 1/5 => 5 days
Answer:D
Question: How long does a train 110 m long running at the speed of 90 km/hr takes to cross a bridge 132 m length?
A.82.1 sec
B.9.68 sec
C.16.1 sec
D.13.1 sec
Answer: B.9.68 sec
Explanation: Speed = 90 * 5/18 = 25 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/25 = 9.68 sec.
Answer:B
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
A.600
B.882
C.772
D.652
Answer: A.600
Explanation: Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600
Answer:A
Question: A computer simulation of a 12 hour analog clock keeps perfect time while it is running, and
has two hands—an hour hand and a minute hand—both of which move continuously around
the 12 hour dial. (For example, at 2:30, the hour hand will be exactly halfway between 2 and
3.) Because of careless programming, the minute hand looks exactly like the hour hand, so
that the two are indistinguishable.
On one day, the clock stops at some time after 12am and before 12pm. How many times could
it have stopped without it being possible after 12pm to tell what time it stopped?
A.11
B.12
C.66
D.132
Answer: D.132
Explanation: A configuration of the hands is called “ambiguous” if you cannot use this broken clock to
distinguish the minute hand from the hour hand.
In the above diagram it must be the minute hand that is pointing to 6 and the hour hand that
is pointing midway between 2 and 3. (If the hour hand were to point to 6, the minute hand
would have to point to 12.) 2:30 is not an ambiguous configuration.
Let m 2 (0; 1) represent the fraction of the way around the clock face for the minute hand and
h 2 (0; 1) the corresponding fraction for the hour hand. For example, 2:30 hasm = 1=2 = 0:5
and h = 2:5=12 = 0:2083.
As the minute hand moves 12 times as fast as the hour hand, a configuration is ambiguous if
m and 12h have the same fractional part. Because the hands are indistinguishable, a time is
also ambiguous when h and 12m have the same fractional part. We express these conditions
as: 12h m( mod 1) and 12m h( mod 1). Thus 144h h( mod 1), and so 143h 0(
mod 1). There are 142 solutions to this equation in the open interval (0; 1): h 2 H1 := f k
143 :
k = 1; 2; : : : ; 142g.
Times when the hour and minute hand perfectly overlap (h = m) are in H1, but these are not
ambiguous times. These configurations occur when 12h h( mod 1). That is, 11h 0(
mod 1). There are 10 such times: h 2 H2 :=
k
11 : k = 1; 2; : : : ; 10
The number of ambiguous times is the cardinality of H1nH2. As H2 H1 the cardinality of
H1nH2 is 142 􀀀 10 = 132, which is answer (d).
correct answer D
Question: The volume of a sphere with radius r is (4/3)*pi*r^3 and the surface area is 4*pi*r^3. If a sperical balloon has a volume of 288 pi cubic centimeters, what is hte surface area of the balloon in square centimeters?
A.a. 40
B.b. 100
C.c. 400
D.d. 1,000
Answer: C.c. 400
Explanation: The surface area is 4.pi.r^2 (its area remember not volume)
as 4/3.pi.r^3=288pi
r=6
so area = 4.pi.r^2= 144.pi= 324 x 3.14 = 400 (approx)
C
Question: What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
A.60 ways
B.40 ways
C.30 ways
D.10 ways
Answer: C.30 ways
Explanation: Explanation:
The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women
= â´Câ‚‚ * âµCâ‚ = (4 * 3)/(2 * 1) * 5
= 30 ways.
Answer: C
Question: 4 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. If the committee has to include at least 4 professor, how many ways can this committee be formed?
A.36
B.64
C.72
D.80
Answer: B.64
Explanation: you count up combinations twice.
4*9*8... and let me name 6 with students A,B,C,..,F
after choosing a professor, when you choose Student A and B, you can choose A first, then B. Or B first, then A. Both combination are same.
I don't think that's the only mistake.
64 is a factor of = 2^2*4^2
144 is a factor of = 2^4*3^2.
These are very different numbers and you cannot divide 144 with something to get to 64. ans B
Question: Lottery balls numbered consecutively from one through one hundred are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 3 on it exactly once?
A.18/100
B.1/10
C.11/100
D.19/100
Answer: A.18/100
Explanation: Probability = No of balls with exactly one 1 / total number of balls
= {3,13, 23, 30,31, 32, 34 to 39, 43,53,63,73,83,93}/100
= 18/100
Answer is A
Question: A cylindrical can has a radius of 3 centimeters and a height of 24 centimeters. What is the area, in square centimeters, of a rectangular label that completely covers the curved surface of the can without over-lapping?
A.16 pi
B.64 pi
C.96 pi
D.144 pi
Answer: D.144 pi
Explanation: They are asking the lateral surface area of the cylinder.
the Lateral surface area = 2* pi * r *h
= 2*pi*3*24=144 pi
Answer is D.
Question: The bus that travels from St. Louis to Chicago and back comes to St. Louis every 3 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 4 hours. If at 6:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?
A.16:00.
B.18:00.
C.20:00.
D.22:00.
Answer: B.18:00.
Explanation: Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 3 hours
Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 4 hours
Time taken by both buses to meet again in St. Louis will be LCM of 3 and 4 = 12
If the buses start at 6:00 o'clock from St. Louis , they will meet again in St. Louis at 18:00 hours
Answer B
Question: We run a business that rents out canoes and kayaks. A canoe rental costs $12 per day, and a kayak rental costs $18 dollars per day. One day, our business rents out 3 canoes for every 2 kayaks and receives a total of $504 in revenue. How many more canoes than kayaks were rented out?
A.5
B.6
C.7
D.8
Answer: C.7
Explanation: Let x be the number of canoes.
Then 2x/3 is the number of kayaks.
12x+(2x/3)*18=504
12x+12x=504
24x=504
x=21 (canoes)
2x/3=14 (kayaks)
There were 21-14 = 7 more canoes rented out.
The answer is C.
Question: Of three numbers, the third is twice the second and the second is 4 times the first. If their average is 78, the smallest of the three numbers is:
A.18
B.19
C.20
D.21
Answer: A.18
Explanation: Explanation:
Let first number be x.
So,2nd no. = 4x & 3rd no.=8x.
So,x+4x+8x=78 × 3 = 234.
13x = 234
x = 234/13
Hence,smallest Number x=18.
Answer: A
Question: What is the unit digit in 4^100?
A.0
B.1
C.6
D.3
Answer: C.6
Explanation: Unit digit in 4^100 = unit digit in [(4^4)^25 ]But unit digit in 4^4=6unit digit 4^100= 6Answer is C
Question: A fruit seller sells mangoes at the rate of Rs.5 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%
A.Rs 6.56
B.Rs 9.56
C.Rs 10.56
D.Rs 11.56
Answer: A.Rs 6.56
Explanation: Explanation:
80 : 5 = 105 : x
x= (5×105/80)
= Rs 6.56
Option A
Question: How many integers from 0 to 53, inclusive, have a remainder of 1 when divided by 3 ?
A.15
B.16
C.17
D.18
Answer: D.18
Explanation: My ans is also C.17.
Explanation:
1 also gives 1 remainder when divided by 3, another number is 4, then 7 and so on.
Hence we have an arithmetic progression: 1, 4, 7, 10,..... 52, which are in the form 3n+1.
Now we have to find out number of terms.
tn=a+(n-1)d, where tn is the nth term of an AP, a is the first term and d is the common difference.
so,52 = 1+(n-1)3
or, (n-1)3 = 51
or, n-1 = 17
or, n = 18
D
Question: How many ways are there to select a subcommittee of 8 members from among a committee of 17?
A.22888
B.24310
C.28791
D.27711
Answer: B.24310
Explanation: Explanation:
Since it does not matter what order the committee members are chosen in, the combination formula is used.
Committees are always a combination unless the problem states that someone like a president has higher hierarchy over another person. If the committee is ordered, then it is a permutation.
C(17,8)= 24310
Answer: B)
Question: The area of rectangular field of length 90 meters and breadth 80 meters is equal to the area of a square plot. What will be the length of the diagonal of the square plot?
A.100m
B.120m
C.95m
D.80m
Answer: B.120m
Explanation: Given that the length of the rectangular field l = 90 m and breadth = b = 80 m.
Then its area lb = 90 x 80 sq.m
We know that the area of square = (1/2)x(diagonal)2
from the given question, we have area of square plot = area of rectangular field
That is, 90 x 80 = 1/2 x diagonal2
diagonal^2 = 2 x 7200 = 14400 = (120)2
diagonal = 120 m.hence B
Question: Which of the following is equal to 5^k*7^(k-1)?
A.5*35^(k-1)
B.5*35^(k-1)
C.35^k
D.5*35^k )
Answer: A.5*35^(k-1)
Explanation: 5^k*7^(k-1) = 5*5^(k-1)*7^(k-1) = 5*35^(k-1)
The answer is A.
Question: The ratio of the area of a square to that of the square drawn on its diagonal is
A.1:2
B.1:0
C.1:7
D.1:5
Answer: A.1:2
Explanation: Answer: A) 1:2
Question: A man can row 18 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream.
A.2 km/hr
B.3 km/hr
C.7 km/hr
D.9 km/hr
Answer: D.9 km/hr
Explanation: Let man’s rate upstream be x kmph.then ,his rate downstream=3xkmph.
So,2x=18 or x=9.
Rate upstream=9 km/hr,rate downstream=27 km/hr.
Hence,rate of stream=1/2(27-9)km/hr=9 km/hr.
ANSWER D 9 km/hr
Question: Look at this series: 31, 29, 24, 22, 17, ... What number should come next?
A.15
B.14
C.13
D.12
Answer: A.15
Explanation: Explanation: This is a simple alternating subtraction series, which subtracts 2, then 5.
Answer: Option A
Question: At 3:40, the hour hand and the minute hand of a clock form an angle of
A.10º
B.75º
C.90º
D.130º
Answer: D.130º
Explanation: Hence the angle
=30(40/5-3)-40/2
=30(8-3)-20
=30 X5-20=130 °
Answer D
Question: If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?
A.1509
B.1528
C.1500
D.1598
Answer: C.1500
Explanation: Let the cost price of an article be Rs. x.
(19% of x) - (12% of x) = 105
19x/100 - 12x/100 = 105 => 7x = 105 * 100
=> x = 1500
Cost price = Rs. 1500.Answer:C
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
A.22.9
B.10.8
C.17.2
D.21.1
Answer: B.10.8
Explanation: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec.Answer: B
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero ?
A.0
B.8
C.3
D.7
Answer: A.0
Explanation: Explanation:
Average of 20 numbers = 0.
Sum of 20 numbers = (0 * 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (- a).
Answer: A
Question: If there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if the total number of wheels is 58?
A.11
B.12
C.13
D.14
Answer: D.14
Explanation: four wheeler=14*4=56(max)
2 wheel=1
so no of 4 wheeler=14
ANSWER:D
Question: A, B and C start a business each investing 10,000. After 6 months A withdrew 5000, B withdrew 4000 and C invests 6000 more. At the end of the year, a total profit of 34,200 was recorded. Find the share of B.
A.9,600
B.21,200
C.28,200
D.20,500
Answer: A.9,600
Explanation: Ratio of the capitals of A, B and C
= 10000 Ã— 6 + 5000 Ã— 6 : 10000 Ã— 6 + 6000 Ã— 6 : 10000 Ã— 6 + 16000 Ã— 6
=90000 : 96000 : 156000 = 90 : 96 : 156
Bâ€™s share = (34200 Ã— 96â„342) = 9600
Answer A
Question: If yesterday was Monday, when will Wednesday be?
A.The day after tomorrow
B.Two days before today
C.Today
D.Tomorrow
Answer: D.Tomorrow
Explanation: Explanation:
Yesterday was Monday
=>Today is Tuesday
=> Tomorrow is a Wednesday
Answer: Option D
Question: An unbiased die is tossed. Find the probability of getting a multiple of 5
A.1/4
B.1/6
C.2/5
D.5/6
Answer: B.1/6
Explanation: Here S = {1,2,3,4,5,6}
E = event of getting a multiple of 5
E = {5}
P(E) = 1/6
Answer is B
Question: A man can row with a speed of 30 kmph in still water. If the stream flows at 11 kmph, then the speed in downstream is?
A.22
B.28
C.20
D.41
Answer: D.41
Explanation: M = 30
S = 11
DS = 30 + 11 = 41.Answer:D
Question: The distance from Steve's house to work is 20 Km. On the way back Steve drives twice as fast as he did on the way to work. Altogether, Steve is spending 6 hours a day on the roads. What is Steve's speed on the way back from work?
A.5.
B.10.
C.14.
D.15.
Answer: B.10.
Explanation: Time is in the ratio 2:1 :: to: fro office
Therefore, 2x+1x=6 hrs
Time take to come back - 2 hrs, distance travelled - 20km => Speed = 10kmph
B
Question: In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys ?
A.33
B.25
C.77
D.28
Answer: B.25
Explanation: Explanation:
The toys are different; The boxes are identical
If none of the boxes is to remain empty, then we can pack the toys in one of the following ways
a. 2, 2, 1
b. 3, 1, 1
Case a. Number of ways of achieving the first option 2 - 2 - 1
Two toys out of the 5 can be selected in \inline {\color{Black} 5C_{2}} ways. Another 2 out of the remaining 3 can be selected in \inline {\color{Black} 3C_{2}} ways and the last toy can be selected in \inline {\color{Black} 1C_{1}} way.
However, as the boxes are identical, the two different ways of selecting which box holds the first two toys and which one holds the second set of two toys will look the same. Hence, we need to divide the result by 2
Therefore, total number of ways of achieving the 2 - 2 - 1 option is ways \inline {\color{Black} 5C_{2}\times 3C_{2}}= 15 ways
Case b. Number of ways of achieving the second option 3 - 1 - 1
Three toys out of the 5 can be selected in \inline {\color{Black} 5C_{3}} ways. As the boxes are identical, the remaining two toys can go into the two identical looking boxes in only one way.
Therefore, total number of ways of getting the 3 - 1 - 1 option is \inline {\color{Black} 5C_{3}} = 10 = 10 ways.
Total ways in which the 5 toys can be packed in 3 identical boxes
= number of ways of achieving Case a + number of ways of achieving Case b
= 15 + 10 = 25 ways.
Answer: B) 25
Question: The price of lunch for 15 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?
A.11.73
B.12
C.13.8
D.14
Answer: B.12
Explanation: x -> Price without Gratuity
207 = x + 0.15x
=> x = 207/1.15 = 180
So average price per person,excluding the gratuity = 180/15 = 12
The answer is B.
Question: Given that E and F are events such that P(E) = 15, P(F) = 10 and P(E n F) = 15,
find P (E|F) and P(F|E)
A.3/2
B.4/5
C.6/2
D.8/5
Answer: A.3/2
Explanation: Here, E and F are events
P(E|F) = P(EnF)/P(F) = 15/5 = 1
P(F|E) = P(EnF)/P(E) = 15/10 = 3/2.
A)
Question: Five years ago, the average age of A, B, C and D was 45 yr. with E joining them now, the average of all the five is 52 yr. How old is E?
A.25 yr
B.62 yr
C.45yr
D.64 yr
Answer: B.62 yr
Explanation: Solution:
Total present age of A, B, C and D,
= (45*4)+(4*5) = 200 yr;
Total age present age of A, B, C, D and E,
= 52*5 = 262 yr.
So, age of E = 62 yr.
Answer: Option B