RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Tony alone can paint a wall in 7 days and his friend Roy alone can paint the same wall in 9 days. In how many days they can paint the wall working together? Round off the answer to the nearest integer.
A.2
B.4
C.6
D.7
Answer: B.4
Explanation: Sol. use formula (xy / x+y)
So nearest value for 3.93 = 4
Answer: Option B
Question: Among 250 viewers interviewed who watch at least one of the three TV channels namely A, BC. 116 watch A, 127 watch C, while 107 watch B. If 70 watch exactly two channels. How many watch exactly one channel?
A.185
B.180
C.165
D.190
Answer: C.165
Explanation: 250 = n(Exactly 1 channel) + n(Exactly 2 channels) + n(Exactly 3 channels)
250 = n(Exactly 1 channel) + 70 + n(Exactly 3 channels)
Let's find the value of n(Exactly 3 channels) = x
250 = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)
Note that each of n(A and B) is the sum of 'number of people watching exactly two channels A and B' and 'number of people watching all three channels'.
250 = 116 + 127 + 107 - n(Exactly 2 channels) - 3x + x
250 = 116 + 127 + 107 -70 - 2x
x = 25
250 = n(Exactly 1 channel) + 70 + 25
n(Exactly 1 channel) = 165
Answer (C)
Question: N is an 80-digit positive integer (in the decimal scale). All digits except the 44th digit (from the left) are 2. If N is divisible by 13, find the 26th digit?
A.5
B.6
C.1
D.2
Answer: B.6
Explanation: DETAILED SOLUTION
To begin with, the question should read "find the 44th digit".
Any number of the form abcabc is a multiple of 1001. 1001 is 7 * 11 * 13. So, any number of the form abcabc is a multiple of 13.
So, a number comprising 42 2's would be a multiple of 13, so would a number comprising 36 2's. So, in effect, we are left with a two digit number 2a, where a is the 44th digit. 26 is a multiple of 13, so the 44th digit should be 6.
CORRECT ANSWER B
Question: The present ages of three persons are in proportions
4 :7 :9. Eight years ago, the sum of their ages was 56. Find their present ages (in years)
A.8, 20, 28
B.16, 28, 36
C.20, 35, 45
D.None of these
Answer: B.16, 28, 36
Explanation: Solution
Let their present ages be 4x,7x and 9x years respectively.
Then, (4x-8)+(7x-8)+(9x-8)	= 56
20x = 80
x= 4.
Their present ages are 16,28,36 years .
Answer B
Question: Rose & Raylene goes to same place for work daily from same house & they work for five days a week. Rose saves 10 minutes on a day than Raylene in her trip. In a month, how much time Rose saves compared to Raylene in traveling? Take in a month there are four weeks (20 working days)
A.3 hours & 20 minutes
B.3 & 10
C.3 hours
D.2 hours & 20 minutes
Answer: A.3 hours & 20 minutes
Explanation: For each day rose saves 10 minutes so for a week 50 minutes (10*5) & which gives a month 200 minutes (50*4).
200 minutes = 3 hours 20 minutes
Answer: A
Question: Goldenrod and No Hope are in a horse race with 9 contestants. How many different arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?
A.362880
B.181440
C.120000
D.24000
Answer: B.181440
Explanation: All 9 horses can finish the race in 9! way (assuming no tie).
If no tie is possible between No Hope and Goldenrod, then in half of these cases No Hope will be before Goldenrod and in half of these cases after (not necessarily right before or right after). How else? So, there are 9!/2=181440 different arrangements of finishes where No Hope always finishes before Goldenrod.
Answer: B.
Question: An inspector rejects 10% of the meters as defective. How many will he examine to reject 10?
A.100
B.120
C.250
D.200
Answer: A.100
Explanation: Then, 10% of x= 10
(10/100)x = 10
x = (10*100*)/10= 100
Answer is A
Question: In a clothing store, there are six different colored neckties (red, orange, yellow, green, blue, and indigo) and four different colored shirts (red, orange, yellow, green, blue, and indigo) that must be packed into boxes for gifts. If each box can only fit one necktie and one shirt, what is the probability that all of the boxes will contain a necktie and a shirt of the same color?
A.719/720
B.1/24
C.2/233
D.3/543
Answer: B.1/24
Explanation: 4 ties and 4 shirts...
red tie can take any of 4 shirts..
orange can take any of the remaining 3 shirts
yellow any of remaining 2..
and so on till last indigo chooses the 1 remaining..
Total ways= 4*3*2*1=24
out of this 720, ONLY 1 way will have same colour tie and shirt..
prob = 1/720
B
Question: The speed of a boat in still water is 18 km/hr and the rate of current is 4 km/hr. The distance travelled downstream in 14 minutes is
A.1.6 km
B.2 km
C.5.1 km
D.4 km
Answer: C.5.1 km
Explanation: Explanation:
Speed downstreams	=(18 + 4)kmph
= 22 kmph.
Distance travelled	= (22 x 14/60)km
= 5.1km
Option C
Question: The average weight of 10 persons increases by 7.2 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
A.120 kg
B.130 kg
C.137 kg
D.190 kg
Answer: C.137 kg
Explanation: Solution
Total weight increased	= (10 x 7.2)kg
= 72 kg.
Weight of new person	= (65 + 72)kg
= 137 kg.
Answer C
Question: A room is half as long again as it is broad. The cost of carpeting the at Rs. 5 per sq. m is Rs. 270 and the cost of papering the four walls at Rs. 10 per m2 is Rs. 1420. If a door and 2 windows occupy 8 sq. m, find the height of the room.
A.4 m
B.4.5 m
C.5 m
D.5.5 m
Answer: C.5 m
Explanation: Explanation:
Let breadth = x m, length = 3x m, height = H metres.
Area of the floor = (Total cost of carpeting)/(Rate/m2)=(270/5)m2=54m2.
x× (3x/2) = 54 =>x2 = (54×2/3) = 36 <=> x = 6.
So, breadth = 6 m and length =(3/2)×6 = 9 m.
Now, papered area = (1420/10)m2 = 142 m2.
Area of 1 door and 2 windows = 8 m2.
Total area of 4 walls = (142 + 8) m2 = 150 m2
2×(9+ 6)× H = 150 <=> H = 150/30 = 5 m.
Answer: Option C
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.83. How much was lent at 5%?
A.388
B.700
C.277
D.500
Answer: B.700
Explanation: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 83
5x/100 + 90 – 6x/100 = 83
x/100 = 7
=> x = 700.Answer: B
Question: If X is invested in a bank at a rate of simple interest of y% p.a. for two years, then the interest earned is 900. if X is invested at y% p.a., for two years when the interest is compounded annually, the interest is 922.50. What is the value of X?
A.9000
B.6000
C.5000
D.4000
Answer: A.9000
Explanation: Simple way to solve this question is to use options.
From SI, we know that X*y=45,000.
Now, put the value of X = 9000, we will have y = 5%
To calculate CI,
Now, we know 1st year Amount= 9000+5% of 9000= 9450.
2nd year, Amount = 9450 + 5% of 9450 = 9922.50.
We can see after 2 years Interest = 9922.50-9000= 922.50. hence, it satisfies the question. Hence A is the correct answer
Question: Walking at 1/3th of its usual speed a cab is 20mnts late. Find its usual time to cover the journey?
A.10m
B.15m
C.20m
D.25m
Answer: A.10m
Explanation: New speed = 1/3th of usual speed
New time = 3 of usual time
3 UT - UT = 20m
2UT = 20m
UT = 10m
Answer is A
Question: If a sum on compound interest becomes three times in 4 years, then with the same interest rate, the sum will become 81 times in:
A.12 years
B.18 years
C.16 years
D.14 years
Answer: C.16 years
Explanation: Explanation:
The sum P becomes 3P in 4 years on compound interest
3P = P(1+R/100)4
â‡’ 3 = (1+R/100)4
Let the sum P becomes 81P in n years
81P = P(1+R/100)n
â‡’ 81 = (1+R/100)n
â‡’ (3)4 = (1+R/100)n
â‡’ ((1+R/100)4)4 = (1+R/100)n
â‡’ (1+R/100)16 = (1+R/100)n
n=16
i.e, the sum will become 81 times in 16 years
ANSWER IS C
Question: 15.06 * 0.00000001 = ?
A.15060000
B.0.001506
C.0.01506
D.1.506e-07
Answer: D.1.506e-07
Explanation: Explanation:
Clearly after decimal 10 digits should be there.
Option D
Question: Jansi went out for shopping. She had in her handbag approximately Rs. 15/- in one rupee notes and 20 p. coins. When she returned she had as many one rupee notes as she originally had and as many 20 p. coins as she originally had one rupee notes. She actually came back with about one-third of what she had started out with.
How much did she spend and exactly how much did she have with her when she started out ?
A.9.6
B.10.6
C.11.0
D.9.4
Answer: A.9.6
Explanation: A
9.60
Let us assume that originally Jansi had X rupees and Y 20 paise coins. Going shopping she had (100X + 20 Y) paise.
She returned with only (100 Y + 20 X) paise.
This last sum, as we know, is one-third of the original and therefore
3(100 Y + 20 X) = 100 X + 20 Y Simplifying we have X = 7 Y
If Y is 1 thenX is 7. Assuming this so Jansi had 7.20 rupees when she set out for shopping.
This is wrong because Jansi actually had about 15 rupees.
Let us see now what we get if Y = 2. Then X = 14. The original sum was 14.40 rupees which accords with the condition of the problem.
If we assume that Y = 3 then the sum will be too big — 21.60 rupees.
Therefore the only suitable answer is 14.40 rupees.
After shopping Jansi had 2 one rupee notes and 14 twenty Paise coins.
This is actually l/3rd of the original sum 1,440:3 = 480. Jansi's purchases, therefore, cost 14.40 — 4.80 = Rs 9.60
Question: If d is a number such that –2 ≤ d ≤ 2, which of the following has the largest possible absolute value?
A.3d – 1
B.x^2 + 1
C.3 – x
D.x – 3
Answer: A.3d – 1
Explanation: Ans is A .. leads to the max value of 7 for d = -2
Question: In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 10 per square m?
A.s.9500
B.s.50000
C.s.57000
D.s.60000
Answer: A.s.9500
Explanation: Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m
Total area of the hall to be covered with mat = 2(lb + bh + hl)
= 2(20 * 15 + 15 * 5 + 5 * 20)
=2(300 + 75 + 100)
= 2 * 475
= 950 sq. m
Total expenditure = 10 * 950
= Rs.9500
A
Question: 220, 218, 214, 208, 200, 190, ?
A.176
B.174
C.178
D.180
Answer: C.178
Explanation: 220
220 - 2 = 218
218 - 4 = 214
214 - 6 = 208
208 - 8 = 200
200 - 10 = 190
190 - 12 = 178
Answer is C.
Question: The total marks obtained by a student in Mathematics and Physics is 20 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.
A.40
B.26
C.20
D.28
Answer: C.20
Explanation: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 20 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (20 + 20) / 2 = 20.Answer:C
Question: If f(x) = k(x - k) and k is a constant, what is the value of f(4) - f(2), in terms of k?
A. 1
B. k
C. 2k
D. k^2 + k
Answer: C. 2k
Explanation: First, distribute f(x). k(x - k) = kx - k^2. Now evaluate f(4) and f(2):
f(4) = k(4) - k^2 = 4k - k^2
f(2) = 2k - k^2
f(4)-f(2)=2k.. Answer C
Question: Different breeds of dogs get older at different rates in “dog years.” Livonian wolfhounds age 7 times as fast as humans, whereas Khazarian terriers age 5 times as fast and Akkadian retrievers age 4 times as fast. If Dan bought a newborn Akkadian on January 1, 2008, a newborn Khazarian 1 year later, and a newborn Livonian 1 year after that, in what year will the sum of the dog-year ages of the Akkadian and the Khazarian first be exceeded by twice the age of the Livonian in dog years, rounding all ages down to the nearest integer?
A.2015
B.2014
C.2013
D.2016
Answer: C.2013
Explanation: chart starting at 2010:
A+K=13
L=0.
Then I added 9 to a+k for each year and 14 to L for each year.
2011:AK=22 L=14
2012:AK=31 L=28
2013:AK=40 L=42
thus, 2013 is the correct answer. => C
Question: Train A and Train B began traveling towards each other from opposite ends of a 420-mile long track at 1:00 PM. If Train A traveled at 35 miles per hour and Train B traveled at 25 miles per hour, at what time did the trains meet?
A.5:40 PM
B.6:00 PM
C.7:20 PM
D.8:00 PM
Answer: D.8:00 PM
Explanation: This question tests your concepts of relative speed:
If two trains are moving in opposite direction, then distance will reduce at a rate of (Speed of 1 + Speed of 2)
If two trains are moving in same direction, then distance will reduce at a rate of (Speed of 1 - Speed of 2)
Here the trains are moving towards each other, hence in opposite direction.
Trains will cover the 500 mile track in a time of 500/(25 + 35) =420/60 = 7 hours
Trains started at 1:00 PM, there they will meet at 8:00 PM
Option D
Question: A constructor estimates that 8 people can paint Mr khans house in 3 days. If he uses 4 people instead of 8,how long will they take to complete the job?
A.6
B.8
C.3
D.4
Answer: A.6
Explanation: Explanation:
Use formula For a work Members Ã— days = constant
8 Ã— 3 = 4 Ã— a
a = 6
so answer is 6 days
Answer: A
Question: There are two cars. One is 100 miles north of the other. Simultaneously, the car to the north is driven westward at 10 miles per hour and the other car is driven eastward at 15 miles per hour. How many miles apart are the cars after 3 hours?
A.125
B.150
C.200
D.225
Answer: A.125
Explanation: Here, drawing a quick sketch of the 'actions' described will end in a diagonal line that you canbuilda right triangle around:
The right triangle will have a base of 75 and a height of 100. The hidden pattern here is a 3/4/5 right triangle (the 75 lines up with the '3' and the 100 lines up with the '4'). In this way, you can deduce that each side is '25 times' bigger than it's corresponding side:
3/4/5 becomes
75/100/125
Thus the distance between the two cars is the length of the hypotenuse of this larger right triangle...
Final Answer: A
Question: A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 25%. Staff are allowed a further 20% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
A.0.6D
B.0.7D
C.0.5D
D.0.8D
Answer: A.0.6D
Explanation: Effective discount = a + b + ab/100 = - 25 - 20 + (-25)(-20)/100 =-40
Sale price = D * ( 1 - 40/100)
Sale price = .6 * D
Answer (A)
Question: What is the twenty-fourth decimal to the right in the fraction 35/36?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: 35/36= 0.97222222222...
The answer is B.
Question: If a coin is tossed three times, what is the probability that on the first toss the coin lands on heads and then lands on tails the next two tosses?
A.1/8
B.1/3
C.1/4
D.1/2
Answer: A.1/8
Explanation: P(HTT) = 1/2*1/2*1/2=1/8
The answer is A.
Question: The ratio of males to females in a class is 2:3. The career preferences of the students in the class are represented in a circle graph. If the area of the graph allocated to each career preference is proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by two-thirds of the males and one-third of the females in the class?
A.160
B.168
C.191
D.192
Answer: B.168
Explanation: 2/3*2/5 + 1/3*3/5 = 4/15 + 3/15 = 7/15
The number of degrees is 7/15 * 360 = 168 degrees
The answer is B.
Question: A train is 360 meter long is running at a speed of 36 km/hour. In what time will it pass a bridge of 140 meter length?
A.50 seconds
B.46 seconds
C.40 seconds
D.97 seconds
Answer: A.50 seconds
Explanation: Speed = 36 Km/hr = 36*(5/18) m/sec = 10 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (1/10)
= 50 seconds
Answer:A
Question: In a kilometer race, A beats B by 54 meters or 12 seconds. What time does A take to complete the race?
A.212
B.190
C.277
D.181
Answer: A.212
Explanation: Time taken by B run 1000 meters = (1000 * 12)/54 = 222 sec.
Time taken by A = 224 - 12 = 212 sec.Answer:A
Question: The events A and B are independent. The probability that event A occurs is r and the probability that event B occurs is s. Which of the following is equal to the probability that exactly one of the events A and B occurs?
A.r − 2rs
B.s − rs
C.r + s− 2rs
D.r + s −rs
Answer: D.r + s −rs
Explanation: Probability of A occuring = p , Probability of A NOT occuring = 1-r
Probability of B occuring = s , Probability of B not occurring = 1-s
Probability of atleast of one of A and B occuring = 1-(1-r)(1-s) =r+s -rs
D
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
A.333 m
B.277 m
C.245 m
D.279 m
Answer: C.245 m
Explanation: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer:C
Question: 7 dogs have got 7 puppies each. Each puppy has got 7 kitten as friend. They are all members of a club along with me. What is the strength of club ?
A.300
B.400
C.500
D.600
Answer: B.400
Explanation: total strength = (7+7*7+7*7*7)+1=400
ANSWER:B
Question: A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 4:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
A.10.18 p.m
B.10.29 p.m
C.11.30 p.m
D.10.38 p.m
Answer: C.11.30 p.m
Explanation: D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
4.30 + 7 h = 11.30 p.m.
Answer:C
Question: The ratio of the ages of Malini and Radha is 2 : 4. The total of their ages is 2.4 decades. The proportion of their ages after 0.8 decades will be
[1 Decade = 10 years]
A.6:5
B.3:4
C.4:5
D.2:3
Answer: D.2:3
Explanation: Let, Malini’s age = 2A and Radha’s age = 4A
Then 2A + 4A = 24
A = 4
Malini’s age = 8 years
and Radha’s age = 16 years
Proportion of their ages after 8 is = (8 + 8) : (16 + 8)
= 16 : 24
= 2 : 3
Answer : D
Question: A university needs to select an eight-member committee on extracurricular life, whose members must belong either to the student government or to the student advisory board. If the student government consists of 9 members, the student advisory board consists of 8 members, and 6 students hold membership in both organizations, how many different committee are possible?
A.165
B.194
C.212
D.236
Answer: A.165
Explanation: student government + the student advisory board consists of 9 + 8 = 17 members.
6 students hold membership in both, so they were counted twice.
The total number of people to choose from is 17 - 6 = 11
The number of ways to choose 8 members from 11 is 11C8 = 165
The answer is A.
Question: The area of a circular field is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 2 per metre approximately
A.2972
B.4567
C.4235
D.4547
Answer: A.2972
Explanation: Explanation:
Area = (17.56 x 10000) m2= 175600 m2.
ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.
Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.
Cost of fencing = Rs. (1485.78 x 2) = Rs. 2972.
Answer: Option A
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 242 runs?
A.6.25
B.5.25
C.6.29
D.6.39
Answer: B.5.25
Explanation: Required run rate
= [242 - (3.2 * 10)]/40
= 210/40
= 5.25
Answer: B
Question: What is the sum of the multiples of 4 from 40 to 80, inclusive?
A.560
B.660
C.800
D.760
Answer: B.660
Explanation: The formula we want to use in this type of problem is this:
Average*Total Numbers=Sum
First, find the average by taking the sum of the F + L number and divide it by 2:
A = (F + L)/2
Second, find the total numbers in our range by dividing our F and L numbers by 4 and add 1.
(80/4) - (40/4) + 1
Multiply these together so what we show Average*Total Numbers=Sum
(80 + 40)/2 * (80/4) - (40/4) + 1 = Sum
60 *11 = 660
B
Question: Mrs. Rodger got a weekly raise of $115. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
A.$ 145.
B.$ 146
C.$ 115
D.$ 148
Answer: C.$ 115
Explanation: Solution:
Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 115.
So after completing the 1st week she will get $ (x+115).
Similarly after completing the 2nd week she will get $ (x + 115) + $ 115.
= $ (x + 115 + 115)
= $ (x + 230)
So in this way end of every week her salary will increase by $ 115.
Answer C
Question: Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 6 days?
A.2/5
B.1/6
C.1/3
D.1/9
Answer: C.1/3
Explanation: A's one day's work = 1/30
B's one day's work = 1/45
(A + B)'s one day's work = 1/30 + 1/45 = 1/18
The part of the work completed in 6 days = 6 (1/18) = 1/3.
ANSWER C
Question: In 130 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
A.20 m
B.25 m
C.22.5 m
D.26 m
Answer: D.26 m
Explanation: Distance covered by B in 9 sec. =	130/45 x 9	m = 26 m.
A beats B by 26 metres.
Answer: Option D
Question: The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $700 per sq. metre.
A.$12537.50
B.$13537.50
C.$14437.50
D.$16437.50
Answer: C.$14437.50
Explanation: C
Area =5.5×3.75 sq. metre.
Cost for 1 sq. metre. = $700
Hence, total cost
=5.5×3.75×700= $14437.50
Question: A bucket contains 2 mixtures A and B in the ratio 3:2. If 5 liters of the mixture is replaced by 5 liters of liquid B, then the ratio of the two liquids becomes 3:5. How much of the liquid A was there in the bucket?
A.8liters
B.10liters
C.12liters
D.15liters
Answer: A.8liters
Explanation: 1st ratio = 3:2
2nd ratio = 3:5
Difference of cross products ratio = 3*5-3*2 = 9
common factor of the 1st ratio
= (quantity replaced/sum of terms in 1st ratio) + (Quantity replaced*term A in 2nd ratio/Difference)
= (5/5) + (5*3/9) = 1+5/3 = 2.67
Quantity of A = 3*2.67 = 8liters approximately
Answer is A
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 900 grams per kg, what is his percent?
A.11
B.25
C.77
D.88
Answer: A.11
Explanation: 900 --- 100
100 --- ? => 11%
Answer:A
Question: 3, 4.5, 6.75, 10.13, 15.18, (...)
A.60
B.60.75
C.22.78
D.32.52
Answer: C.22.78
Explanation: 3
(3Ã—3)Ã· 2 = 4.5
(4.5Ã—3)Ã· 2 = 6.75
(6.75Ã—3)Ã· 2 = 10.13
(10.18Ã—3)Ã· 2 = 15.18
(15.18Ã—3)Ã· 2 = 60.75
Answer is C
Question: Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards.
What is the probability that first two cards are queens and the third card drawn is an ace?
A.1/2324
B.2/13235
C.2/5525
D.5525/2
Answer: C.2/5525
Explanation: Let Q denote the event that the card drawn is queen and A be the event that
the card drawn is an ace. Clearly, we have to find P (QQA)
Now P(Q) = 4/52
Also, P (Q|Q) is the probability of second queen with the condition that one queen has
already been drawn. Now there are three queen in (52 - 1) = 51 cards.
Therefore P(Q|Q) = 3/51
P(A|QQ) is the probability of third drawn card to be an ace, with the condition
that two queens have already been drawn. Now there are four aces in left 50 cards.
Therefore P(A|QQ) = 4/50
By multiplication law of probability, we have
P(QQA) = P(Q) P(Q|Q) P(A|QQ)
= 4/52 × 3/51 × 4/50
= 2/5525.
C
Question: To be considered grade AE, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AE eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AE eggs are used, the shells are all discarded, and no mass is lost in the cooking process?
A.800
B.840
C.864
D.900
Answer: B.840
Explanation: We're asked for the smallest possible mass, so what could the lowest mass be per egg AE? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is B.
Question: A 300 metre long train crosses a platform in 39 seconds while it crosses a post in 18 seconds. What is the length of the platform?
A.150 metre
B.380 metre
C.350 metre
D.200 metre
Answer: C.350 metre
Explanation: Speed of the train =300/18 m/s=50/3 m/s
Distance covered in 39 seconds=39 Ã— 50/3 =650 metre
Length of the train =650-300=350 metre
ANSWER: C
Question: The price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980. If its price of $1.30 in 1970 was 150 percent of its price in 1960, what was its price in 1980?
A.a) $ 1.80
B.b) $ 1.95
C.c) $ 2.40
D.d) $ 2.70
Answer: B.b) $ 1.95
Explanation: The price in 1970 was 150 percent of its price in 1960, means that the percent increase was 50% from 1960 to 1970 (and from 1970 to 1980).
Therefore the price in 1980 = $1.3*1.5 = $1.95.
Answer: B.