RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Three pipes of same capacity can fill a tank in 8 hours. If there are only two pipes of same capacity, the tank can be filled in.
A.11 hours
B.12 hours
C.15 hours
D.16 hours
Answer: B.12 hours
Explanation: The part of the tank filled by three pipes in one hour = 1/8
=> The part of the tank filled by two pipes in 1 hour = 2/3 * 1/8 = 1/12.
The tank can be filled in 12 hours.
Answer: B
Question: ?% of 360 = 126
A.277
B.35
C.64
D.72
Answer: B.35
Explanation: ?% of 360 = 126
or, ? = 126×100/360=35
Answer B
Question: A man drive his car to the office at 20miles/hr.
After reaching office, he realize that its a new year holiday so he went back home at a speed of 30miles/hr.
Discounting the time spent in the stoppage what was his average speed of his journey ?
A.23miles/hr
B.24miles/hr
C.25miles/hr
D.26miles/hr
Answer: B.24miles/hr
Explanation: Solution:
24miles/hr (not 25miles/hr which might be guessed by many)
D : distance traveled
T1 : time of going to office
T2 : time of returning back
Y : Average Speed
D = 20 * T1
T1 = D/20
D = 30 * T2
T2 = D/30
2D = Y(T2 + T1)
2D = Y(D/20 + D/30)
2D = Y(3D/60 + 2D/60)
2D = Y(5D/60)
Y = 120D/5D
=> Y = 24
Answer B
Question: Each person in a group of 110 investors has investments in either equities or securities or both. Exactly 25 of the investors in equities have investments in securities, and exactly 40 of the investors in securities have investments in equities. How many have investments in equities?
A.65
B.80
C.120
D.180
Answer: B.80
Explanation: Explanation :
The investors can be categorized into three groups:
(1) Those who have investments in equities only.
(2) Those who have investments in securities only.
(3) Those who have investments in both equities and securities.
Let x, y, and z denote the number of people in the respective categories. Since the total number of investors is 110, we have :-
=>x+y+z=110 ------------- (1).
Also,
The number of people with investments in equities is x+z and
The number of people with investments in securities is y+z.
Since exactly 25% of the investors in equities have investments in securities, we have the equation
=>(25/100)×(x+z)=z.
=>(25/100)×x=75z/100.
=>x=3z. -------------- (2)
Since exactly 40% of the investors in securities have investments in equities, we have the equation
=>(40/100)×(y+z)=z.
=>(y+z)=5z/2.
=>y=3z/2. -----------------(3)
Substituting equations (2) and (3) into equation (1) gives:-
=>3z+(3z/2)+z=110.
=>11z/2=110.
=>z=110×2/11=20.
Hence, the number of people with investments in equities is:
=>x+z=3z+z=3×20+20=60+20= 80.
Answer : B
Question: If the price of an article went up by 50%, then by what percent should it be brought down to bring it back to its original price?
A.16 2/3%
B.16 4/3%
C.33 1/3%
D.16 6/3%
Answer: C.33 1/3%
Explanation: Let the price of the article be Rs. 100.
50% of 100 = 50.
New price
= 100 + 50 = Rs. 150
Required percentage
= (150 - 100)/150 * 100
= 50/150 * 100
= 100/3
= 33 1/3%.
Answer:C
Question: A bus takes 3 hours to cover a distance of 500 Km. how much should the speed in Kmph be maintained to cover the same direction in 5/3th of the previous time?
A.75 Kmph
B.100 Kmph
C.90 Kmph
D.65 Kmph
Answer: B.100 Kmph
Explanation: Time = 3
Distance = 500
5/3 of 3 hours = 3 * 5/3 = 5 Hours
Required speed = 500/5 = 100 Kmph
B
Question: Two trains having equal lengths, take 10 seconds and 15 seconds respectively to cross a post. If the length of each train is 120 meters, in what time (in seconds) will they cross each other when traveling in opposite direction?
A.10
B.11
C.12
D.13
Answer: C.12
Explanation: speed of train1 = 120/10 = 12 m/s
speed of train2 = 120/15 = 8 m/s
if they travel in opposite direction, relative speed = 12+8 = 20 m/s
distance covered = 120+120 = 240 m
time = distance/speed = 240/20 = 12 s
Answer is C.
Question: An ore contains 25% of an alloy that has 90% iron. Other than this, in remaining 75% of the ore ,there is no iron. How many kgs of the ore are needed to obtain 60 kg. of pure iron.?
A.266.69
B.266.67
C.266.66
D.263.66
Answer: D.263.66
Explanation: Explanation:
Let us take 100x kgs of ore. Now it contains 25x kgs of alloy and it contains 90% (25x) kgs of iron.
90% (25x) = 60 kg ⇒ x = 60×10090×12560×10090×125 = 8383
So iron ore required = 100 × 8383 = 266.66
Answer: D
Question: The mean of a data set is equal to 10 and its standard deviation is equal to 1. If we add 5 to each data value, then the mean and standard deviation become
A.mean = 15 , standard deviation = 6
B.mean = 10 , standard deviation = 6
C.mean = 15 , standard deviation = 1
D.mean = 10 , standard deviation = 1
Answer: C.mean = 15 , standard deviation = 1
Explanation: Solution
Since 5 is added to all data values, the mean will also increase by 5 and becomes 15. But the standard deviation which measure the "distance" between the mean and the data values does not change.
Answer C
Question: A room of 5 m 44 cm long and 3 m 74 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
A.136
B.146
C.166
D.176
Answer: D.176
Explanation: area of the room = 544 * 374 sq cm
size of largest square tile = H.C.F of 544 cm and 374 cm= 34 cm
area of 1 tile = 34*34 sq cm
no. of tiles required = (544*374) / (34 * 34) = 176
answer :D
Question: Sandeep's age after six years will be three-seventh of his father's age. Ten years ago the ratio of their ages was 1:5. What is Sandeep's father's age at present?
A.50
B.40
C.30
D.60
Answer: A.50
Explanation: Let the age of Sandeep and his father before 10 years be x and 5x respectively.
Given that Sandeep's age after six years will be three-seventh of his father's age
⇒x+16=37(5x+16)⇒7x+112=15x+48⇒8x=64⇒x=8
Sandeep's father's present age
=5x+10=5×8+10=50
Answer is A.
Question: The final exam of a particular class makes up 40% of the final grade, and Moe is failing the class with an average (arithmetic mean) of 45% just before taking the final exam. What grade does Moe need on his final exam in order to receive the passing grade average of 60% for the class?
A.75%
B.82.5%
C.85%
D.90%
Answer: B.82.5%
Explanation: Lets Assume that total marks are 100.
Final exam weightage : 40
Rest of the exams : 60
Percentage scored by Moe out of 60 = 45%
Hence, Total marks obtained out of 60 = 45% of 60 = 27
Marks required in the final exam to get 60% in end = 60(marks) - 27 = 33 marks
i.e. 33 marks required out of 40 = 82.5 marks required out of 100 in final exam
ANS: 82.5 % (B)
Question: The U.S. Defense Department has decided that the Pentagon is an obsolete building and that it must be replaced with an upgraded version: the Hexagon. The Secretary of Defense wants a building that is exactly 70 feet high and 200 feet on a side, and that has a hexagonal bull's-eye cutout in the center (somewhat like the current one) that is 45 feet on a side. What will be the volume of the new building in cubic feet?
A.3,937,500 cubic feet
B.15,750 cubic feet
C.6,906,336 cubic feet
D.15,750√3 cubic feet
Answer: C.6,906,336 cubic feet
Explanation: Volume of the Hexagon with side 200 and height 70 = Area * height
= 6*(sqrt(3)/4)(200^2)(70)
Volume of the center bull's eye that is similar in shape of a hexagon but side 45
= 6 * (sqrt(3)/4)(45^2)*70
Volume of the building = 6*(sqrt(3)/4)(200^2)(70) - 6 * (sqrt(3)/4)(45^2)*70=6,906,336
Answer is C
Question: -64*29+468=?
A.1430
B.1302
C.-2801
D.-1388
Answer: D.-1388
Explanation: => -64*(30-1)+468;
=> -(64*30)+64+468;
=> -1920+532=-1388.
Correct Option: D
Question: If a man walks to his office at ¾ of his usual rate, he reaches office 1/3 of an hour late than usual. What is his usual time to reach office?
A.1 hour
B.4 hour
C.2 hour
D.7 hour
Answer: A.1 hour
Explanation: Speed Ratio = 1:3/4 = 4:3
Time Ratio = 3:4
1 -------- 1/3
3 --------- ? è 1 hour
Answer: A
Question: On Saturday, Will ran 15 miles. Morgan ran 60% of the distance Will ran. Jackie ran 1/3 more distance than Morgan did, and Denilo ran 1 less mile than Jackie. How many miles did Denilo run?
A.12
B.13
C.11
D.15
Answer: C.11
Explanation: C
11
Will ran 15 miles.
Morgan ran 60% of the distance that Will did.
Morgan= 15 x .6
=9
Jackie ran 1/3 more distance than Morgan.
Morgan = 9 + (9 x 1/3)
= 9 + 3
= 12
Denilo ran one less mile than Jackie.
Denilo= 12-1
=11
Denilo ran 11 miles.
The correct answer is C.
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
A.66 Kmph
B.68 Kmph
C.88 Kmph
D.55 Kmph
Answer: B.68 Kmph
Explanation: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer: B
Question: How high shall you count before you make use of the letter A?
A.1000
B.1200
C.1120
D.1800
Answer: A.1000
Explanation: A
1000
Question: Calculate how many seconds it will take for 4 bells to toll together again, given that they begin to toll together respectively at the intervals of 9, 12, 15 and 18 seconds?
A.186
B.130
C.180
D.181
Answer: C.180
Explanation: LCM of 9, 12, 15 and 18 is
180
LCM=180
ANSWER:C
Question: A shopping mall give 40% sale on T-shirts and increase 25% price of pants. The cost price of pants and T-shirts are 1500 and 400 respectively. Overall they makes a?
A.200
B.250
C.300
D.215
Answer: D.215
Explanation: Let the SP of the pants and T-shirts be Rs. p and Rs. t respectively.
p = 1500(1 + 25/100) = 1500 + 375
t = 400(1 - 40/100) = 400 - 160
Total SP - Total CP = p + t - (1500 + 400) = 375 - 160 = Rs. 215
As this is positive, an overall profit of Rs. 500 was made.
Answer: D
Question: Find the odd man out
1, 3, 7, 11, 15, 18, 21
A.3
B.7
C.18
D.21
Answer: C.18
Explanation: The 18 is the only even number in the series.
ANSWER:C
Question: Six friends go to see a comedy at the local movie theater and sit in a particular row together. If Grady and Howard are among those 6 friends but can never sit next to each other, how many 6-person seating arrangements are possible?
A.360
B.420
C.480
D.600
Answer: C.480
Explanation: Ways to arrange 6 people in a row = 6! = 720
From this we want to subtract all the arrangements where Grady and Howard are next to each other. If we consider Grady and Howard one unit (GH), then the number of arrangements of the GH unit and the 4 other friends is 5! And the number of arrangements of G and H within the GH unit are 2 (GH or HG). So the total number of arrangements of the 6 friends with Grady and Howard together are 5!*2
Number of permutations where Grady and Howard are not seated next to each other = 6! - 5!*2 = 720-120*2 = 480
Answer: C
Question: A boat can travel with a speed of 42 km/hr in still water. If the speed of the stream is 10 km/hr, find the time taken by the boat to go 70 km downstream
A.1 hour 40 min
B.2 hour 40 min
C.1 hour 21 min
D.1 hour 30 min
Answer: C.1 hour 21 min
Explanation: Speed of the boat in still water = 42 km/hr
speed of the stream = 10 km/hr
Speed downstream = (42+10) = 52 km/hr
Distance travelled downstream = 70 km
Time taken =distance/speed
=70/52
= 1.35 hours
= 1 hour 21 min.
ANSWER:C
Question: A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:
A.15 days
B.20 days
C.25 days
D.30 days
Answer: C.25 days
Explanation: Explanation:
(A + B)'s 1 day's work =1/10
C's 1 day's work =1/50
(A + B + C)'s 1 day's work =1/10+1/50=6/50=3/25.. (i)
A's 1 day's work = (B + C)'s 1 day's work .... (ii)
From (i) and (ii), we get: 2 x (A's 1 day's work) =3/25
A's 1 day's work =	3/50
B's 1 day's work=1/10-3/50=2/50=1/25
So, B alone could do the work in 25 days.
ANSWER IS C
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
A.10 sec
B.20 sec
C.15 sec
D.40 sec
Answer: D.40 sec
Explanation: speed = 45*6/18 = 25/2
tot dist = 360+140 = 500
time = d/s
=500*2/25 = 40 sec
ANSWER D
Question: Helen went to the stationers and bought things worth Euro 40, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
A.Euro 15
B.Euro 15.7
C.Euro 19.7
D.Euro 34.7
Answer: D.Euro 34.7
Explanation: Explanation: Let the amount taxable purchases be Euro x.
Then, 6% of x = 30/100
x = (30/100 x 100/6) = 5.
Cost of tax free items = Euro [40 - (5 + 0.30)] = Euro 34.70
Answer: Option D
Question: city A to city B, Andrew drove for 1 hour at 50 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
A.56
B.57.5
C.58
D.58.13
Answer: B.57.5
Explanation: The total distance is 1×50+3×60=2301×50+3×60=230. And the total time is 4 hours. Hence,
Average Speed=(Total DistanceTotal Time)=2304=57.5
B
Question: If w, x, and y are consecutive odd positive integers and w < x < y, which of the following could be equal to w - x - y ?
A.-7
B.-2
C.-1
D.0
Answer: A.-7
Explanation: Since W, X and Y are CONSECUTIVE ODD POSITIVE INTEGERS and W < X < Y, we can start with the easiest set of values that comes to mind:
W = 1
X = 3
Y = 5
The question asks for what COULD be the value of W - X - Y.
In this case, the value would be...
1 - 3 - 5 = -7
-7 IS among the answer choices, so we're done.
A
Question: Two cars start from the opposite places of a main road, 150 km apart. First car runs for 25 km and takes a right turn and then runs 15 km. It then turns left and then runs for another 25 km and then takes the direction back to reach the main road. In the mean time, due to minor break down the other car has run only 35 km along the main road. What would be the distance between two cars at this point?
A.65
B.38
C.20
D.28
Answer: A.65
Explanation: Answer: A) 65 km
Question: Stock / Number of shares
V ------------ 68
W ---------- 112
X ------------ 56
Y ------------ 94
Z ------------ 45
The table shows the number of shares of each of the 5 stocks owned by Mr Sami. If Mr. Sami was to sell 20 shares of Stock X and buy 23 shares of stock Y, what would be the increase in the range of the numbers of shares of the 5 stocks owned by Mr. Sami?
A.4
B.6
C.9
D.14
Answer: D.14
Explanation: Based on the original number of shares, the range would be: 112 - 45 = 67
However, the prompt tells us that two of the values in the table are going to change. After the changes, the values will be:
V 68
W 112
X 36
Y 117
Z 45
Now the range is 117 - 36 = 81
The INCREASE in the range requires us to compare thenewrange to theoldrange: 81 - 67 = 14
D
Question: A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many apples F did each person get before 45 people joined the feast?
A.20.
B.21.
C.22.
D.23.
Answer: C.22.
Explanation: Before solving it algebraically, let us prime factorize 1430 = 2*5*11*13.
Since number of apples per person * total persons F= 1430, the answer should be a factor of 1430. Only C is. And that's your answer.C
Question: If X,Y is 22%,30% smaller than Z then how much percentage is Y greater than X?
A.10 10/39%
B.13%
C.13 1/2%
D.14%
Answer: A.10 10/39%
Explanation: X = 78 %
Y = 70 %
Z = 100 %
X-Y/X × 100 = 8/78 × 100 = 10 10/39% greater than X
A)
Question: A merchant purchased a jacket for $150 and then determined a selling price that equaled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?
A.$0
B.$3
C.$4
D.$10
Answer: D.$10
Explanation: Let selling price = x
So, x = 150 + 25x/100
Calculating above, x = 200
Selling price =200
20% Discount on Selling price = 160
So, profit = 160-150 = 10 Answer = D
Question: There are 200 female managers in a certain company. Find the total number Y of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers.
A.300
B.Y=400
C.Y=500
D.Y=600
Answer: C.Y=500
Explanation: {Managers} = {Female Managers} + {Male Managers};
We are told that the total number of managers in the company is 2/5 of all the employees , thus{Managers} = 2/5 (M + F), where M and F are number of female and male employees, respectively.
Also, we know that 2/5 of all male employees are managers:{Male Managers} = 2/5 * Mas well as there are total of 200 female managers:{Female Managers} = 200;
Thus:2/5 (M + F) = 200 + 2/5 * M-->F = 500.
Answer: C.
Question: The number of meters in MB is equal to the square root of the number of centimeters in MB. What is the length of MB (1 meter=100 centimeters)?
A.100 meters
B.10 meters
C.100 centimeters
D.10 centimeter
Answer: A.100 meters
Explanation: I'd plug in the options for this question.
Check option A: if the number of meters in MB is 100, then the number of centimeters is 100*100. The square root of 100*100 is 100: 100 = 100.
Answer: A.
Question: On a summer camp, 25% of the campers paid $100 each, 35% paid $80 each and the rest paid $65 each. What percentage of the total amount paid came from the campers who paid $80?
A.18%
B.21%
C.26%
D.35.44%
Answer: D.35.44%
Explanation: let the total no of campers be 100
total amount = (25*100)+(35*80)+(40*65) = 2500+2800+2600= $7900
required percentage = (28/79)*100 = 400/12 = 100/3 =35.44%
D
Question: The average of 6 no.'s is 4.60. The average of 2 of them is 3.4, while the average of the other 2 is 3.8. What is the average of the remaining 2 no's?
A.2.3
B.6.6
C.3.6
D.4.5
Answer: B.6.6
Explanation: Sum of the remaining two numbers = (4.6 * 6) - [(3.4 * 2) + (3.8 * 2)]
= 27.60 - (6.8 + 7.6) = 27.60 - 14.40 = 13.20.
Required average = (13.2 / 2) = 6.6.
Answer : B
Question: A and B together can do a work in 6 days. If A alone can do it in 10 days. In how many days can B alone do it?
A.10
B.15
C.77
D.55
Answer: B.15
Explanation: 1/6 – 1/10 = 1/15
=> 15
Answer: B
Question: A = {1, 2, 3} and B = {4, 5, 6}.Find A-B
A.{2,8,4}
B.{1,3,5}
C.{1,2,3}
D.{5,10,15}
Answer: C.{1,2,3}
Explanation: A = {1, 2, 3}
B = {4, 5, 6}
correct answer :A - B = {1, 2, 3}
C
Question: Every disk in a bag is either blue, yellow or green. The ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8. If the total number of disks in the bag is 108, how many more green disks than blue disks are in the bag?
A.25
B.28
C.30
D.35
Answer: C.30
Explanation: Let B:Y:G = 3x:7x:8x.
3x + 7x + 8x = 18x = 108 --> x= 6.
G - B = 8x - 3x = 5x = 30.
The answer is C.
Question: How many meters are there in 220 centimeters?
A.220 meters
B.20 meters
C.22 meters
D.2.2 meters
Answer: D.2.2 meters
Explanation: Solution:
1 meter = 100 centimeters
Just divide 220 by 100
550 Ã· 100 = 2.2, so there are 2.2 meters in 220 centimeters
Option D
Question: Frances can complete a job in 16 hours, and Joan can complete the same job in 8 hours. Frances starts the job at 9 a.m., and stops working at 3 p.m. If Joan starts working at 4 p.m. to complete the job, at what time is the job finished?
A.9 p.m.
B.7 p.m.
C.8 p.m.
D.10 p.m.
Answer: A.9 p.m.
Explanation: Let the total work be 24 units.
Frances can complete 1.5 units/hr
Joan can complete 3 units/hr
Work done by Frances in 6 hours is 9 units ; work left for Joan is 15 units ( 24 - 9)
Time required by Jones to complete the remaining work will be 15/3 => 5 hours
Given Jones starts at 4PM , so she would complete the work at 9 PM
Answer will be (A)
Question: A owes B Rs.50. He agrees to pay B over a number of consecutive days on a Monday, paying single note or Rs.10 or Rs.20 on each day. In how many different ways can A repay B.
A.2
B.8
C.9
D.6
Answer: B.8
Explanation: He can pay by all 10 rupee notes = 1 way
3 Ten rupee + 1 twenty rupee = 4!3!×1!4!3!×1! = 4 ways
1 Ten rupee + 2 twenty rupee notes = 3!2!×1!3!2!×1! = 3 ways
Total ways = 1 + 4 + 3 = 8
Answer:B
Question: Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability Q that private Benjamin will be chosen for latrine duty?
A.1/10
B.1/5
C.2/5
D.3/5
Answer: C.2/5
Explanation: Easier way : Desired probability = 1- 'excluded' probability
In this case, Excluded probability = probability of Benjamin not being a part of the 4 volunteers. We can choose 4 out of 9 remaining soldiers in 9C4 ways. total ways possible = 10C4.
Thus excluded probability = 9C4/10C4 = 3/5
Thus, the desired probability Q= 1- 3/5 = 2/5. Thus C is the correct answer.
Question: A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?
A.30000
B.20000
C.23000
D.21020
Answer: B.20000
Explanation: Explanation:
Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50
The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50
Total SP = 11x/50 + 38x/50 = 49x/50
Overall loss = x - 49x/50 = x/50
x/50 = 400 => x = 20000
Answer: B
Question: For a certain set, the value range of its members is 108.4. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set?
A.24.1
B.27.1
C.54.4
D.98.4
Answer: B.27.1
Explanation: Let x and z be the smallest and largest of the original set, respectively.
z - x = 108.4
The smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4.
Then the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 108.4 / 4 = 27.1
The answer is B.
Question: A present value of a machine is $1000. Its value depletiation rate is 10% per annum then find the machine value after 2 years?
A.$900
B.$810
C.$915
D.$715
Answer: B.$810
Explanation: P= $1000
R = 10%
T = 2 years
Machine value after 2 years = P[(1-R/100)^T]
=1000*9/10 * 9/10
=$810
Answer is B
Question: Month Noah Landing Bellaville
1 3 2
2 2 0
3 0 4
4 2 X
5 1 1
Monthly rainfall was recorded for two towns over a five-month period using the chart above. If the median rainfall in Noah’s Landing was equal to the average (arithmetic mean) rainfall in Bellaville, what is the value of x?
A.1
B.8/5
C.2
D.3
Answer: D.3
Explanation: Arrange Noah's landing rainfall in order which is 0,1,2,2,3 and hence median is 2
Given median of Noah's landing = AM of Bellaville
So 5 * 2 is the sum of all values,
to find x , 10 = 1 + 2+ 4 + x
gives x = 3 ,
Answer is D
Question: If a natural number p has 8 factors, then which of the following cannot be the difference between the number of factors of p^3 and p?
A.14
B.30
C.32
D.56
Answer: B.30
Explanation: p has 8 factors. That gives following possibilities:
a) p has one prime factor with power 7
=> p^3 will have 22 factors. Difference with number of factors of p = 22-8 = 14: A is ok
b) p has two prime factors with powers 3 and 1
=> p^3 will have 40 factors. Difference with number of factors of p =40-8 = 32 : C is ok
c) p has three prime factors with powers 1 each
=> p^3 will have 64 factors. Difference with number of factors of p=64-8 = 56 : D is ok
There are no other possibilities. Hence remaining answer choice B is not possible.
Answer B
Question: If t is an even integer and q is an odd integer, which of the following must be an odd integer?
A.t/q
B.tq
C.2t+q
D.2(t+q)
Answer: C.2t+q
Explanation: this is a must question:
A. t/q
can be a non-integer
B. tq
always even
C. 2t+q
2t = even -> even+odd = odd
D. 2(t+q)
always even - t+q = odd *2 -> even
E. 3t/q
might be a non integer.
C
Question: On a game show, a contestant spins three different wheels; each wheel is numbered 1 to 12. What is the probability that the contestant will spin all tens?
A.52
B.1/1728
C.67
D.2/58
Answer: B.1/1728
Explanation: All 12s:
1st wheel = 12= 1/12
2nd wheel = 12 = 1/12
3rd wheel = 12 = 1/12
(1/12)(1/12)(1/12) = 1/1728
Answer: B
Question: Find the value of * in the following
(1 5/3) ÷ 3/11 × */11 = (2 2/3 × 7/5 × 6/7)
A.1
B.1.5
C.3.6
D.4
Answer: C.3.6
Explanation: Option 'C'