RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In a normal 5-day work week, each of 12 employees produces 300 items per day-last week, 1/3 of the employees were absent from work for 2/5 of the days in the week. how many total items were produced last week?
A.18000
B.14400
C.6000
D.15600
Answer: D.15600
Explanation: 1 employee produces 300 items per day
1/3 of the employees were absent for 2/5 days of last week.
==> 4 employees were absent for 2 days.
Items produced by them in 3 days
= 300*3*4
=3600
Items produced by other employees
=8*5*300
=12000
Total items produced = 12000+3600
=15600
ANSWER:D
Question: A small company employs 3 men and 5 women. If a team of 3 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 men?
A. 5/7
B. 1/7
C. 2/7
D. 3/7
Answer: A. 5/7
Explanation: Total ways to choose 4 employees from 8 employees = 8C3
Two men = 5C2
Two women = 3C1
P = (5C2 * 3C1)/8C2 = 5/7 hence A.
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is
A.11
B.12
C.13
D.14
Answer: A.11
Explanation: Explanation:
Age of the 15th student = [15 * 15 - (14 * 5 + 16 * 9)] = (225-214) = 11 years. Answer: A
Question: If f is a number such that –2 ≤ f ≤ 2, which of the following has the largest possible absolute value?
A.3f – 1
B.x^2 + 1
C.3 – x
D.x – 3
Answer: A.3f – 1
Explanation: Ans is A .. leads to the max value of 7 for f = -2
Question: In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
A.24
B.35
C.13
D.61
Answer: B.35
Explanation: The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.
Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.
Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.
Therefore, the total number of ways the 5 letters can be posted in 3 boxes is
3 * 3 * 3 * 3 * 3 = 35
Ans: B
Question: The length of an edge of a hollow cube open at one face is √3 metres. What is the length of the largest pole that it can accommodate?
A.2 metres
B.3 metres
C.4 metres
D.3√3metres
Answer: B.3 metres
Explanation: Solution
Required length	= Diagonal
‹=›√3 a
‹=›(√3×√3) m
‹=›3 m.
Answer B
Question: The volume of cube is equal to the surface area of that cube. Then find the distance of side of the cube?
A.7
B.10
C.4
D.6
Answer: D.6
Explanation: Cube volume = a(power)3 cubic units
Surface area = 6 a(power)2 sq.units
a(power)3 = 6 a(power)2
a = 6 m
Answer is D.
Question: The cost price of 40 articles is the same as the selling price of x articles. If the profit is 25%, what is x?
A.26
B.28
C.30
D.32
Answer: D.32
Explanation: Let the cost price = y
The cost price of 40 articles = 40y
The selling price of x articles = 1.25y*x
1.25y*x = 40y
x = 40 / 1.25 = 32
The answer is D.
Question: How long does a train 120 m long running at the speed of 70 km/hr takes to cross a bridge 145 m length?
A.13.9 sec
B.12.1 sec
C.17.9 sec
D.13.9 sec
Answer: D.13.9 sec
Explanation: Speed = 70 * 5/18 = 19 m/sec
Total distance covered = 120 + 145 = 265 m.
Required time = 265/19 = 13.9 sec.
Answer:D
Question: A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?
A.11
B.45
C.66
D.72
Answer: B.45
Explanation: Let the distance to be travelled to catch the bus be x km
x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km
By traavelling 30 kmph time taken = 60/30 = 2 hours
By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph.
Answer: B
Question: Which of the following is NOT a factor of 10! ?
A.1440
B.625
C.160
D.80
Answer: B.625
Explanation: 625=5*5*5*5 and we dont have four 5 in 10! answer is B
Question: If population of certain city increases at the rate of 5%. If population in 1981 was 138915, then population in 1978 was?
A.1,20,000
B.1,20,080
C.1,20,900
D.1,29,000
Answer: A.1,20,000
Explanation: X * (105/100) * (105/100) * (105/100) = 138915
X = 138915/1.157625
X = 120000
Answer:A
Question: There are 28 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station?
A.800
B.820
C.850
D.870
Answer: D.870
Explanation: The total number of stations= 30
From 30 Stations we have to choose any two stations and the direction of travel (Ernakulam to Chennai is different from Chennai to Ernakulam) in 30P2 ways.
30P2= 30*29= 870
ANSWER:D
Question: The total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
A.75
B.267
C.299
D.266
Answer: A.75
Explanation: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.
P + C + M = 150 + P
C + M = 150
Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 150/2 = 75.Answer: A
Question: If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 240 responses are needed, what is the minimum number of questionnaires that should be mailed?
A.400
B.500
C.600
D.700
Answer: A.400
Explanation: Let x be the minimum number of questionnaires to be mailed.
0.6x = 240
x = 400
The answer is A.
Question: How many words can be formed by using all letters of the word 'PIG' ?
A.6
B.8
C.9
D.5
Answer: A.6
Explanation: The word PIG contains 3 different letters
Required number of words = 3P3 = 3! = 3*2*1 = 6
Answer is A
Question: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
A.132 km
B.167 km
C.143 km
D.162 kilometres
Answer: D.162 kilometres
Explanation: D
12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km.
Question: If x and y are integers such that |y + 3| ≤ 3 and 2y – 3x + 6 = 0, what is the least possible value R of the product xy?
A.	-12
B.	-3
C.	0
D.	2
Answer: C.	0
Explanation: How to deal with inequalities involving absolute values? First example shows us the so callednumber case
In this case we have |y + 3| ≤ 3 which is generalized |something| ≤ some number. First we solve as if there were no absolute value brackets:
y + 3 ≤ 3
y ≤ 0
So y is 0 or negative
Second scenario - remove the absolute value brackets. Put a negative sign around the other side of the inequality,ANDflip the sign:
y + 3 >= -3
y >= -6
Therefore we have a possible range for y: -6=<y<=0
Ok, so far so good, we're half way through. What about x?
Here's the formula: 2y – 3x + 6 = 0, rewrite it as 2y + 6 = 3x.
You can say that 2y + 6 is a multiple of 3 (=3x). So all values which must be integer must also satisfy this constraint. I'm just saying that, so it's easier to evaluate all the possible numbers (-6, -3, 0). If you plug in y = 0, x will be 2 and xy = 0 as the lowest possible value R.
Hence, Answer Choice C is the one to go.
Question: A cube is divided into 512 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that, the cube is painted with green on one set of opposite faces, red on another set of opposite faces, and blue on the third set of opposite faces. How many cubelets are painted with exactly one colour?
A.216
B.264
C.296
D.312
Answer: A.216
Explanation: Each face of the cube has 8 x 8 = 64 cubelets.
On each face, only the interior cubelets are painted one colour.
On each side, 6 x 6 = 36 cubelets are painted one colour.
Since the cube has six sides, the number of cubes with one colour is 6*36 = 216
The answer is A.
Question: John has $2500 in his bank account that earns 10% interest every year. How much will be in John's bank account after one year?
A.$2600
B.$3000
C.$2250
D.$2750
Answer: D.$2750
Explanation: Final number = Initial number + 20%(original number) = 2500 + 10%(2500) = 2500 + 250 = 2750.
Answer D
Question: Mary works in a restaurant a maximum of 45 hours. For the first 20 hours, she is paid $8 per hour. For each overtime hour, she is paid at a rate which is 25% higher than her regular rate. How much Mary can earn in a week?
A.300
B.420
C.410
D.320
Answer: C.410
Explanation: Mary receives $8(20)=$160 for the first 20 hours.
For the 25 overtime hours, she receives $8(0.25) +$8 = $10 per hour, that is $10(25)=$250.
The total amount is $160+$250 = $410
Answer C 410.
Question: What is the probability W of randomly selecting an arrangement of the letters of the wordMEDITERRANEANin which the first letter is E and the last letter is R?
A.1/13
B.1/20
C.1/26
D.1/50
Answer: C.1/26
Explanation: Why do you calculate the total combinations and everything, it is much easier to calculate as follows:
3/13 * 1 * 1 * 1 * 1 ..... * 2/12 = 6/156 = 1/26
This is because 3/13 = Probability that first letter will be E and 2/12 = probability that thefirstletter will be R. Between everything else cuts down to 1*1*1... e.g. probability W of the second letter is 11/11 = 1, > we do not care what's in between.C
Question: A sum of Rs 12,500 amounts to Rs. 15,500 in the 4 years at the rate of simple interest. Find the rate percent
A.6 %
B.7 %
C.8 %
D.9 %
Answer: A.6 %
Explanation: Explanation:
S.I.=P∗R∗T/100=>R=S.I.∗100/P∗T
So, S.I = 15500 - 12500 = 3000.
=>R=3000∗100/12500∗4=6%
Option A
Question: Chlorination is used in industry for the purification of water; 1gm solution of chlorine will remove half of the germs in 1 liter of water. If water containing less than 0.09% of germs is considered clean, what is the minimum amount of chlorine required to purify 150 liter of water containing 0.3 liter of harmful substances?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: Assuming that it's SUPPOSED to state "0.3" liters of harmful substances, here's how you can answer this question.
First, we have to figure out what .09% of 150 liters is...
1% = .01
.1% = .001
.09% = .0009
So, .0009(150) = .135 liters
We need enough doses of chlorine to get the 0.3 liters down to LESS than .135 liters. Each "dose" of chlorine will remove HALF of the harmful substances...
Start = 0.3 liters
After 1st dose = .15 liters
After 2nd dose = .075 liters
We're now below the .135 liters that we need to be less than.
Final Answer:B
Question: A luxury liner, Queen Marry II, is transporting several cats as well as the crew (sailors, a cook, and one-legged captain) to a nearby port. Altogether, these passengers have 14 heads and 41 legs. How many cats does the ship host?
A.5
B.6
C.7
D.8
Answer: C.7
Explanation: sa's +co +ca +cats = 14. sa's + 1 +1 +cats =14 or sa's +cats =12.
sa's(2) +2 +1 +cats*4 =41 sa's*2 +cats*4 = 38 or sa's +cats*2 =19 or 12-cats +cat*2 =19
then cats =7
C
Question: Two pipes A and B can fill a tank in 4 and 5 hours respectively. If they are turned up alternately for one hour each, the time taken to fill the tank is?
A.4 hrs 54 min
B.4 hrs 24 min
C.4 hrs 14 min
D.4 hrs 34 min
Answer: B.4 hrs 24 min
Explanation: 1/4 + 1/5 = 9/20
20/9 = 2 2/9
9/20 * 2 = 9/10 ---- 4 hours
WR = 1 - 9/10 = 1/10
1 h ---- 1/4
? ----- 1/10
2/5 * 60 = 24 = 4 hrs 24 min
Answer:B
Question: What is the lowest possible common multiple of 2 distinct integers, each greater than 140?
A.141
B.142
C.282
D.141*141
Answer: C.282
Explanation: The least common multiple of two numbers greater than 140 is 2(141) = 282, where the two distinct integers are 141 and 282.
The answer is C.
Question: if i earn a profit 50$ in a day and I have 9 employees . After keeping 10 percent profit for me, and distribute remianing money equally among my employees then how much each employee would get?
A.$3
B.$7
C.$1
D.$5
Answer: D.$5
Explanation: Since I earned $50 sp 10 percent would be 5$ and 45$ would remain. Dividing 45 by 9, each employee would get 5$ each and hince option D is correct.
Question: A box contains six bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
A.125/167
B.14/15
C.125/126
D.125/186
Answer: B.14/15
Explanation: Required probability
= 1 - 1/15
= 14/15
Answer: B
Question: One day a car rental agency rented 3/4 of its cars, including 3/5 of its cars with CD players. If 3/5 of its cars have CD players, what percent of the cars that were not rented had CD players?
A.29/30
B.24/25
C.19/20
D.14/15
Answer: B.24/25
Explanation: The cars with CD players which were not rented is (2/5)(3/5) = 6/25 of all the cars.
The cars which were not rented is 1/4 of all the cars.
The percent of non-rented cars which had CD players is (6/25) / (1/4) = 24/25
The answer is B.
Question: A sock drawer contains 6 socks, each one a different solid color. The colors of the socks are red, orange, yellow, green, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks?
A.12
B.15
C.21
D.36
Answer: B.15
Explanation: Since the order in which we select the socks does not matter, we can use combinations.
We can select 2 socks from 6 socks in 6C2 ways.
6C2 = 15
Answer : B
Question: Mrs. Napier has 23 stickers to give to 9 students for a reward. How many
stickers will each student get? Will there be any stickers left over?
A.2-5
B.2-4
C.2-6
D.2-3
Answer: A.2-5
Explanation: 23/9 = 2 R 5 Mrs. Napier will give each student 2 stickers and there
will be 5 left over.
correct answer A
Question: A rectangular garden is 12m by 5m, what is its area?
A.12 square meters
B.5 square meters
C.44 square meters
D.60 square meters
Answer: D.60 square meters
Explanation: Area of a Rectangle: A = w × h
D) 60 square meters
Question: How many ways are there to award a gold, silver and bronze medal to 11 contending teams?
A.11 x 10 × 9
B.10!/(3!7!)
C.10!/3!
D.360
Answer: A.11 x 10 × 9
Explanation: we clearly know that there can be only one winning team which deserves the gold medal. we can do the selection in 11 ways
if gold medal is given to 1 of the teams then only possible 10 teams can be considered for silver medal. we can do selection in 10 ways
similarly if gold and silver medals are awarded then only remaining 9 teams can be considered for a bronze medal. we can do the selection in 9 ways
Total number of ways to select the 3 possible medal winners = 11*10 * 9
Correct answer - A
Question: If the true discount on s sum due 2 years hence at 14% per annum be Rs. 140, the sum due is:
A.s. 768
B.s. 640
C.s. 1960
D.s. 2400
Answer: B.s. 640
Explanation: td=pw*r*t/100 so 140=pw*14*2/100 so pw=500
sum=pw+td..
sum=500+140=640
ANSWER:B
Question: Souju's age is 131% of what it was 10 years ago, but 80 2/3% of what it will be after 10 years. What is her present age?
A.46 years
B.27 years
C.36 years
D.42 years
Answer: D.42 years
Explanation: Let the age before 10 years =x. Then,
131x/100=x+10
â‡’131x=100x+1000
â‡’x=1000/31=32
Present age =x+10=32+10=42
ANSWER:D
Question: By selling 175 apples, a shopkeeper gains the price of 25 apples. His gain per cent is
A.18.66%
B.17.66%
C.16.66%
D.15.66%
Answer: C.16.66%
Explanation: Suppose S.P of 175 apples = Rs 175
Therefore, Gain = Rs 25 => C.P = Rs 150
Gain % = 25/150 x 100 = 16.66%
Gain = 16.66%
ANSWER:C
Question: Exactly 5% of the reporters for a certain wire service cover local politics in Country X. If 30% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics?
A. 20%
B. 42%
C. 44%
D. 92%
Answer: D. 92%
Explanation: You are correct. People who cover local politics are a subset of people who cover politics.
30% of reporters who cover politics do not cover local politics so 70% DO cover local politics.
Reporters covering local politics= 70% of reporters covering politics= 5% of all reporters
Reporters covering politics/All Reporters = 5/70 = 1/14
Reporters not covering politics/All Reporters = 13/14 = 92%=D
Question: If k is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 3, 6, and k?
A.0
B.1
C.2
D.3
Answer: D.3
Explanation: (6-3) < k < (6+3)
3 < k < 9
Thus k = 4, 5, 6, 7, 8
Since 2 < k < 7, then k can be 4, 5, or 6.
The answer is D.
Question: Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
A.40 days
B.40/9 days
C.39/9 days
D.30/9 days
Answer: B.40/9 days
Explanation: B
40/9 days
A's one hour work = 1/8.
B's one hour work = 1/10.
(A+B)'s one hour work = 1/8+1/10 = 9/40.
Both A & B can finish the work in 40/9 days
Question: A grocer has a sale of Rs. 4435, Rs. 4927, Rs. 4855, Rs. 5230 and Rs. 4562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 4500?
A.s. 1991
B.s. 2991
C.s. 3991
D.s. 4991
Answer: B.s. 2991
Explanation: Explanation:
Total sale for 5 months = Rs. (4435 + 4927 + 4855 + 5230 + 4562) = Rs. 24009.
Required sale = Rs. [ (4500 x 6) â€“ 24009 ]
= Rs. (27000 â€“ 24009)
= Rs. 2991.
Answer B
Question: A straight line in the xy-plane has a slope of 2 and a y-intercept of 2. On this line, what is the x-coordinate of the point whose y-coordinate is 480 ?
A.249
B.498
C.239
D.823
Answer: C.239
Explanation: slope of 2 and a y-intercept of 2
y-coordinate is 480
y = 2x + 2
478 = 2x
x = 239
Answer:
C. 239
Question: 3^4+3^4+3^4=?
A.a) 3^3
B.b) 3^4
C.c) 3^5
D.d) 3^6
Answer: C.c) 3^5
Explanation: The correct answer is C 3^5
3^5 = 3^4+3^4+3^4
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 8 kmph, what is the time taken to row a distance of 60 km downstream?
A.30/16 hours
B.80/13 hours
C.30/73 hours
D.15/7 hours
Answer: D.15/7 hours
Explanation: Speed downstream = 20 + 8 = 28 kmph.
Time required to cover 60 km downstream
= d/s = 60/28
= 15/7 hours.
Answer:D
Question: A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:
A.48 km/hr
B.54 km/hr
C.66 km/hr
D.82 km/hr
Answer: D.82 km/hr
Explanation: Explanation:
Let the speed of the second train be x km/hr.
Relative speed	= (x + 50) km/hr
=(x + 50) x 5/18 m/sec
=250 + 5x	/18 m/sec
Distance covered = (108 + 112) = 220 m.
220/ [(250+5x)	/18]=6
250 + 5x = 660
x = 82 km/hr.
ANSWER IS D
Question: A trained covered x km at 30 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
A.20kmph
B.22.5kmph
C.25kmph
D.30kmph
Answer: B.22.5kmph
Explanation: Total time taken = x/30 + 2x/20 hours
= 8x/60 = 2x/15 hours
Average speed = 3x/(2x/15)
= 22.5 kmph
Answer:B
Question: If each side of a square is increased by 25%, find the percentage change in its area.
A.26.5%
B.36.25%
C.46.25%
D.56.25%
Answer: D.56.25%
Explanation: Let each side of the square be a. Then, area = a2.
New side =(125a/100) =(5a/4). New area = (5a/4) 2=(25a2)/16.
Increase in area = ((25 a2)/16)-a2=(9a2)/16.
Increase% = [((9a2)/16)*(1/a2)*100] % = 56.25%.
ANSWER D 56.25%
Question: In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?
A.20
B.30
C.40
D.50
Answer: B.30
Explanation: Here given 120 men = 200 children
therefore 1 child = 3/5 of Man------ step I
Now given that the food was consumed by 150 children
From step I we get 150 children =90 Men ( 1 child = 3/5 Man ie , 150 X 3/5 = 90)
So the food is for (120-90) men = 30 Men
ANSWER:B
Question: A rectangular circuit board is designed to have a width of W inches, a length of L inches, a perimeter of P inches, and an area of D square inches. Which of the following equations must be true?
A.2W^2 + PW + 2D = 0
B.2W^2 − PW − 2D = 0
C.2W^2 − PW + 2D = 0
D.W^2 + PW + D = 0
Answer: C.2W^2 − PW + 2D = 0
Explanation: P = 2(L+W)-----------------1)
A= LW------------------------2)
option A is not possible why ?? because all the terms are positive.
lets try option B , put value of P and A from 1 and 2 we have,
2W^2-2(L+W)W + 2(LW)
2W^2 - 2LW - 2W^2 + 2LW=0.
hence answer is C.
Question: Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?
A.2888
B.2999
C.2799
D.1000
Answer: D.1000
Explanation: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 140
X = 1000
Answer: D
Question: When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?
A.√10/2
B.√10
C.4
D.5
Answer: B.√10
Explanation: V = pi(R^2)(H)
We have the Volume (22 cubic meters) and the Height (0.7 meters)...
22 = pi(R^2)(0.7)
pi = about 3.14
.7(pi) = about 2.2
22 = 2.2(R^2)
10 = R^2
\sqrt{10} = R
Final Answer:
B
Question: On a bright morning, Ashley and Cecilia decided to take out their old cars from the garage and check their speeds. Just to make things for interesting, they decided to race and find out whose car was fast. So they halted their car at the starting point and began with full throttle till the finish line.
When both the car crossed the finishing line, they realized that Ashley's car was 1.2 times faster than Cecelia. Also, Cecelia had reached the finishing line 1 minutes 30 seconds later than Ashley. Ashley's car had reached the finishing line at an average speed of 60 Km/h.
With all this data given, can you find out the total distance between the starting and the finishing lines?
A.6.5Km
B.8.5Km
C.7.4Km
D.7.5Km
Answer: D.7.5Km
Explanation: D
7.5Km
Explanation:
Denoting Ashley with A and Cecelia with C
Speed A = 60 km/hr = 1.2 x Speed C [km/hr] = 1 km/ min
Hence Speed C = 60/1.2 [km/hr] = 50 [km/hr] = 5/6 km/ min
Time C = D [km] /Speed C [km/min] = D/Speed C [min] = D/(5/6) min = 6D/5 min = 1.2 D min
Time A = D [km] /Speed A [km/min] = D/Speed A [min] = D/(1) min = D min
Since Time C � Time A = 1.5 min
Then (1.2 � 1)D min = 0.2D min = 1.5 min
Hence D = 1.5/0.2 km = 1.5*5 = 7.5 km
The total distance as calculated above is 7.5 Km.
Question: On a certain plane, 2/5 of the passengers speak French and 3/4 speak Hebrew. If all of the passengers on the plane speak at least one of these languages, what is the smallest number of passengers that could be on the plane?
A.12
B.15
C.40
D.54
Answer: C.40
Explanation: Assume the total members = x
French = .4x
Hebrew = .75x
French + Hebrew = 1.15x, but this is not possible hence 15 people speak both languages.
Only French = .25x, Only Hebrew = .6x, both = .15x
Since these are all people, all of these should be whole numbers.
Checking the options:
A. 12. Only Hebrew = 12*0.6 = 7.2 We do not get the people as whole numbers. INCORRECT
B. 15. Only French = 0.25*15 Again we do not get the people as whole numbers. INCORRECT
C. 40 Only Farsi = .25*40 = 10, Only Hebrew = .6*40 = 24, both = .15*40 = 6. We have the people as whole numbers. CORRECT
D. 54
E. 60
Since we have to find the lowest number, no need to calculate for the rest of the options.
Correct Option: C
Question: If there are 6 seats and 3 students, in how many ways can they be seated?
A.120
B.124
C.128
D.132
Answer: A.120
Explanation: The first student has 6 choices, the second student has 5 choices, and the third student has 4 choices. The number of ways to sit is 6*5*4 = 120.
The answer is A.
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 880 cm is?
A.A)15
B.B)10
C.C)14
D.D)12
Answer: B.B)10
Explanation: 2 * 22/7 * 14 * x = 880 => x = 10
ANSWER:B