RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $30,000?
A.$38,796.
B.$29,232.
C.$38,976.
D.$39,679.
Answer: B.$29,232.
Explanation: 30,000 *1.16*.84= Unit and tens digit of the expression is 6 and 7 respectively.
Only option B fulfills the condition and hence is the answer
Question: The ratio of two numbers is 4 : 5 and their H.C.F. is 4. Their L.C.M. is
A.48
B.22
C.56
D.80
Answer: D.80
Explanation: Explanation:
Let the numbers be 4x and 5x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 16 and 20.
L.C.M. of 16 and 20 = 80.
Option D
Question: If Ajay drives at 4/5th of his usual speed to his office, he is 6 minutes late. What is his usual time to reach his office?
A.36
B.24
C.30
D.18
Answer: B.24
Explanation: Explanation:
Let t be his usual time to reach his office and v be his usual speed.
v = d/t ……….(d is the distance Ajay travels while going to his office)
vt = d
At v1 = 4v/5 ; t1 = t + 6
4v/5 = d/(t + 6)
4v/5* (t + 6) = d
4v/5* (t + 6) = vt
On solving we get,
t = 24 minutes
ANSWER B
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?
A.150 meter
B.299 meter
C.666 meter
D.155 meter
Answer: A.150 meter
Explanation: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9
= 150 meter
Answer: A
Question: In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 155 m. Then, A wins by:
A.60 m
B.20m
C.40 m
D.20m
Answer: C.40 m
Explanation: To reach the winning post A will have to cover a distance of (500 - 155)m, i.e., 345 m.
While A covers 3 m, B covers 4 m.
While A covers 345 m, B covers 4 x 345/3	m	= 460 m.
Thus, when A reaches the winning post, B covers 460 m and therefore remains 40 m behind.
A wins by 40 m.
Answer:	C
Question: A city council will select 2 of 9 available firefighters and 1 of 5 available police officers to serve on an advisory panel. How many different groups of 3 could serve on the panel?
A.36
B.72
C.144
D.180
Answer: D.180
Explanation: OA D
9C2 * 5C1
using the combination formula to choose 2 from 9 and 1 from 5
D
Question: A train passes a station platform in 35 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
A.228
B.240
C.225
D.166
Answer: C.225
Explanation: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/35 = 15 => x = 225 m.
Answer: C
Question: Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
A.5.9%
B.5.6%
C.5.6%
D.9.6%
Answer: C.5.6%
Explanation: C.P. of 1 toy = 375/12 = Rs. 31.25
S.P of 1 toy = Rs. 33
Profit = 1.75/31.25 * 100 = 28/5 = 5.6%
Answer: C
Question: City A and City B are 140 miles apart. Train C departs City A, heading towards City B, at 4:00 and travels at 40 miles per hour. Train D departs City B, heading towards City A, at 4:35 and travels at 20 miles per hour. The trains travel on parallel tracks. At what time do the two trains meet?
A.5:00
B.5:30
C.6:00
D.6:35
Answer: D.6:35
Explanation: Train C has traveled 20 mi in the half hour before Train D has started its journey.
140-20=120
40+20 =60 mph
120 mi/ 60 mph = 2 hrs
4:35pm + 2 hrs = 6:35pm
Answer:
D. 6:35
Question: If a: b :: 3 : 7, then what is (5a+2b): (a-2b)?
A.57:11
B.-57:11
C.11 : 10
D.-29 : 11
Answer: D.-29 : 11
Explanation: a/b= 3/7
Dividing numerator & denominator of ' (5a+6b)/(a-2b) 'by b,
[5(a/b)+2]/[(a/b)-2]= [5*(3/7)+2]/[(3/7)-2]= -29/11
ANSWER:D
Question: Two full tanks one shaped like the cylinder and the other like a cone contain liquid fuel the cylindrical tank held 500 lts more then the conical tank After 200 lts of fuel is pumped out from each tank the cylindrical tank now contains twice the amount of fuel in the canonical tank How many lts of fuel did the cylindrical tank have when it was full?
A.1200
B.279
C.2879
D.27976
Answer: A.1200
Explanation: Let the cylindrical tank capacity x + 500 then the conical tank capacity = x
After 200 lts pumped out, then remaining fuel with the tanks = x +300, x - 200
Given that first term is doubt the second.
x+300x−200=21x+300x−200=21
Solving we get x = 700
Cylindrical tank capacity = 1200 lts
Answer:A
Question: By selling 12 pens for a rupee a woman loses 20%. How many for a rupee should he sell in order to gain 20%?
A.12
B.14
C.45
D.8
Answer: D.8
Explanation: D
80% --- 12
120% --- ?
80/120 * 12 = 8
Question: In a class, the teacher wrote a set of consecutive integers beginning with 1 on the blackboard. Little Johnny came and erased one number. The average of the remaining numbers was 2741327413. What was the number that Little Johnny erased?
A.7
B.9
C.11
D.13
Answer: C.11
Explanation: We have S = the sum of all integer from 1 to N
x = the missing integer
So as sum = average * Nb of terms
S-x= 27(4/13) * (N-1) (A)
As S-x should be an integer N-1 should be a multiple of 13.
So we have some possible scenario
N-1= 13 => N=14
N-1= 26 => N=17
N-1= 39 => N=40
N-1= 52 => N=53
....
Back to our formula (A)
x = S - 27(4/13)*(N-1)
x = (N(N+1))/2 - 27(4/13)*(N-1)
As x>0
(N(N+1))/2 > 27(4/13)*(N-1)
approx 27(4/13) by 27
(N(N+1))/2 > 27*(N-1)
N(N+1) > 54*(N-1)
So we see than N=53 is working (indeed 53*54>54*52)
So if N=53:
x = (53(54))/2 - 27(4/13)*(52)
x = (53(54))/2 - (27+4/13)*(52)
x = (53(54))/2 - 27*52-(4/13)*52
x = 53*27 - 27*52-(4/13)*52
x = 53*27 - 27*52-4*4
x = 27*(53-52) - 16
x = 27 - 16
x=11
ANSWER:C
Question: If a cloth merchant sells ‘a’ metres of cloth for Rs.x, then what is the selling price of ‘b’ metres of cloth?
A.Rs.{(b*x)/b}
B.Rs.{(b*x)/a}
C.Rs.{(b*x)/j}
D.Rs.{(b*x)/l}
Answer: B.Rs.{(b*x)/a}
Explanation: Explanation:
Cost of ‘a’ metres of cloth = Rs.x. Therefore, each metre of cloth costs Rs. (x/a).
The cost of ‘b’ metres of cloth = Rs. b*(x/a) = Rs. {(b*x)/a}
ANSWER:B
Question: A mixture of certain quantity of milk with 16 liters of water is worth 90 P per liter. If pure milk be worth Rs1.08 per liter, how much milk is there in the mixture?
A.100
B.90
C.80
D.75
Answer: C.80
Explanation: The mean value is 90 P and price of water is 0 P
By the alligation rule : Quantity of milk / Quantity of water
= (90 - 0) / (108 - 90)
= 90 / 18
= 5/1
proportion milk is 5/1 there in the mixture
therefore 5 * 16 = 80 liters milk is there in the mixture.
Ans - C
Question: Tough and Tricky questions: Arithmetic.
(56^2 + 56^2)/28^2 =
A.4
B.18
C.29
D.8
Answer: D.8
Explanation: Ans is 8
my approach was:
(56^2 + 56^2)/28^2 =56(56+56)/28*28
=56*112/28*28=2*4=8
D
Question: A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 840 in 4 years. The rate on interest per annum is.
A.4%
B.5%
C.6%
D.7%
Answer: B.5%
Explanation: S.I. on Rs 800 for 1 year = 40
Rate = (100*40)/(800*1) = 5%
Answer: Option B
Question: Of the 200 stamps in a collection, 80 are foreign and 50 are more than 10 years old. If 20 stamps are both foreign and more than 10 years old, how many stamps are neither foreign nor more than 10 years old?
A.60
B.90
C.100
D.130
Answer: B.90
Explanation: 20 stamps are both foreign and more than 10 years old.
60 stamps are foreign only.
30 stamps are 10 years old only.
The number of remaining stamps is 200 - (20+60+30) = 90
The answer is B.
Question: In a tennis match if the first serve is not legal, that means a fault a second serve is allowed. Normally, 20 to 40 serves are required in a set of tennis match. At the end of a set, set summary stats reveal that first serves percentage was 63%. If m out of n were first serves then m + n is equal to
A.1.43n
B.1.53n
C.1.63n
D.2.63n
Answer: C.1.63n
Explanation: m=n*(63/100)=63n/100
so,
m+n= 63n/100 + n
= 163n/100
= 1.63n
ANSWER:C
Question: In the faculty of Reverse-Engineering, 200 second year students study numeric methods, 400 second year students study automatic control of airborne vehicles and 100 second year students study them both. How many students are there in the faculty if the second year students are approximately 60% of the total?
A.834
B.750
C.633
D.654
Answer: A.834
Explanation: Total number of students studying both are 400 + 200 - 100 = 500 (Subtracting the 100 since they were included in the both the other numbers already).
So 60% of total is 500, so 100% is approx. 834.
Answer is A
Question: Three friends-whose walking rates are 1 ft./sec., 3ft./sec.,and 6ft./sec. start together walking in the same direction around a circular track that is 180 feet in circumference.After how many minutes are the three of them together again?
A.3 mins
B.10 mins
C.15 mins
D.3 mins
Answer: A.3 mins
Explanation: Answer will be A.
The time they take will be what the 1st friend takes to complete one circumference as he is the slowest and that is the point all 3 of them will be together at the end of 3 mins.
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is ?
A.1/26
B.1/20
C.1/25
D.1/29
Answer: A.1/26
Explanation: Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26.Answer: A
Question: In an arithmetic progression the difference between the any two consecutive terms is a constant. What is the arithmetic mean of all of the terms from the first to the 25th in an arithmetic progression if the sum of the 11th and 15th terms of the sequence is 96?
A.48
B.63
C.55
D.96
Answer: A.48
Explanation: Let x be the difference between any two consecutive terms.
The mean of a sequence like this is the middle term, thus the 13th term in the sequence.
Then the mean of the 12th and 14th term is also equal to the overall mean, because the 12th term is (13th term - x) and the 14th term is (13th term + x).
Similarly the mean of the 11th and 15th term is also equal to the mean.
etc...
Thus the mean is 96/2 = 48
The answer is A.
Question: A train running at the speed of 90 km/hr crosses a pole in 10 seconds. Find the length of the train.
A.150
B.180
C.250
D.200
Answer: C.250
Explanation: Speed = 90*(5/18) m/sec = 25 m/sec
Length of Train (Distance) = Speed * Time
25 *10 = 250 meter
Answer:C
Question: Exactly two sides of a certain 10-sided die are red. What is the probability that Kumar rolls the die 2 times and the die lands with a red side up for the first time on the second roll?
A.0.16
B.0.2
C.0.3
D.0.32
Answer: A.0.16
Explanation: Total no. of sides = 10
Sides that are red = 2
Probability that the die lands with red side up = 2/10
Therefore, Probability that the die does not land with red side up = 1 - 2/10 = 8/10
Probability that Kumar rolls the die 2 times and the die lands with a red side up for the first time on the second roll
= (1st roll - non red face) X (2nd roll - red face)
= 8/10 x2/10
= 16/100
=0.16
= 0.128
A
Question: The average salary per head of the entire staff of an college including the lecturer and professors is Rs.90. The average salary of professors is Rs.600 and that of the lecturer is Rs.84. If the number of professors is 2, find the number of professors in the office?
A.900
B.1000
C.1020
D.1200
Answer: C.1020
Explanation: 1->12
85->1020
C
Question: The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period(in years) is?
A.2 years
B.7 years
C.9 years
D.5 years
Answer: A.2 years
Explanation: Amount = (30000 + 4347) = Rs. 34347
Let the time be n years. Then,
30000(1 + 7/100)n = 34347
= (107/100)n = 34347/30000 = (107/100)2
n = 2 years.
Answer: A
Question: In how many years will a sum of money doubles itself at 5% per annum simple interest
A.25 years
B.28 years
C.10 years
D.20 years
Answer: D.20 years
Explanation: let the initial sum be x
then,Amount=2x(because sum will be double)
Amount = Principal + S.I
2x = x + s.I
S.I = x
S.I = (p*r*t)/100
x = (x*5*t)/100
therefore,t = 20 years
ANSWER:D
Question: An equity analyst needs to select 5 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 10, in how many ways can she choose and rank her top 5 picks?
A.21548
B.31502
C.21250
D.30240
Answer: D.30240
Explanation: Number of ways of choosing 5 stocks = 10C5
Number of ways of ranking the chosen stocks = 5!
Hence total ways of chosing and ranking = 10C5 * 5! = 30240
Correct Option: D
Question: A man walking at the rate of 6 km/hr crosses a bridge in 15 minutes. The length of the bridge is ______.
A.1000 m
B.1250 m
C.1500 m
D.1800 m
Answer: C.1500 m
Explanation: Hint: To find the answer in meter, we will first convert distance from km/hour to meter/sec by multiplying it with 5/18 .Also, change 15 minutes to seconds by multiplying it with 60.
Distance = Speed x Time
1. Convert speed into m/sec:
6 x	5 / 18 m/s = 1.66 m/s
2. Convert time from minutes into seconds = 15 x 60 s = 900 sec
3. Calculate : Distance = 1.66 x 900 = 1500 m
ANSWER IS C
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
A.1 kmph
B.7 kmph
C.2 kmph
D.4 kmph
Answer: A.1 kmph
Explanation: Explanation:
DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: Option A
Question: If 70 percent of the members of a certain organization are women and 7/8 of the members of the organization are married men, which of the following statements concerning the membership must be true? I. The number of women in the organization is greater than the number of married men in the organization. II. The number of women in the organization is greater than the number of unmarried men in the organization. III. The number of married men in the organization is greater than the number of unmarried men in the organization.
A.I
B.I,II
C.III
D.II
Answer: B.I,II
Explanation: 7/10 (70%) of the members are women and 7/8 of the members are married men. Let the total numbers of members is 80 (the LCM of 10 and 8). Then there are:
7/10*80 = 56 women;
80 - 56= 24 men;
7/8*24 = 21 married men;
24 - 21 = 3 unmarried men.
So, option I,II is true.
Answer: B
Question: A certain deck of cards contains 2 black cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both be not black?
A.15/28
B.1/4
C.9/16
D.1/32
Answer: A.15/28
Explanation: The question asks they will both be not black. Considering that these are draws without replacement there are following possibilities :
draw 1, draw 2
===== =====
1) Not black, black;
2) black, Not black;
3) black, black;
4) Not black, not black;
The answer has to be either P(4) OR all exclusion of the 3 previous conditions i.e. 1- [P(1) + P(2) + P(3)] => neither of the draws are black
P(4) = 6/8*5/7=15/28
1- [P(1) + P(2) + P(3)] = 1 - [ (6/8 * 2/7) + (2/8*6/7) + (2/8*1/7)] = 1 - [26/8*7] = 1 - [13/28] = 15/28
A
Question: A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slips back 20 feet before he again starts climbing in the beginning of the next hour. If he begins his ascent at 6.00 a.m., at what time will he first touch a flag at 120 feet from the ground?
A.4 p.m.
B.5 p.m.
C.6 p.m.
D.7 p.m.
Answer: A.4 p.m.
Explanation: Explanation:
Net ascent of the monkey in 1 hour = (30 - 20) feet = 10 feet.
So, the monkey ascends 90 feet in 9 hours i.e. till 3 p.m.
Clearly, in the next 1 hour i.e. till 4 p.m. the monkey ascends remaining 30 feet to touch the flag.
Answer:A
Question: A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he
covers with aspeed 4km/hr. Total time of travel is 18 hours. What is the maximum distance he
can cover?
A.20km
B.40km
C.60km
D.80km
Answer: D.80km
Explanation: t=d/s, so
18=x/2*1/5+x/2*1/4(because half distance with 5 km/ph, and remaining half with 4km/hr)
18=x(18/80)
x=80km
ANSWER:D
Question: In the exam the average was found to be p mark. After deducting typographical error the average marks of 94 student reduced from 84 to 64 . Due to this the average came down by 18.8 marks. What was the number of students who took the exam?
A.100
B.120
C.110
D.130
Answer: A.100
Explanation: Explanation :
Number of student = (84-64) * 94/18.8 = 100
Answer : A
Question: A vessel of capacity 2 litre has 25% of alcohol and another vessel of capacity 6 litre had 30% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
A.23%.
B.71%.
C.49%.
D.29%.
Answer: A.23%.
Explanation: 25% of 2 litres = 0.5 litres
30% of 6 litres = 1.8 litres
Therefore, total quantity of alcohol is 2.3 litres.
This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 23%
ANSWER:A
Question: A car starts from X and moves towards Y. At the same time another car starts from Y and moves towards X. Both travel at a constant speed and meet after 4 hours. During that time, the faster car traveled 1/3 of the distance XY. How long would it take the slower car to travel the distance XY?
A.6 hours
B.8 hours
C.10 hours
D.12 hours
Answer: A.6 hours
Explanation: If one car travelled 1/3, then the other car must have travelled only 2/3, as they are meeting after 4 hours in a certain point. So:
(2/3)XY= 4*y --> It took the car 4 hours to travel 2/3 of the distance at a constant speed y.
So if we solve this last equation:
2XY= 3*4*y= 6*y --> It will take this car 6 hours in total to reach its final destination.
Answer: A
Question: If 0.45: x : : 4 : 2, then x is equal to
A.0.225
B.0.228
C.0.254
D.0.256
Answer: A.0.225
Explanation: Sol.
(x×4) = (0.45×2) ⇒ x = 0.9/4 = 0.225.
Answer A
Question: A man on tour travels first 160 km at 56 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
A.31.11 km/hr
B.35.55 km/hr
C.65.9 km/hr
D.36 km/hr
Answer: C.65.9 km/hr
Explanation: Total time taken = 160/56 + 160/80 = 2720/560 = 34/7 hours
--> Average speed = 320 x 7/34 = 65.9 km/hr.
Answer : C.
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 800 m long?
A.200 Sec
B.190 Sec
C.167 Sec
D.197 Sec
Answer: A.200 Sec
Explanation: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 2000 m
T = D/S
T = 2000/10
T = 200 Sec
Answer: A
Question: A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
A.25 days
B.24
C.22 days
D.27 days
Answer: B.24
Explanation: B
24 days
B = 1/8 – 1/2 = 1/24 => 24 days
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
A.33 1/7 %
B.33 9/3 %
C.33 1/3 %
D.39 1/3 %
Answer: C.33 1/3 %
Explanation: The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %
Answer:C
Question: if price of t.v set is reduced by 18%, then its sale increases by 72%, find net effect on sale value
A.41
B.45
C.46
D.47
Answer: A.41
Explanation: - a + b + ((-a)(b)/100)
= -18+72+(-18*72)/100
= -18+72-13
=41
ANSWER:A
Question: If g, h, and i are each equal to 1 or 0, which of the following options will not be a correct value for e, given the equation e = g/5 + h/5^2 + i/5^3.
A.2/25
B.1/5
C.1/25
D.6/25
Answer: A.2/25
Explanation: e = g/5 + h/5^2 + i/5^3
= g/5 + h/25+ i/125
= (25g + 5h + i ) /125
Depending on whether g, h and i take 0 or 1:
substitute 0 or 1 for the different values of g, h and i.
Answer A
Question: If the speed of X meters per second is equivalent to the speed of Y meters per hour, what is Y in terms of X? (1 kilometer=1000 meters)
A.15x/18
B.3600x
C.18x/5
D.60x
Answer: B.3600x
Explanation: x=y/3600
y = 3600x
Answer : B
Question: What least number must be added to 1056, so that the sum is completely divisible by 23 ?
A.2
B.1
C.3
D.23
Answer: A.2
Explanation: 1056/23 = 45.91
that is 23 * 45 = 1035
Now,
1056 - 1035 = 21
To get completely divided by 23 add 2 to 1056
Ans -A
Question: A car dealership has 40 cars on the lot, 20% of which are silver. If the dealership receives a new shipment of 80 cars, 50% of which are not silver, what percentage of total number of cars are silver?
A.30%
B.35%
C.40%
D.45%
Answer: C.40%
Explanation: The number of silver cars is 0.2*40 + 0.5*80 = 48
The percentage of cars which are silver is 48/120 = 40%
The answer is C.
Question: Of the votes cast on a certain proposal, 68 more were in favor of the proposal than were against it. If the number of votes against the proposal was 40 percent of the total vote, what was the total number of votes cast? (Each vote cast was either in favor of the proposal or against it.)
A.300
B.340
C.380
D.420
Answer: B.340
Explanation: Let x be the total number of votes cast.
0.6x = 0.4x + 68
0.2x = 68
x = 340
The answer is B.
Question: Which of the following is satisfied with |x-4|+|x-3|<5?
A.1<x<6
B.2<x<5
C.2.5<x<4.5
D.2.5<x<4
Answer: A.1<x<6
Explanation: --> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<5-> |x-4+x-3|<5 -> |2x-7|<5, -5<2x-7<5, 2<2x<12, 1<x<6
Therefore, the answer is A.
Question: Susan, Tim, Matt and Kim need to be seated in 4 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
A.360
B.12
C.80
D.240
Answer: B.12
Explanation: Total # of arrangement of 4 people is 4!.
In half of the cases Susan will be seated left to Tim and in half of the cases Susan will be seated right to Tim (why should one seating arrangement have more ways to occur than another?).
So, # of arrangements to satisfy the given condition is 4!/2=12.
Answer: B.
Question: Five balls of different colors are to be placed in three different boxes such that any box contains at least 1 ball . What is the maximum number of different ways in which this can be done?
A.60
B.90
C.120
D.150
Answer: D.150
Explanation: Since in each box there must be at least one ball, we have the possibilities of (2,2,1), (2,1,2), (1,2,2) OR (3,1,1), (1,3,1), (1,1,3) balls in the three boxes.
For the 2,2,1 type arrangements, we have [5!/(2!2!1!)]*3 = 90 possibilities. Inside a box, it doesn't matter the order of the balls.
For the 3,1,1 type arrangements, we have [5!/(3!1!1!)]*3 = 60 possibilities.
Total of 90 + 60 = 150 possibilities.
Answer D.
Question: In a school of 800 students, 44% wear blue shirts, 28% wear red shirts, 10% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)?
A.120
B.132
C.144
D.156
Answer: C.144
Explanation: 44 + 28 + 10 = 82%
100 – 82 = 18%
800 * 18/100 = 144
The answer is C.
Question: If 10 gallons of grape juice are added to 30 gallons of a mixture, which contains 10 percent grape juice then what percent of the resulting mixture is grape juice?
A.14%
B.25%
C.28%
D.32.5%
Answer: D.32.5%
Explanation: OFFICIAL SOLUTION:
If we start with 40 gallons of a mixture that is 10% grape juice, then we have:
30 × 0.10 = 3 gallons of grape juice.
30 × 0.90 = 27 gallons of other components.
If we add 10 gallons of grape juice, we will end up with 13 gallons of grape juice and 36 gallons of other components, and we will have a total of 40 gallons of the mixture.
So 13/40 of the new mixture is grape juice. Now we convert this to a percent:Percent Grape Juice = 32,5%.
The correct answer is choice (D)
Question: The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly copied. The first is 17 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.
A.40.3
B.40.4
C.40.6
D.40.8
Answer: A.40.3
Explanation: Sum of 10 numbers = 402
Corrected sum of 10 numbers
= 402 – 13 + 31 – 17 = 403
Hence, new average = 403⁄10 = 40.3
Answer A