RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The average height of 35 boys in a class was calculated as 182cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places?
A.187.89 cm
B.180.29 cm
C.123.98 cm
D.149.98 cm
Answer: B.180.29 cm
Explanation: Calculated average height of 35 boys = 182 cm.
Wrong total height of 35 boys = 182 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 182 cm - (166 cm - 106 cm)/35
= 182 cm - (166 cm - 106 cm)/35 = 182 cm - 60 /35 cm
= 182 cm - 1.71 cm = 180.29 cm.
Answer: B
Question: Read the following three equations:
5 ~ 4 ~ 3 ~ 9 = 4215
6 ~ 9 ~ 2 ~ 6 = 3816
4 ~ 7 ~ 3 ~ 3 = 1122
Now based on the rule that has been used, solve the following equation:
7 ~ 2 ~ 7 ~ 4 = ____
A.3538
B.2418
C.2873
D.3258
Answer: B.2418
Explanation: B
The rule that is being followed here is
P ~ Q ~ R ~ S = [first digit of (P * S)] [last digit of (Q * R)] [first digit of (Q * R)] [last digit of (P * S)]
Using the same rule in the incomplete equation,
7 ~ 2 ~ 7 ~ 4 = [first digit of (7 * 4)] [last digit of (2 * 7)] [first digit of (2 * 7)] [last digit of (7 * 4)]
= 2418
Thus 2418 is the missing number.
Question: The speed at which a man can row a boat in still water is 9.5 kmph. If he rows downstream, where the speed of current is 8.5 kmph, what time will he take to cover 45.5 metres?
A.18 seconds
B.8.4seconds
C.5 seconds
D.9.1 seconds
Answer: D.9.1 seconds
Explanation: Speed of the boat downstream = 9.5 +8.5
= 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 45.5 m = 45.5/5
= 9.1 seconds.
Answer:D
Question: If x is 20 percent more than y and y is 30 percent less than z, then x is what percent of z?
A.500%
B.250%
C.500/3%
D.84%
Answer: D.84%
Explanation: Z = 100 ; Y = 70 so X = 84
X as % of Z = 84/100 * 100 => 84%
Answer will be (D)
Question: Tommer spent six lucky days in Las Vegas. On his first day he won a net amount of only $20, but on each of the following days, the daily net amount he won grew by d dollars. If Tommer won a total net amount of $1620 during his stay in Las Vegas, how much did he win on the last day?
A.330
B.500
C.520
D.540
Answer: C.520
Explanation: I drew a diagram:
1 - $20
2 -
3 -
4 - $320
5 -
6 -
Total: $1,620
Between 1 and 6 are 5 days where he won $1,600. This means he averaged $320 per day (1600/5). You can put $320 by 4 because it's the middle number. Now you just find the two points betwenn $20 and $320 (320-20 = 300 / 3 = 100). So each day, he earned $100 more. This means on day 6, tommer earned$520. Answer choice C.
Question: Let f(x) = x^2 + bx + c. If f(1) = 0 and f(-7) = 0, then f(x) crosses the y-axis at what y-coordinate?
A.-7
B.-1
C.0
D.1
Answer: A.-7
Explanation: When x = 1 and when x = -7, the expression f(x) = x² + bx + c equals 0.
Then f(x) = (x-1)(x+7)
f(0) = -7
The answer is A.
Question: In 2000 there were 10000 women stockbrokers in the United States. By 2005 the number had increased to 20000. Approximately what was the percent increase?
A.1%
B.2%
C.1.5%
D.3%
Answer: A.1%
Explanation: The percent increase is (20000-10000)/10000=10000/10000=1%
So the approximate answer is A
Question: At present the son's age is same as was his father's age at the time of his birth. If father's age is 48. Find the son's age after 4 years from now.
A.30 years
B.24 years
C.28 years
D.29 years
Answer: C.28 years
Explanation: Let x be the son's age
And y be the father's age
Then, y=48.
And, x=y-x
==> 2x=y
==> x=y/2
So, x=48/2
x=24.
Son's age after four years,
x+4 = 24+4
= 28 years.
ANSWER:C
Question: A train 220 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 4 km/hr in the direction opposite to that in which the train is going?
A.5
B.12
C.7
D.9
Answer: B.12
Explanation: Speed of train relative to man = 60 + 4 = 64 km/hr.
= 64 * 5/18 = 160/9 m/sec.
Time taken to pass the men = 220 * 9/160 = 12 sec.Answer: B
Question: If 2x=4y=z, what is x-y, in terms of z?
A.z/4
B.z/2
C.z
D.2z
Answer: A.z/4
Explanation: 2x=4y=z
i.e. x = z/2
and y = z/4
x-y = z/2 - z/4 = z/4
Answer: Option A
Question: The population of cities A and B is equal. The population of city A increases in two successive years by 20% and 15% respectively and that of city B increases successively by 20% and 10% respectively. If the difference in the population of two cities after 2 years is 768, then what was the total population of the two cities initially?
A.12,800
B.26,500
C.24,600
D.25,600
Answer: D.25,600
Explanation: Population of city A = Population of city B = A
M . F of A = 120/100*115/100 = 138/100
M . F of B = 120/100*110/100 =132/100
Population of A after 2 years = A*138/100
Population of B after 2 years = A*132/100
Difference = A/100( 138 –132 ) = 768
A = 768*100/6 = 12800
Total initial population = 12800+12800 = 25,600
ANSWER:D
Question: A man deposits $1000 in a bank at 2% per annum and $ 1500 in UTI at 7% per annum. Find the rate of interest for the whole sum.
A.5%
B.8%
C.3%
D.7%
Answer: A.5%
Explanation: Following the above formula,we have the rate of interest for the whole sum
=(1000*2)+(1500*7)/1000+1500=12500/2500=5%.
Answer is A
Question: Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?
I. 4
II. 12
III. 24
A.I, II, and III
B.I and II only
C.II and III only
D.I and III only
Answer: A.I, II, and III
Explanation: Answer = A. I, II, and III
With dimensions of only 2 sides given (for a triangle), this becomes an open ended question
Any area is possible out of the three
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
A.33 1/9%
B.73 1/3%
C.33 1/3%
D.33 1/9%
Answer: C.33 1/3%
Explanation: 1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Answer:C
Question: Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
A.18 min
B.19 min
C.11 min
D.28 min
Answer: D.28 min
Explanation: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
4 --------- ? è 28 m
Answer: D
Question: If 15 lions can kill 15 deers in 15 minutes how long will it take 100 lions to kill 100 deers?
A.1 minutes
B.15 minute
C.100 minutes
D.10000 minutes
Answer: B.15 minute
Explanation: we can try the logic of time and work,our work is to kill the deers so 15(lions)*15(min)/15(deers)=100(lions)*x(min)/100(deers)hence answer is x=15
ANSWER:B
Question: The length of a rectangular floor is more thanits breadth by 200%. If Rs.324 is requiredto paint the floor at the rate of Rs.3/sq m, what would be the length of the floor?
A.12
B.18
C.20
D.22
Answer: B.18
Explanation: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.
B
Question: A military commander has to choose 3 soldiers out of a company of 6 for guarding the headquarters. How many different group combinations of 3 does he have to choose from?
A.20
B.15
C.16
D.27
Answer: A.20
Explanation: A military commander has to choose 3 soldiers out of a company of 7.
different group combinations of 3
He can do this in 6C3 ways
6*5*4/3*2*1= 20 ways
ANSWER:A
Question: I. x2 + 11x + 30 = 0,
II. y2 + 15y + 56 = 0 to solve both the equations to find the values of x and y?
A.If x < y
B.If x > y
C.If x ≤ y
D.If x ≥ y
Answer: B.If x > y
Explanation: I. x2 + 6x + 5x + 30 = 0
=>(x + 6)(x + 5) = 0 => x = -6, -5
II. y2 + 8y + 7y + 56 = 0
=>(y + 8)(y + 7) = 0 => y = -8, -7
=> x > y
ANSWER:B
Question: A room contains 120 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
A.10
B.20
C.30
D.40
Answer: C.30
Explanation: Say group of x people left the room.
# of women in the room was 0.15*120=18;
# of women in the group that left 0.3x;
# of women in the room after the group left it is 0.1(120-x);
So, 18-0.3x= 0.1(120-x) --> x=30.
Answer: C.
Question: A crow leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. The distance between the nest and the ditch is 250 meters. In one and a half hours, the crow manages to bring worms to its nest 15 times. What is the speed of the crow in kilometers per hour?
A.1
B.3
C.4
D.5
Answer: D.5
Explanation: The distance between the nest and the ditch is 250 meters.
15 times mean = A crow leaves its nest, and flies back ( going and coming back) i.e. 2 times we get total 30 rounds.
So the distance is 30 * 250 = 7500.
D = ST
7500/1.5 = T , I think we can take 7500 meters as 7.5 km, then only we get T = 5.( 1000 meters = 1 km)
D)
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 42 years now, the son's age 8 years back was:
A.13 years.
B.14 years.
C.17 years.
D.16 years.
Answer: A.13 years.
Explanation: Let the son's present age be x years. Then, (42 - x) = x
2x = 42.
x = 21
Son's age 8 years back (21- 8) = 13 years.
ANSWER :A
Question: A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :
A.4 days
B.6 days
C.8 days
D.18 days
Answer: A.4 days
Explanation: Explanation:
Ratio of rates of working of A and B = 2 : 1.
So, ratio of times taken = 1 : 2.
B's 1 day's work =1/12
A's 1 day's work =	1/6 ; (2 times of B's work)
(A + B)'s 1 day's work = (1/6 +1/12)=3/12=1/4
So, A and B together can finish the work in 4 days.
ANSWER IS A
Question: A motorist travel to a place 150 km away at an avearge speed of 50 km/hr and returns ar 30
km/hr.His average speed for the whole jouney in km/hr is
A.36.5 km/hr
B.37.5 km/hr
C.35.5 km/hr
D.34.5 km/hr
Answer: B.37.5 km/hr
Explanation: Explanation:
Average speed will be
2xyx+ykm/hr
= \frac{2(50)(30)}{50+30} km/hr
= 37.5 km/hr
Answer: Option B
Question: If a book has twelve thousand words, two long chapters, and four short chapters, how many words are in a short chapter if there are as many words in the four short chapters put together as in one long chapter?
A.Eleven thousand words
B.Five thousand words
C.Two thousand words
D.One thousand words
Answer: D.One thousand words
Explanation: D. A long chapter has 1/3 of the total words. A short chapter has 1/4 of 1/3 of the total words. 1/4 of 1/3 is 1/12. 1/12 of twelve thousand is one thousand, so the answer is D.
Question: In a supermarket the single-yolk and double-yolk eggs got mixed. If the total number of yolks was 15 more than the total number of eggs. Find the number of double-yolk eggs.
A.8
B.13
C.15
D.11
Answer: C.15
Explanation: Let the number of single-yolk eggs be X and the number of double-yolk eggs be Y. Then
=> X+(2*Y)= 15+(X+Y)
=>2Y=15+Y
=>Y=15
Option C
Question: What is the smallest possible common multiple of three integers, all larger than 25?
A.27.
B.26
C.846.
D.19,656.
Answer: B.26
Explanation: The Least common positive multiple would be for the immediate least number(s) after 25 i.e 26.
Since nowhere is it stated that the three integers must be different, the integers could be 26,26 and 26... leading to least possible positive common multiple to be 26. Answer B.
Question: The ratio of boarders to day students at a school was originally 2 to 5. However, after a number of new boarders join the initial 120 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school?
A.30
B.50
C.70
D.80
Answer: A.30
Explanation: Let x be the number of new boarders.
The ratio changed from 2:5 = 4:10 up to 1:2 = 5:10.
120 / (120+x) = 4/5
x = 30
The answer is A.
Question: A sporting good store sells one type of baseball bat and one type of baseball. The cost for 2 bats and 4 balls is $220. The cost for 1 bat and 6 balls is $190, as well. If someone were to buy an equal number of bats and balls, at most how many bats can he purchase if he has a budget of $270 for the purchase?
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: IMO it should be C that is 4
reason:
formed an equation... bat = b ball = c
2b+4c=220
1b+6c=190
solving both we get b that is bat = 70 and c that is ball = 20
new equation 270 to be divided in equal
3b+3c=270
3*70 + 3*20 = 270
210+ 60 = 270
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets $2.40 per hour for regular work and $3.20 per hours for overtime. If he earns $432 in 4 weeks, then how many hours does he work for ?
A.135
B.278
C.175
D.195
Answer: C.175
Explanation: C
175
Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.40 + x x 3.20 = 432
3.20x = 432 - 384 = 48
x = 15.
Hence, total hours of work = (160 + 15) = 175.
Question: X and Y invested in a business. They earned some profit which they divided in the ratio of 2 : 3. If X invested Rs. 40,000, the amount invested by Y is ?
A.60229
B.62887
C.60000
D.61298
Answer: C.60000
Explanation: Suppose Y invested Rs. y. Then 40000/y
= 2/3 or y
= 60000 .
Answer: C
Question: 70 60 55 50 40 55 30 ? ?
A.25 15
B.55 85
C.35 55
D.20 55
Answer: D.20 55
Explanation: 70-10=60
again 55
60-10=50
50-10=40
again 55
40-10=30
30-10=20
again 55
then answer is 20 ,55
ANSWER:D
Question: In a four numbers set, the second number is twice the first number, the first is one-third of the third and the third is 5 times the fourth. The average of the numbers is 24.75. The largest of these numbers is:
A.9
B.25
C.30
D.35
Answer: D.35
Explanation: Explanation :
Let the fourth number be x.
Then, third number = 5x, first number = 5x/3
And second number = 10x/3
x + 5x + 10x/3 + 5x/3 = (33 x 4) or 11x = 132 or x = 12.
So, the numbers are 20, 40, 60 and 12.
Largest number = 60.
Answer : D
Question: There are 84 supermarkets in the FGH chain. All of them are either in the US or Canada. If there are 14 more FGH supermarkets in the US than in Canada, how many FGH supermarkets are there in the US?
A.20
B.31
C.42
D.49
Answer: D.49
Explanation: x + (x - 14) = 84 --> x = 49.
Answer: D.
Question: In covering a distance of 30 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:
A.5 km/h
B.8 km/h
C.10 km/h
D.15 km/h
Answer: A.5 km/h
Explanation: Let A's speed be X km/hr.
Then, 30/x - 30/2x = 3
6x = 30
x = 5 km/hr.
Answer : A.
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when No boy gets more than one prize?
A.10
B.15
C.16
D.24
Answer: D.24
Explanation: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 4 ways. The second in 3 ways and the third in 2 ways. But fundamental principle, (4 x 3 x 2) ways = 24 ways
4: Or 4p = — 4:- 4X3X2X1- 24 ways
D
Question: The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
A.180
B.290
C.729
D.720
Answer: A.180
Explanation: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 655.
(P + Q)/2 = 85 and R = 125
P + Q = 170 and R = 125
P + Q + R = 295
S + T = 655 - (P + Q + R) = 360
Average of the last two numbers = (S + T)/2 = 180.
Answer:A
Question: At Sandi’s Pet Shop, 25 cups of bird seed are used every 5 days to feed 15 parakeets. How many cups of bird seed would be required to feed 14 parakeets for 7 days?
A.40.5
B.32.34
C.6.23
D.9
Answer: B.32.34
Explanation: Let's go step-by-step.
25 cups are used over a 5 day period, which means 5 cups a day. This feeds 15 parakeets, which means each parakeet needs 1/3 of a cup every day.
For 14 parakeets, we need 14*1/3cups = 4.62 cups a day. Over 7 days, we need 32.34 cups. Choice B.
Question: A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 850 in 4 years. The
rate on interest per annum is.
A.4.20%
B.50%
C.60%
D.6.25%
Answer: D.6.25%
Explanation: Explanation:
S.I. on Rs 800 for 1 year = 50
Rate = (100*50)/(800*1) = 6.25%
Answer: D
Question: The ratio of the age of a gentleman and his wife is 4 : 3. After 4 years this ratio will be 9 : 7. If at the time of their marriage the ratio was 5 : 3, how many years ago they were married?
A.10 years
B.8 years
C.12 years
D.15 years
Answer: C.12 years
Explanation: Let the present age of gentleman (G) and wife (W) be 4x and 3x resp....
thus after 4 yrs the ratio will be (4x+4)/(3x+4)=9:7..
on solving we get the value as x=8..i.e present ages are G=32,W=24...
Now at the time of marriage the ratio will be :
(32-y)/(24-y)=5:3
on solving we get y=12...
Thus 12 yrs ago they got married.
ANSWER:C
Question: Set A is {1, 3, 5, 7, 9}
Set B is {12, 14, 16, 18, 20}
For the sets of numbers above, which of the following is true?
I. The mean of Set B is greater than the mean of Set A.
II. The median of Set B is greater than the median of Set A.
III. The standard deviation of Set B is greater than the standard deviation of Set A.
A.I only
B.I and II only
C.I and III only
D.II and III only
Answer: B.I and II only
Explanation: The mean and median of Set A is 5.
The mean and median of Set B is 16.
Thus statements I and II are both true.
The standard deviation is related to the distance from the mean.
Since the elements of both sets are spaced identically around the mean (+/- 2, +/- 4), the standard deviations of both sets are equal.
The answer is B.
Question: If r = 2^4 * 5^2 * 7 and s = 2^3 * 3^2 * 5, which of the following is equal to the greatest common divisor of r and s?
A.2 * 5
B.2^2 * 5
C.2^3 * 5^2
D.2*3*5*7
Answer: B.2^2 * 5
Explanation: GCD = product of prime factors raised to the least power = 2^3 * 5
The answer is B.
Question: Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?
A.9
B.5
C.6
D.2
Answer: B.5
Explanation: Explanation:
x + y = 15
2x â€“ 3y = 5
x = 10 y = 5
Answer: B
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
A.238
B.177
C.120
D.298
Answer: C.120
Explanation: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
Answer: C
Question: Sudhir started a business with Rs.10,000 and after 8 months Ravi joined him with Rs.60,000. If they get a profit of Rs.28000 then ratio of their shares will be
A.1:2
B.2:3
C.4:3
D.3:4
Answer: A.1:2
Explanation: 10000*12:60000*(12-8)
=120000 :240000
=1:2
ANSWER:A
Question: In digging a pond 20 m * 10 m * 8 m the volumes of the soil extracted will be?
A.3387
B.1600
C.2866
D.2787
Answer: B.1600
Explanation: 20 * 10 * 8 = 1600
Answer: B
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.55 less, he could have gained 25%. What is the cost price?
A.197
B.375
C.275
D.278
Answer: C.275
Explanation: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
55 ----- ? => 275
Answer:C
Question: In how many ways can 21 books on English and 19 books on French be placed in a row on a shelf so that two books on French May not be Together ?
A.3990
B.1540
C.1995
D.3672
Answer: B.1540
Explanation: In order that two books on French are never together, we must place all books as under
X E X E X E X E X E .....X E X
where E denotes the position of an English book and X that of a French book.
Since there are 21 books on English, the number of places marked X are therefore, 22.
Now, 19 places out of 22 can be chosen in 22C19 = 22C3 = (22x21x20)/(3x2x1) = 1540 ways
Answer B.
Question: total 100 members are writing exam. In the 48 members are writing first exam. 45 members are writing second exam. 38 members are writing third exam. 5 members are writing all the three exams.How many members are writing 2 exams?
A.20
B.21
C.22
D.23
Answer: B.21
Explanation: It's basic set theory problem using venn diagram.
Draw three intersecting circles 1,2,3. and name all the parts a,b,c,d,e,f,g. 'e' being common in all circles.
these will be the equation.
a+b+c+d+e+f+g= 100 ........(1)
a+b+d+e=48.......................(2) (members are writing first exam)
b+e+f+c=45........................(3) (members are writing second exam)
d+e+f+g=38........................(4) (members are writing third exam)
e=5......................................(5) (members are writing all the three exams)
we have to find the value of d+b+f=?
add eq 2,3,4 and put the value of a+c+g from 1.
you will get d+b+f=21.
ANSWER:B
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
A.31.5
B.31.9
C.31.6
D.31.3
Answer: C.31.6
Explanation: 100*(80/100)*(90/100)*(95/100) = 68.4
100 - 68.4 = 31.6
Answer: C
Question: Dacid obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
A.75
B.45
C.23
D.28
Answer: A.75
Explanation: Average = (76 + 65 + 82 + 67 + 85)/5 = 375/5 = 75.
Answer: A
Question: On dividing 16698 by a certain number, we get 89 as quotient and 14 as remainder. What is the divisor?
A.743
B.154
C.187
D.741
Answer: C.187
Explanation: Divisor *quotient+remainder=dividend
divisor=(dividend)-(remainder)/quotient
(16698-14)/89=187
Answer(C)
Question: The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 148, what is the difference between the ages of Patrick and Monica?
A.27
B.48
C.45
D.72
Answer: B.48
Explanation: Ages of P and Mi=3x+5x
Ages of Mi and Mo=3x:5x
Rationalizing their ages. ratio of their ages will be 9x:15x:25x
Sum=47x=148
x=3
Difference if ages of Pa and Mo=25x-9x=16x=16*3=48
Answer B
Question: In a class of 10 students there are 3 girls. In how many ways can they be arranged in a row such that no three girls are consecutive?
A.32*6!
B.42*8!
C.25*5!
D.45*5!
Answer: B.42*8!
Explanation: Number of girls = 3
Number of boys = 7
7 boys can be arranged in a row in 7! ways
Now there are 8 places for 3 girls
3 girls can be arranged in 8P3 ways
Required number of ways = 8P3 * 7! = 8!*7!/5! = 42*8!
Answer is B
Question: A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?
A.378
B.288
C.287
D.646
Answer: D.646
Explanation: 840 = P [1 + (10*3)/100]
P = 646
Answer: D
Question: A number whose fifth part increased by 7 is equal to its fourth part diminished by 7 is ?
A.160
B.180
C.200
D.280
Answer: D.280
Explanation: Answer
Let the number be N.
Then, (N/5) + 7 = (N/4) - 7
â‡’ (N/4) - (N/5) = 14
â‡’ (5N - 4N)/20 = 14
âˆ´ N = 280
Option: D
Question: If the product of the integers from 1 to n is divisible by 630, what is the least possible value of n?
A.7
B.14
C.21
D.28
Answer: A.7
Explanation: 630 = 2 x 3 x 3 x 5 x 7
N must include at least up to the number 7.
The answer is A.
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?
A.3
B.7
C.4
D.2
Answer: C.4
Explanation: 150 = (750*5*R)/100
R = 4%
Answer: C
Question: Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. four years from today, the difference between the age of the boy and the combined ages of the girls will be
A.1
B.2
C.-3
D.–2
Answer: C.-3
Explanation: Approach I (Plugin's)
Girl I ............... Girl II ................ Boy
1 ....................... 1 ........................ 3 (Assume the current ages)
1 + 1 < 3 .......... (Satisfies the given condition)
1 Year later there ages are
2 ....................... 2 ......................... 4
2 + 2 = 4 ............ (Satisfies the given condition)
After 4 years there ages are
5 ....................... 5 ............................ 7
Difference = 7 - (5+5) = 7 - 10 = -3
Answer = C
Question: How many minutes does it take John to type u words if he types at the rate of x words per minute?
A.x/y
B.u/x
C.xy
D.60x/y
Answer: B.u/x
Explanation: time*rate=job --> time*x=u --> time=u/x.
Answer: B.