RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A scooter costs 25,000 when it is brand new. At the end of each year, its value is only 80% of what it was at the beginning of the year. What is the value of the scooter at the end of 3 years?
A.10,000
B.12,500
C.12,800
D.12,000
Answer: C.12,800
Explanation: After first year, the value of the scooter = 20,000
After second year, the value of scooter = 16,000
After third year, the value of scooter = 12,800
Answer C
Question: If a certain number is divisible by 16 and 30, it is NOT necessarily divisible by which of the following?
A.8
B.12
C.21
D.24
Answer: C.21
Explanation: If a certain number is divisible by 16 and 30, it is NOT necessarily divisible by which of the following?
let the certain number be 240, which is both divisible by 16 and 30.
240/21 = 80/7
C. 21
Question: Sakshi can do a piece of work in 10 days.Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work :
A.8
B.16
C.18
D.25
Answer: A.8
Explanation: Solution
Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4 .
Suppose Tanya taken x days to do the work.
5 : 4 : : 10 : x ⇒ x = (10x4/5) ⇒ x = 8 days.
Hence,Tanya takes 8 days is complete the work.
Answer A
Question: A man buys an article for $10. and sells it for $15. Find the gain percent?
A.25%
B.50%
C.20%
D.15%
Answer: B.50%
Explanation: C.P. = $10
S.P. = $15
Gain = $5
Gain% = 5/10 *100 = 50%
Answer is B
Question: The number of new words that can be formed by rearranging the letters of the word 'RAM' is ?
A.5
B.6
C.10
D.13
Answer: A.5
Explanation: Number of words which can be formed = 3! - 1
= 6 - 1
= 5
Answer:A
Question: When 16 is divided by the positive integer k, the remainder is 1, for how many different values of k is this true?
A.1
B.2
C.3
D.5
Answer: C.3
Explanation: When 16 is divided by k, remainder is 1 i.e. there is 1 ball leftover after grouping. so k must be greater than 1.
It also means that 15 is completely divisible by k.
Factors of 15 are 1, 3, 5, 15
Out of these, k can be 3, 5 and 15.
Answer (C)
Question: Find the Unit’s digit in the product (76^41) * (41^14) * (14^87) * (87^76)
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: units digit of 87^76 = 1 because 87^3n+1 has units place as 1
units digit of 14^87 = 4 because 14^(some odd no.) has units place as 4
units digit of 41^14 = 1 because 41^(some even no. )has units place as 1
units digit of 76^41 = 6 because 76^(any positive no.)has units place as 6
so , units digit of the product is = " 4 " (units digit of 1*4*1*6)
ANSWER:D
Question: If ABC is a quarter circle and a smaller circle is inscribed in it; if radius of quarter circle is 1.414units. Find the radius of smaller circle
A.0.48
B.0.58
C.0.68
D.0.78
Answer: B.0.58
Explanation: if r be radius of smaller circle then
distance b/n centres = √2 * r
so, r + r√2 = R here,R = 1.414 =√2
=> r=(√2 -1)R
r = 0 .586 unit
ANSWER:B
Question: A straight line is formed using two points A(3,3) and B(6,6). Another point P(x,y) lies between A and B such that AP/BP = 7. What are the coordinates of P?
A.(5/8, 5/8)
B.(15/8, 15/8)
C.(45/8, 45/8)
D.(21/8, 21/8)
Answer: C.(45/8, 45/8)
Explanation: The equation of the straight line is y = x, so the x- and y-coordinates of P are the same.
The x, y coordinates are 7/8 of the distance from 3 to 6.
x = 3 + (6-3)*(7/8) = 3 + 21/8 = 45/8 = y
The answer is C.
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?
A.81000
B.81028
C.27772
D.29889
Answer: A.81000
Explanation: 64000* 9/8 * 9/8 = 81000.Answer:A
Question: 324 Ã· ? Ã— 15 + 270 = 405
A.24
B.25
C.36
D.39
Answer: C.36
Explanation: Explanation:
324 Ã· ? Ã— 15 = 405 - 270 = 135
(324 Ã— 15)/? = 135
? = (324 Ã— 15)/135 = 36
Answer: Option C
Question: The average of ten numbers is 7. If each number is multiplied by 11, then what is the average of the new set of numbers?
A.11
B.18
C.77
D.110
Answer: C.77
Explanation: The sum of the ten numbers is 7*10 = 70
If each number is multiplied by 11, the new sum is 11*(70).
The average is then 11*7 = 77
The answer is C.
Question: Two cars cover the same distance at the speed of 80 and 84 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car?
A.1350
B.1000
C.1200
D.1400
Answer: C.1200
Explanation: 80(x + 1) = 84x
X = 20
60 * 20 = 1200 km
Answer:C
Question: 8 years ago there were 5 members in the Arthur's family and then the average age of the family was 36 years. Mean while Arthur got married and gave birth to a child. Still the average age of his family is same now. What is the age of his wife at the time of his child's birth was.If the difference between the age of her child and herself was 26 years.
A.15 years
B.26 years
C.16 years
D.11 years
Answer: B.26 years
Explanation: Explanation:
Since we know that the difference b/w the age of any two persons remains always constant, while the ratio of their ages gets changed as the time changes.
so, if the age of his child be x (presently)
Then the age of wife be x + 26 (presently)
Thus the total age = x + ( x + 26) = 32 [\inline \because 252-220 =32]
\inline \Rightarrow x = 3
\inline \therefore The age of her child is 3 years and her self is 29 years. Hence her age at the time of the birth of her child was 26 years.
Answer: B
Question: In order to fulfill a local school’s request for x cakes, B parents agreed to each bake an equal number of cakes. If p of the parents did not bake any cakes, which of the following represents the additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes to be fulfilled?
A.px/B
B.px/(B(B - P))
C.x/(B - P)
D.p/(B - Px)
Answer: B.px/(B(B - P))
Explanation: No of cakes each parent has to bake : x/B
No of parents did not bake cake = p
No of cakes that were not baked by p parents = p*x/B
No of parents has to bake additional cakes = B-p
additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes = px/(B(B - P))
Answer B
Question: Twenty percent of the skiers that tried out for the ski patrol were selected. Of those that were not selected, 25 skiers were CPR certified and 31 were not. How many skiers tried out for the ski patrol?
A.40
B.50
C.60
D.70
Answer: D.70
Explanation: Not Selected = 80%
If total is x.
Then 0.8x=25+31=56
x=70
Hence answer is D.
Question: Gopi gives Rs. 90 plus one turban as salary to his servant for one year. The servant leaves after 9 months and receives Rs. 45 and the turban. Find the price of the turban.
A.27
B.36
C.29
D.90
Answer: D.90
Explanation: Let the price of turban be x.
Thus, for one year the salary = (90 + x)
For 9 months he should earn 3434 (90 + x).
Now he gets one turban and Rs. 45.
Thus, 3434 (90 + x) = 45 + x or 270 + 3x = 180 + 4x or x = 90
Answer:D
Question: The only people in each of rooms A and B are students, and each student in each of rooms A and B is either a junior or a senior. The ratio of the number of juniors to the number of seniors in room A is 4 to 5, the ratio of the number of juniors to the number of seniors in room B is 3 to 17, and the ratio of the total number of juniors in both rooms A and B to the total number of seniors in both rooms A and B is 5 to 7. What is the ratio of the total number of students in room A to the total number of students in room B ?
A.29/12
B.59/10
C.65/8
D.48/5
Answer: D.48/5
Explanation: Ratio in A: 4/5 so total students in A = 9x
Ratio in B: 3/17 so total students in B = 20y
(4x+3y)/(5x+17y) = 5/7
solving, x/y = 64/3
required ratio = 9x/20y = (64*9)/(3*20) = 48/5
ANSWER:D
Question: Ahmed, Babu, Chitra, David and Eesha each choose a large different number. Ahmed says, “ My number is not the largest and not the smallest”. Babu says, “My number is not the largest and not the smallest”. Chitra says, “My number is the largest”. David says, “ My number is the smallest”. Eesha says, “ My number is not the smallest”. Exactly one of the five children is lying. The others are telling the truth. Who has the largest number?
A.Eesha
B.David
C.Chitra
D.Babu
Answer: A.Eesha
Explanation: Largest ->	A	B	C	D	E
A	F	T/F	T/F	T/F	T/F
B	T/F	F	T/F	T/F	T/F
C	F	F	T	F	F
D	T/F	T/F	T/F	F	T/F
E	T/F	T/F	T/F	T/F	T
Ans: A
Question: What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, x
A.23
B.26
C.36
D.35
Answer: D.35
Explanation: (D)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 30 + 5 = 35.
Question: Meera purchased two three items from a shop. Total price for three items is Rs.6000/- She have given Rs. 10000/- What is the balance amount meera got?
A.6000
B.3500
C.5000
D.4000
Answer: D.4000
Explanation: Total cost of Items : 6000/-
amount Paid : 10000/-
Balance receivable : 10000- 6000= 4000/-
Answer is D
Question: Ifaequals the sum of the even integers from 2 to 40, inclusive, andbequals the sum of the odd integers from 1 to 39, inclusive, what is the value of a - b ?
A.1
B.10
C.19
D.20
Answer: D.20
Explanation: This is a solution from Beatthegmat:
even numbers:
(40-2)/2 + 1 = 20 even integers.
(40+2)/2 = 21 is the average of the even set.
sum = avg*(#of elements) = 21*20 =420 = a
odd numbers:
(39-1)/2 + 1 = 20 odd integers.
(39+1)/2 = 20 is the average of the odd set.
sum = avg*(#of elements) = 20*20 = 400 = b
a-b = 420 - 400 = 20.
Answer : D
Question: A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 48 now, the son age 5 years back was
A.14
B.17
C.11
D.19
Answer: D.19
Explanation: Let the son's present age be x years .Then, (48 - x) = x x= 24.
Son's age 5 years back = (24 - 5) = 19 years
Answer: D
Question: Mr.Jones gave 40% of the money he had to his wife. he also gave 20% of the remaining amount to his 3 sons. half of the amount now left was spent on miscellaneous items and the remaining amount of Rs.12000 was deposited in the bank. how much money did Mr.Jones have initially?
A.100
B.1000000
C.1000
D.1
Answer: B.1000000
Explanation: Let the initial amount with Mr.Jones be Rs.x
Then, (1/2)[100-(3*20)]% of x=12000
 (1/2)*(40/100)*(60/100)*x=12000
x=((12000*25)/3)=100000
ANSWER B
Question: What number has a 5:1 ratio to the number 10?
A.42
B.50
C.55
D.62
Answer: B.50
Explanation: Explanation:
5:1 = x: 10
x = 50
ANSWER IS B
Question: An analyst will recommend a combination of 4 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 8 stocks are possible?
--
A.12
B.19
C.90
D.180
Answer: C.90
Explanation: 5C4 * 4C2 * 3C2 = 5*6*3 = 90.
Answer: C.
Question: 3-3*6+2=
A.2
B.-13
C.-18
D.-17
Answer: B.-13
Explanation: It is easy and you have to follow BODMAS..
3-3*6+2 = 5-18 = -13...
Your OA -17 would be if the equation is 3-(3*6+2)....
so the answer is -13.
ANSWER:B
Question: A construction company wants to number new houses using digit plates only. If the company puts an order for 312 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1).
A.140
B.150
C.160
D.170
Answer: A.140
Explanation: You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there?
99+(312-9-90*2)/3=140
Answer : A
Question: Find the average of all prime numbers between 12 and 24.
A.30
B.33.6
C.18
D.20
Answer: C.18
Explanation: Sol.
There are five prime numbers between 12 and 24.
They are 13, 17, 19, 23
âˆ´ Required average = [13+ 17+ 19+ 23 / 4] = 72/ 4 = 18
Answer C
Question: A man can swim in still water at 5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
A.1.78
B.1.667
C.1.15
D.1.5
Answer: B.1.667
Explanation: M = 5
S = x
DS = 5 + x
US = 5 - x
5 + x = (5 - x)2
5 + x = 10 -2x
3x = 5
x = 1.667
Answer:B
Question: In the parking lot there are 28 vehicles, 18 of them are buses, and the rest are cars. The color of 14 vehicles is red, of which 11 are buses. How many cars can be found in the parking lot which are not colored red?
A.7
B.8
C.9
D.10
Answer: A.7
Explanation: The number of cars is 28-18 = 10.
The number of red cars is 14-11=3.
The number of cars which are not red is 10-3=7.
The answer is A.
Question: Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
A.1245 m^2
B.1345 m^2
C.2520 m^2
D.2560 m^2
Answer: C.2520 m^2
Explanation: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Question: A train crosses a platform of 170 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
A.A)150m
B.B)170m
C.C)180m
D.D)70m
Answer: D.D)70m
Explanation: Length of the train be ‘X’
X + 170/15 = X + 250/20
4X + 680 = 3X + 750
X = 70m
Answer: D
Question: In how many different ways can the letters of the word 'EVE' be arranged?
A.3 ways
B.20 ways
C.30 ways
D.60 ways
Answer: A.3 ways
Explanation: Totally there are 3 letters on the word EVE. it contains 2E,1V.
The no of ways is 3!/2!=3 ways.
ANSWER:A
Question: Mohan's salary was first increased by 20% and then decreased by 20%. If his present salary is Rs. 7200, then what was his original salary?
A.7508
B.7500
C.7506
D.7566
Answer: B.7500
Explanation: Let Mohan's salary be Rs.100.
When increased by 20%, Mohan's salary = Rs.120
Again when decreased by 20%, Mohan's salary = 120 - 24 = Rs. 96.
But present salary is Rs. 7200
for, 96 ---> 100 ; 7200 ---> ?
Required salary is 7200/96 * 100 = Rs.7500
Answer: B
Question: In an election between two candidates, 70% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 65520 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.
A.130000
B.12500
C.14000
D.12000
Answer: A.130000
Explanation: Explanation :
Solution: let the total number of votes enrolled be x. then, number of votes cast = 70% of x. valid votes = 96% of(70% of x). .'. 75% of(96% of (70% of of x)) = 65520.
(75/100 * 96/100 * 70/100 * x) = 65520.
=> x = (65520*100*100*100)/(75*96*70) = 130000
Answer : A
Question: In how many different number of ways 4 boys and 4 girls can sit on a bench such that girls always sit together.
A.A)720
B.B)2000
C.C)2880
D.D)780
Answer: C.C)2880
Explanation: 2880
Option 'C'
Question: How many values of c in x^2 - 5x + c, result in rational roots which are integers?
A.23
B.27
C.25
D.12
Answer: C.25
Explanation: Explanation:
By the quadratic formula, the roots of x2−5x+c=0x2−5x+c=0 are −(−5)±−52−4(1)(c)−−−−−−−−−−−√2(1)−(−5)±−52−4(1)(c)2(1) = 5±25−4c−−−−−−√25±25−4c2
To get rational roots, 25−4c25−4c should be square of an odd number. Why? because 5 + odd only divided by 2 perfectly.
Now let 25 - 4c = 1, then c = 6
If 25 - 4c = 9, then c = 4
If 25 - 4c = 25, then c = 0 and so on...
So infinite values are possible.
Answer:C
Question: ? x 48 = 173 x 240
A.545
B.685
C.865
D.495
Answer: C.865
Explanation: Let y x 48 = 173 x 240
Then y = (173 x 240) / 48
=173 x 5
= 865 .
ANSWER :C
Question: What percent of a day is five hours?
A.20.83%
B.16x1/2%
C.18x2/3%
D.22x1/2%
Answer: A.20.83%
Explanation: Explanation :
Required percentage = (5/24100)%
= (125 / 6)%.
= 20.83%.
Answer : A
Question: A and B started a business investing Rs. 24,000 and Rs 18,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?
A.4 : 3
B.9:2
C.18:20
D.1:4
Answer: A.4 : 3
Explanation: A: B =24000 : 18000 = 8 : 6 = 4 : 3
ANSWER:A
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
A.3
B.7
C.5
D.9
Answer: A.3
Explanation: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer: A
Question: Train X and train Y pass one another traveling in opposite directions. Twelve minutes later they are 100 miles apart. If train X’s constant speed is 30 miles per hour greater than train Y’s, how far does train X travel during that time?
A.28
B.40
C.53
D.72
Answer: C.53
Explanation: Let the rate of the Train Y be R
Then the rate of the Train X will be R+30 (given)
As per relative rate concept, the rate at which they are increasing the distance between them is R+(R+30) [add the rates] i.e. 2R+30
d=100 and t = 12 min i.e 12/60 hr
using RTD table, (2R+30) * 12/60 = 100 ==> R= 235 miles/hr
So the rate of train X is 265 miles/hr (since R+30)
The distance traveled by Train X in 12 min is R*T = 265 * 12/60 = 53 miles (C)
Question: The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is?
A.200
B.400
C.450
D.500
Answer: B.400
Explanation: Let the numbers be x and y.
Then, xy = 9375 and x = 15.
y
xy = 9375
(x/y) 15
y2 = 625.
y = 25.
x = 15y = (15 x 25) = 375.
Sum of the numbers = x + y = 375 + 25 = 400.
Option is B
Question: On a trip, a cyclist averaged 12 miles per hour for the first 18 miles and 10 miles per hour for the remaining 18 miles. If the cyclist returned immediately via the same route and took a total of 7.3 hours for the round trip, what was the average speed (in miles per hour) for the return trip?
A.8.4
B.8.6
C.8.8
D.9
Answer: D.9
Explanation: The time to go 36 miles was 18/12+18/10=1.5+1.8=3.3 hours.
The average speed for the return trip was 36 miles/4 hours= 9 mph.
The answer is D.
Question: The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
A.Rs. 3700
B.Rs. 3800
C.Rs. 3900
D.Rs. 4000
Answer: C.Rs. 3900
Explanation: Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.
Then, 10x = 4y or y = 5 x.
2
15x + 2y = 4000
15x + 2 x 5 x = 4000
2
20x = 4000
x = 200.
So, y = 5 x 200 = 500.
2
Hence, the cost of 12 chairs and 3 tables = 12x + 3y
= Rs. (2400 + 1500)
= Rs. 3900.
C)
Question: Consider a Number 3.1n3
n represent the hundredths digit in the number shown above. If the number is rounded to the nearest hundredth, which of the following could be the tenths digit in the rounded number?
A.2
B.1
C.3
D.4
Answer: B.1
Explanation: In this ques we are given the thousandth digit as 3, so the hundreth digit can take any value from 0-9. For the hundreth digit i considered 2 set of values (i) 0, 1, 2, 3 and (ii) 4, 5, 6, 7, 8, 9. Given that the thousandth digit is 3, the hundreth digit has to go up by 0, and correspondingly, the tenth digit should remain same.i.e 0-9.say 1
B
Question: Tomy started a software business by investing Rs.50,000. After 6months, Nanda joined her with a capital of $80,000. After 3years, they earned a profit of $24,500. What was Simran's share in the profit?
A.$8,500
B.$9,500
C.10,500 dollars
D.$11,500
Answer: C.10,500 dollars
Explanation: Tomy : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.
Tomy 's share = $24500 x	3/7	= $10,500.
C
Question: If the radii of umbra and penumbra cast by an object on a wall are of the ratio 2:6, what is the area of the penumbra ring around the umbra of the latter’s radius is 40 cms?
A.40288.57 centimeter square
B.40388.57cm^2
C.40488.57cm^2
D.40588.57cm^2
Answer: A.40288.57 centimeter square
Explanation: et the radius of umbra and penumbra are 2k and 6k.
Then as given radius of umbra=40cm
so 2k=40
k=20
radius of penumbra=20*6=120
area of penumbra ring around the umbra= area of penumbra-area of umbra
22/7*[(120)^2-(40)^2]
=40288.57cm^2
ANSWER:A
Question: A circle in the coordinate plane passes through points (-3, -2) and (1, -4). What is the smallest possible area of that circle?
A.13π
B.26π
C.262√π
D.5π
Answer: D.5π
Explanation: The distance between the two points is sqrt(20).
radius = sqrt(20)/2
Area= pi*(sqrt(20)/2)^2
D. 5π
Question: A cube with volume of 125 cm^3 is dropped in a fish tank with dimensions 3 m x 1 m x 2 m. If the tank is full of water, how much water will remain after the cube is droppped?
A.5.9999999 m^3
B.5.725 m^3
C.5.650 m^3
D.5.999875 m^3
Answer: D.5.999875 m^3
Explanation: Volume of fish tank = 3m x 1m x 2m = 6 m^3
125 cm^3 x (1 m^3 / 1,000,000 cm^3) = 0.000125 m^3
6-.000125 = 5.999875 m^3
Answer is D
Question: The fourteen digits of a credit card are to be written in the boxes shown above. If the sum of every three consecutive digits is 18, then the value of x is :
A.1
B.3
C.8
D.7
Answer: B.3
Explanation: Sol : A
Explanation:
Let us assume right most two squares are a , b
Then Sum of all the squares = 18 x 4 + a + b .......... (1)
Also Sum of the squares before 7 = 18
Sum of the squares between 7, x = 18
and sum of the squares between x , 8 = 18
So Sum of the 14 squares = 18 + 7 + 18 + x + 18 + 8 + a + b (2)
Equating 1 and 2 we get x = 3
Answer:B
Question: f(x) = 1/(1-x) find(f(f(f(x)))
A.1
B.x
C.2x
D.3x
Answer: B.x
Explanation: f(x) = 1/(1-x)
==>f(f(x)) = f(1/(1-x))
= 1/(1-(1/(1-x)))
= 1/((1-x-1)/(1-x))
= 1/(-x/(1-x))
= x-1/x
==> (f(f(f(x)))=f(x-1/x)
= 1/(1-(x-1/x))
= 1/((x-x+1)/x)
= 1/(1/x)
= x
ANSWER:B
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.192 in 4 Years?
A.5%
B.6%
C.3%
D.9%
Answer: B.6%
Explanation: 192 = (800*4*R)/100
R = 6%
Answer: B
Question: A children's gift store sells gift certificates in denominations of $3 and $5. The store sold 'm' $3 certificates and 'n' $5 certificates worth $93 on a Saturday afternoon. If 'm' and 'n' are natural numbers, how many different values can 'm' take?
A.5
B.7
C.6
D.31
Answer: C.6
Explanation: Explanatory Answer
Step 1: Key data
1. Total value of all certificates sold = $93.
2. Certificates sold were in denominations of $3 and $5.
3. Both 'm' and 'n' are natural numbers.
Step 2: Approach
The value of all certificates sold, 93 is divisible by 3.
So, a maximum of 31 $3 certificates and no $5 certificates could have been sold.
However, the question states that both 'm' and 'n' are natural numbers.
Hence, at least 1 $5 certificate should have been sold.
Let us reduce the number of $3 certificates from theoretical maximum count of 31 by say 'x' and correspondingly increase $5 certificates by 'y'.
Evidently, 3x = 5y because the value of $3 certificates reduced should be the same as the value of $5 certificates increased.
It means that x has to be a multiple of 5 and y has to be a multiple of 3.
Or $3 certificates reduce in steps of 5 certificates.
Step 3: List down possibilities
The following combinations are possible
1. m = 26, n = 3
2. m = 21, n = 6
3. m = 16, n = 9
4. m = 11, n = 12
5. m = 6, n = 15
6. m = 1, n = 18
An alternative way to think of the same concept - Replacing five $3 certificates with three $5 certificates leads to no change in the overall value of certficates sold and gives us a new combination each time. We need to see how many such combinations are possible.
Answer C
Question: A pump can fill a tank with a water in 2 hours. Because of a leak, it took 3 and 1/3 hours to fill the tank. The leak can drain all the water of the full tank in how many hours?
A.5 hrs
B.7 hrs
C.12 hrs
D.14 hrs
Answer: A.5 hrs
Explanation: The rate of the pump + leak = 3/10
1/2 - leak's rate = 3/10
leak's rate = 1/5
The leak will empty the tank in 5 hours.
The answer is A.
Question: A man counted his animals, 80 heads and 250 legs (ducks and goats). how many goats are there?
A.30
B.40
C.50
D.45
Answer: D.45
Explanation: let no of ducks=d and no of goat=g
d+g=80(heads)----------> eq 1
each duck has 2 legs and goat has 4 legs
2d+4g=250 and divide 2d+4g=250 by 2 we get d+2g=125 -----------> eq2
subtract eq1 from eq2
we get no of goats=45
ANSWER:D
Question: To asphalt 1km road, 30 men spent 12 days working 8 hours per day. How many days, 20 men will spend to asphalt a road of 2km working 8 hours a day?
A.40
B.36
C.42
D.44
Answer: B.36
Explanation: Man-hours required to asphalt 1 km road=30*12*8=2880
Man-hours required to asphalt 2 km road=2880*2=5760
Man-hours available per day=20*8=160
Therefore number of days=5760/240=36 days
Ans=B
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
A.1000
B.2288
C.2777
D.2999
Answer: A.1000
Explanation: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer:A