RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?
A.30
B.10
C.18
D.28
Answer: C.18
Explanation: Answer
Let A be the set of students who have enrolled for English and B be the set of students who have enrolled for German.
Then, (A U B) is the set of students who have enrolled at least one of the two subjects. As the students of the class have enrolled for at least one of the two subjects, A U B = 40
We know A U B = A + B - (A n B)
i.e, 40 = A + 22 - 12
or A = 30 which is the set of students who have enrolled for English and includes those who have enrolled for both the subjects.
However, we need to find out the number of students who have enrolled for only English = Students enrolled for English - Students enrolled for both German and English
= 30 - 12 = 18.
choice is (C)
Question: There are 10 points in a plane out of which 4 are collinear. Find the number of triangles formed by the points as vertices.
A.102
B.116
C.103
D.512
Answer: B.116
Explanation: The number of triangle can be formed by 10 points = 10C3.
Similarly, the number of triangle can be formed by 4 points when no one is collinear=4C3.
In the question, given 4 points are collinear, Thus, required number of triangle can be formed,
= 10C3-4C3 = 120-4 = 116.
Ans: B
Question: If 99<x<199 and 10<y<100, then the product xy CANNOT be equal to:
A.19,104
B.19,903
C.19,356.732
D.19,502
Answer: B.19,903
Explanation: Correct Answer: (B)
Determine the range of xy by multiplying the two extremes of each individual range together. The smallest value of xy must be greater than 99 * 10. The largest value must be less than 199 * 100. This means that 990 < xy < 19,900. (B) is outside of this range, so it is not a possible product of xy.
Question: Three numbers are in the ratio 4 : 5 : 6 and their average is 25. The largest number is :
A.30
B.98
C.27
D.21
Answer: A.30
Explanation: Explanation:
Let the numbers be 4x, 5x and 6x, Then, (4x + 5x + 6x ) / 3 = 25
=> 5x = 25
=> x = 5.
Largest number 6x = 30.'
Answer: A) 30
Question: If x and y are integers such that x^2= 2y and xy = 256, then x – y = ?
A.-30
B.-24
C.-5
D.5
Answer: B.-24
Explanation: here x and y are integers .
x^2=2y,xy =256.
substitute (x^2)/2=y in xy => x^3=256*2=>x^3=512.
here x^3 is positive ,
x is also positive.
x=8 then y=32.
x-y=-24
so option B is correct
Question: The entire contents of a full sack of flour can be used to make 15 cupcakes and 8 pizzas. The same full sack of flour can be used to make 5 cupcakes and 14 pizzas. If a full sack of flour is used to make only pizzas, how many pizzas can be made?
A.18 1/4
B.18 1/2
C.18 3/4
D.17
Answer: D.17
Explanation: 15x+8y=5x+14y
x=3/5y. Answer D
Question: If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?
A.Rs.1520
B.Rs.1570
C.Rs.1500
D.Rs.1550
Answer: C.Rs.1500
Explanation: Let the cost price of an article be Rs. x.
(19% of x) - (12% of x) = 105
19x/100 - 12x/100 = 105 => 7x = 105 * 100
=> x = 1500
Cost price = Rs.1500
Answer:C
Question: A manufacturer is using glass as the surface for the multi-touch screen of its smartphone. The glass on the manufactured phone has a 7% probability of not passing quality control tests. The quality control manager bundles the smartphone in groups of 10. If that bundle has any smartphone that does not pass the quality control test, the entire bundle of 10 is rejected.
What is the probability that a smartphone bundle that will be rejected by quality control?
A. 0.25
B. 1-0.93^10
C. 1-0.95^10
D. 1-0.05^10
Answer: B. 1-0.93^10
Explanation: Find the probability of the opposite event and subtract from 1.
The opposite event is that bundle will NOT be rejected by quality control, which will happen if all 10 phones pass the test, so P(all 10 phones pass test)=0.93^10.
P(at least one phone do not pass the test)=1- P(all 10 phones pass test)=1-0.93^10.
Answer: B.
Question: If there are half as many women as men in a group and an equal number of men and women do not own cars - a group that is 30% of the total. What fraction of the total is men who own cars?
A.3⁄20
B.31⁄60
C.9⁄40
D.1⁄3
Answer: B.31⁄60
Explanation: Consider a group of 100 women and 200 men, a total of 300 people. 30% of them, which is 90, form a group of people who don't own a car.
Half of them are men, and the other half are women, more precisely 45.
It means that there are 200 - 45 = 155 men who own a car, and this represents 155/300 = 31/60 of the total.
Answer B
Question: The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?
A.74%
B.44%
C.68%
D.64%
Answer: D.64%
Explanation: r = 3 πr2 = 9
r = 5 πr2 = 25
25 π – 16 π
100 ---- ? => 64%
Answer: D
Question: Running at the same constant rate, 6 identical machines can produce a total of 390 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
A.648
B.1800
C.2600
D.10800
Answer: C.2600
Explanation: Let the required number of bottles be x.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
Machines	6	:	10	:: 390 : x
Time (in minutes)	1	:	4
6 x 1 x x = 10 x 4 x 390
x =	(10 x 4 x 390)/(6)
x = 2600.
ANSWER:C
Question: Each child has 2 pencils and 13 Skittles. If there are 11 children, how many pencils are there in total?
A.16
B.12
C.18
D.22
Answer: D.22
Explanation: 2*11=22.Answer is D.
Question: Line R has the equation 3x + y = 7. Which of the following lines is perpendicular to Line R?
A. y = 3x + 4
B. y = –3x – 6
C. y = (1/3)x – 1
D. y = (–1/3)x + 2
Answer: C. y = (1/3)x – 1
Explanation: I first rewrote the equation in the standard y=mx+b form. Therefore, Line R as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7.
Thought process next is what line would be perpendicular to Line R? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one.
Question: In a village the average age of n people is 42 years. But after the verification it was found that the age of a person had been considered 20 years less than the actual age, so the new average, after the correction,increased by 1. The value of n is?
A.33
B.20
C.88
D.37
Answer: B.20
Explanation: It is the same as a person with 20 years more age replaces an existing person of the group ( or village)
Since the total age of the village having n persons, is being increased by 20 years and the average age of village is being increased by 1 year, hence there are total 20 people in the village.
Alternatively : ( n x 42 ) + 20 = ( n x 43 )
=> n=20
Answer: B
Question: The average (arithmetic mean) of the even integers from 0 to 80 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 40 inclusive?
A.20
B.24
C.28
D.36
Answer: A.20
Explanation: The sum of even numbers from 0 to N is 2 + 4 +...+ N
= 2(1 + 2 + ...+ N/2)
= 2(N/2)(N/2+1)/2 = (N/2)(N/2+1)
The average is (N/2)(N/2+1)/(N/2+1) = N/2
The average of the even numbers from 0 to 80 is 80/2 = 40
The average of the even numbers from 0 to 40 is 40/2 = 20
The answer is A.
Question: A train, 130130 metres long travels at a speed of 4545 km/hr crosses a bridge in 3030 seconds. The length of the bridge is
A.270 metres
B.245 metres
C.235 metres
D.220 metres
Answer: B.245 metres
Explanation: Explanation:
Solution 1Speed =45 km/hr=45Ã—518 m/s=12.5 m/s=45 km/hr=45Ã—518 m/s=12.5 m/s
Time =30 s=30 s
Distance travelled =12.5Ã—30=375 m=12.5Ã—30=375 m
Length of the bridge =375âˆ’130=245 m
ANSWER IS B
Question: At what rate percent per annum will the simple interest on a sum of money be 1/5 of the amount in 10 years?
A.2%
B.7%
C.9%
D.3%
Answer: A.2%
Explanation: Let sum = x. Then, S.I. = x/5, Time
= 10 years.
Rate = (100 * x) / (x * 5 * 10)
= 2%
Answer: A
Question: 45 x ? = 35% of 900
A.16.2
B.7
C.5
D.500
Answer: B.7
Explanation: Answer
Let 45 x A = (35 x 900)/100
∴ A = (35 x 9)/45 = 7
Correct Option: B
Question: If a% of b is the same as 8/9 of 450, then the value of ab is?
A.40000
B.45120
C.65200
D.32560
Answer: A.40000
Explanation: a/100 * b = 8/9 * 450
xy = 400*100 = 40000
Answer is A
Question: How many four-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number.
A.480
B.475
C.485
D.490
Answer: B.475
Explanation: N=(4*5-1)*5*5=475
where
4 cases of first digit {2,4,6,8}
5 cases of second digit {0,2,4,6,8}
1 case of 44 for two leftmost digit
5 cases of third digit {1,3,5,7,9}
5 cases of fourth digit {1,3,5,7,9}
B
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
A.Rs. 4800
B.Rs. 3600
C.Rs. 3560
D.Rs. 4530
Answer: D.Rs. 4530
Explanation: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5 = Rs. 4530
ANSWER:D
Question: A watch was sold at a loss of 15%. If it was sold for Rs.400 more, there would have been a gain of 5%. What is the cost price?
A.1600
B.2998
C.2778
D.2788
Answer: A.1600
Explanation: 85%
120%
--------
25% ---- 400
100% ---- ? => Rs.1600
Answer:A
Question: Look at this series: 22, 21, 23, 22, 24, 23, ... What number should come next?
A.22
B.24
C.25
D.26
Answer: C.25
Explanation: Explanation: In this simple alternating subtraction and addition series; 1 is subtracted, then 2 is added, and so on.
Answer: Option C
Question: If the Average of 10 consecutive integers is 22.5 then the 10th integer is :-
A.15
B.20
C.23
D.27
Answer: D.27
Explanation: The average falls between the 5th and 6th integers,
integer 5 = 22, integer 6 = 23.
Counting up to the tenth integer
we get 27.
ANSWER:D
Question: The entrance ticket at the Imax theatre in Chennai is worth Rs 250. The sale of tickets increased by 50% when the price of the ticket was lowered. However, the collections recorded a decrease of 17.5%. The price of the ticket is reduced by how much rupees?
A.Rs150
B.Rs112.50
C.Rs105
D.Rs120
Answer: B.Rs112.50
Explanation: let the no. of tickets sold before = x
then the no. of tickets sold after = 1.5x
Collection Before = x*250
Collection after = 1.5x* = (250x*82.5)100
=137.5
change in price =250 - 137.5
=112.5
ANSWER:B
Question: Harkamal purchased 8kg of grapes at the rate of 90 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
A.A)1055
B.B)1215
C.C)1065
D.D)1070
Answer: B.B)1215
Explanation: Cost of 8 kg grapes = 90 × 8 = 720.
Cost of 9 kg of mangoes = 55 × 9 = 495.
Total cost he has to pay = 720 + 495 = 1215.
B)
Question: A store sells eight different kinds of shirts. If we want to buy two different kinds of shirts, how many possible combinations of two shirts can we buy?
A.22
B.24
C.26
D.28
Answer: D.28
Explanation: 8C2=28.
The answer is D.
Question: In a barrel of juice there is 40 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?
A.3:2.
B.2:1.
C.3:1.
D.4:3.
Answer: A.3:2.
Explanation: Price of 40 L juice= 3x
1L= 3x/40
Price of 80 L beer= 4x
1L= 4x/80
Ratio of 1 L price = 3x/40/4x/80= 3:2
A is the answer
Question: A individuals pledged to pay equal contributions so that a charity’s goal of $x could be reached. If d of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal?
A.dx/A(A - d)
B.dx
C.a
D.A-d
Answer: A.dx/A(A - d)
Explanation: Number of individuals = A
Amount paid by each individual = n
Total expected amount = Charity's goal = nA = x
n = x/A
Number of individuals who fail to pay = d
Contribution from individuals who would fail to pay = dx/A --> Additional amount
Number of individuals who are paying = A - d
Additional amount has to be divided among the (A - d) individuals --> dx/A(A - d)
A
Question: A girl was riding her scooter. Her father wanted to calculate her speed. He knew that the street was 600 meters from end to end. He saw his daughter make the roundtrip 6 times. It took her 20 minutes to complete those 6 trips. How fast was the girl riding her scooter in kilometers per hour?
A.2
B.2.4
C.1.2
D.2.1
Answer: B.2.4
Explanation: The distance of the street was 600 meters.
The made the roundtrip 6 times, which would be 2 trips for each roundtrip.
Multiply 12 times 600 to get the total distance. 600 * 12 = 7200 meters of 7.2 km.
The question asked for the speed in km/hour and 20 minutes is one third of an hour.
Multiply 7200 by 1/3 to get approximately 2400 meters.
Correct answer is B
Question: An staff identification code consists of a vowel followed by a 3-digit number greater than 200. Exactly 2 of the 3 digits in the code should be identical. How many different codes is it possible to form?
A.211
B.216
C.1075
D.1080
Answer: C.1075
Explanation: An staff identification code will be of the type -,-,-,-
first digit can be selected from any of the 5 vowels in 5C1 ways
now for the remaining three digit lets consider the following two cases
case 1: when the number is greater than 200 but less than 300
number will be of the type 2,_,_. now suppose repeating number is same as first digit number i.e. 2. and the third number is one of the remaining 9 numbers (we are rejecting 2 here, because it will result in 222, which is not acceptable as per the given condition). thus these two number can arrange themselves in two blank spaces in 2! ways. hence total number of numbers in which repeating digit is same as the first digit = 1.9.2! =18
now, suppose that repeating number is different than first digit. thus possible case in this case are 8 as listed below:
211
233
244
255
266
277
288
299
here again we have rejected 200( because number must be greater than 200) and 222 ( exactly two repeating digits are allowed)
thus total possible cases are 18 + 8 =26
case 2: number ranging from 300 to 999
here for first digit we have 7 cases (3,4,5,6,7,8,9)
now if the repeating number is same as the first number then we will have 18 cases ( same reasoning as mentioned in the previous case)
if the repeating number is different than first digit number then we will have 9 cases ( because here number ending with two zeros are allowed)
hence total number of ways = 7(18+9) = 189
thus different number of codes = 5(189+26) = 1075
hence C
Question: A thief is spotted by a policeman from a distance of 100metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 15km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ?
A.A)1km
B.B)300m
C.C)650m
D.D)750m
Answer: B.B)300m
Explanation: Relative speed of the policeman = 20-15 = 5 km/hr
time taken by policeman to cover 100m = (100/1000)*(1/5) = 1/50 hr
In 1/50 hr the thief covers a distance of 15/50 km = 3/10 km = 300m
Answer is B
Question: The total of the ages of Jayant, Prem and Saransh is 93 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Jayant?
A.24 years
B.32 years
C.34 years
D.38 years
Answer: A.24 years
Explanation: Solution
Let the ages of Jayant, Prem and Saransh 10 years ago be 2x, 3x and 4x years respectively. Then,
(2x + 10)+(3x + 10)+(4x + 10)	= 93.
‹=›9x = 63
x = 7.
∴ Jayant's present age = 2x + 10 = 24 years.
Answer A
Question: Cereal A is 8% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
A. 2:9
B. 2:7
C. 1:2
D. 1:4
Answer: C. 1:2
Explanation: (8/100)A+(2/100)B = (4/100)(A+B)
4A =2B
=> A/B = 1/2
Answer is C.
Question: What is the range of all the roots of |x^2 - 3| = x ?
A.4
B.3
C.2
D.1
Answer: C.2
Explanation: we get 2 quadratic equations here ..
1) x^2-x-3=0 ....... roots 2 , -1
2) x^2+x-3=0 ........ roots -2, 1
Inserting each root in given equation , it can be seen that -1 and -2 do not satisfy the equations .
So value of x for given equation .... x=3 or x=1
I guess range is 3-1 =2
C
Question: Will must choose a 3-character computer password, consisting of 3 distinct digits, in any order.From how many different passwords can Will choose?
A.390
B.2,340
C.4,320
D.7,020
Answer: C.4,320
Explanation: 10C1*9C1*8C1 = 720.
=>720 * 3 ! = 4320.
Option E is correct answer...but OA is C.
Question: A train moves past a post and a platform 264 metre long in 8 seconds and 20 seconds respectively. What is the speed of the train?
A.79.2 km/hr
B.82.4 km/hr
C.69.7 km/hr
D.49.8 km/hr
Answer: A.79.2 km/hr
Explanation: The train can cover a distance equal to its length in 8 seconds. Therefore, additional
(20âˆ’8)=12 seconds was taken to cross the platform.
Hence, speed of the train=264/12=22 m/s
=22 Ã— 18/5=79.2 km/hr
ANSWER:A
Question: A person buys 18 local tickets for Rs 110. Each first class ticket costs Rs 10 and each second class ticket costs Rs 3. What will another lot of 18 tickets in which the numbers of first class and second class tickets are interchanged cost?
A.112
B.118
C.121
D.124
Answer: D.124
Explanation: Explanation :
Let, there are x first class ticket and (18-x) second class tickets.
Then,
110 = 10x + 3(18−x).
=>110=10x+54−3x.
=>7x=56.
=>x=8.
If the number of the first class and second class tickets are interchanged, then the total cost would be 10×10 + 3 × 8=124.
Answer : D
Question: In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 6 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
A.30
B.58
C.60
D.90
Answer: B.58
Explanation: I believe there is a better way to do it.
Basically one of the options should satisfy the given criteria.
60 did
1/5 *60 =12
2/3*60=40
so total distance
52 + remaining 6 =58
Answer B
Question: The price of a microchip declines by 67 percent every 6 months. At this rate, approximately how many years will it take for the price of an $81 microchip to reach $1?
A.1.5 years
B.2 years
C.3 years
D.13 years
Answer: B.2 years
Explanation: I think the fastest way is
81 *(1/3)^n = 1
n =4
So 2 yrs
ANSWER:B
Question: Find the invalid no.from the following series 13, 18, 25, 30, 37, 40
A.23
B.26
C.40
D.42
Answer: C.40
Explanation: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong.
C
Question: 20% of major airline companies equip their planes with wireless internet access. 70% of major airlines offer passengers free on-board snacks. What is the greatest possible percentage of major airline companies that offer both wireless internet and free on-board snacks?
A.20%
B.30%
C.40%
D.70%
Answer: A.20%
Explanation: To maximize the percentage of companies offering both, let's assume that all 20% of companies which offer wireless internet also offer snacks.
The answer is A.
Question: A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
A.5
B.6
C.2
D.3
Answer: D.3
Explanation: 40*(40/100) = 16 --- 64
? --- 12 => Rs.3
Answer: D
Question: A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 32%?
A.Rs. 21000
B.Rs. 17500
C.Rs. 19000
D.Rs. 24500
Answer: A.Rs. 21000
Explanation: Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.
Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)
=> 130/100 x + 140/100 (35000 - x) = 35000 + 32/100 (35000)
x = 28000
35000 - x = 7000
Difference in the cost prices of televisions = Rs. 21000
ANSWER:A
Question: Mother,her daughter and her grand child weighs 140 kg. daughter and her daughter(child) weighs 60 kg. child is 1/5th of her grand mother. What is the age of the daughter?
A.44
B.47
C.48
D.49
Answer: A.44
Explanation: mother + daughter + child = 140kg
daughter + child = 60kg
mother = 140 - 60 = 80kg
child = 1/5th of mother = (1/5)*80 = 16kg
So now daughter = 140 -(mother + child) = 140 - (80+16) = 44kg
ANSWER:A
Question: If two dice are thrown simultaneously, then find the probability that the sum of numbers appeared on the dice is 6 or 7?
A.5/6
B.7/36
C.5/36
D.11/36
Answer: D.11/36
Explanation: The sum of numbers appeared is 6 or 7. Therefore, the required sums are 6 or 7, i.e., the required events are (1,5), (5,1), (2,4), (4,2), (3,3), (1,6), (6,1), (2,5), (5,2), (3,4), (4,3)
i.e., for 6, n(E) = 5 and for 7, n(E) = 6
Therefore, the required probability = n(E)/n(S) = 11/36.
ANSWER:D
Question: The average age of 36 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?
A.66
B.77
C.51
D.98
Answer: C.51
Explanation: Explanation:
Age of the teacher = (37 * 15 - 36 * 14) years = 51 years.
Answer: C) 51 years
Question: If a car went the first third of the distance at 80 kmh, the second third at 18 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?
A.34 kmh
B.40 kmh
C.42 kmh
D.44 kmh
Answer: A.34 kmh
Explanation: Assume D/3 = 720 (this number is convenient because it is divisible by 80, 18 and 48)
So:
720 = 80*T1 = 9 hrs
720 = 18*T2 = 40 hrs
720 = 48*T3 = 15 hrs
T = T1 + T2 + T3 = 64 hrs
D = RT
(720*3) = R*64
R = 33.75
ANSWER: A
Question: Cindy has her eye on a sundress but thinks it is too expensive. It goes on sale for 15% less than the original price. Before Cindy can buy the dress, however, the store raises the new price by 25%. If the dress cost $68 after it went on sale for 15% off, what is the difference between the original price and the final price?
A.$0.00
B.$1.00
C.$3.40
D.$5.00
Answer: D.$5.00
Explanation: 0.85*{Original Price} = $68 --> {Original Price} = $80.
{Final Price} = $68*1.25 = $85.
The difference = $85 - $85 = $5.
Answer: D.
Question: A train 360 m long is running at a speed of 54 km/hr. In what time will it pass a bridge 140 m long?
A.40 sec
B.11 sec
C.88 sec
D.33.33 sec
Answer: D.33.33 sec
Explanation: Speed = 54 * 5/18 = 15 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 1/15 = 33.33 sec
Answer: D
Question: After 10% of the inhabitants of a village disappeared, a panic set in during which 25% of the remaining inhabitants left the village. At that time, the population was reduced to 5535. What was the number of original inhabitants?
A.7900
B.8200
C.8500
D.8800
Answer: B.8200
Explanation: Let the total number of original inhabitants be x.
(75/100) * (90/100) * x = 5535
(27/40) * x = 5535
x = 5535 * 40 / 27 = 8200
The answer is B.
Question: A particular parking garage is increasing its rates by 30 percent per month. Bob decides to reduce the number of days he uses the garage per month so that the amount he spends at the garage per month remains unchanged. Which of the following is closest to Bob’s percentage reduction in the number of days he uses the garage each month?
A.12%
B.16%
C.20%
D.23%
Answer: D.23%
Explanation: Let x be the original number of days that Bob used the garage.
Let P be the original cost per day.
Let N*x be the new number of days that Bob uses the garage.
N*x*1.3P = x*P
N*x = x/1.3 which is about 0.77x, thus a 23% reduction.
The answer is D.