RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.36, the number of 25 paisa coins is?
A.30
B.36
C.32
D.34
Answer: B.36
Explanation: 5x 6x 2x
50 25 100
250x + 150x + 200x = 3600
600x = 3600
x = 6 => 6x = 36
ANSWER:B
Question: Bob bikes to school every day at a steady rate of c miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?
A.(c + y) / t
B.2(c + t) / cy
C.2cyt / (c + y)
D.2(x + y + t) / xy
Answer: C.2cyt / (c + y)
Explanation: If we choose for d (distance): 10 miles, for c 10 and for y 5.
t would be 90 minutes or 1,5 hours.
If I try this for answer choice C it fits.
Question: A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone?
A.1 1/9 days
B.1 1/2 days
C.1 2/2 days
D.2 1/2 days
Answer: B.1 1/2 days
Explanation: 3/20 * 2 + (2 + x)/5 = 1
x = 1 1/2 days
Answer:B
Question: A 60 cm long wire is to be cut into two pieces so that one piece will be 2/4th of the other, how many centimeters will the shorter piece be?
A.A)73
B.B)20
C.C)83
D.D)21
Answer: B.B)20
Explanation: Explanation:
1: 2/4 = 4: 2
2/6* 60 = 20
Answer: Option B
Question: The GDP of a country is $13.8 billion, and the total production of one of its industries is $3.3 billion. If the GDP were to grow by 5% per year in the future, which of the following would be the MINIMUM required annual growth in this industry that would it represent more than half of the GDP in ten years?
A.10%
B.15%
C.20%
D.25%
Answer: B.15%
Explanation: GDP in 10 years with this rate would be - 13.8 (1+0.05)^10
Half of the above value - 6.9 (1.05)^10
Industry's annual growth (say x is the rate of growth of the industry annually) = 3.3 (1+(x/100))^10
Now, the minimum of above value has to be greater than the half of the value of GDP.
3.3 (1+(x/100))^10 > 6.9 (1.05)^10
((1+(x/100))/1.05)^10 > 2 (approx)
Minimum value of x to satisfy this equation is 15
Hence B
Question: If Scott has earned 924 dollars by working 6 hrs/day a week at a constant daily rate for 2 weeks, which of the following represents his daily wage?
A.13
B.12
C.11
D.17
Answer: C.11
Explanation: Scott total earning = 924
No days he worked = 6 * 7 = 42
Rate = 2 week
Daily wage = total / (Rate * days)
= 924/(6*7*2)
= 11
C is correct answer...
Question: A speaks truth in 75% case and B in 80% of the cases. In what percentage of cases are they likely to contradict each other, narrating the same incident?
A.20%
B.25%
C.30%
D.35%
Answer: D.35%
Explanation: P( A)=75/100, P(B)=80/100
P( A’)=1/4
P(B’)=1/5
P( A and B contradict each other)=P(A).P(B’)+P(A’).P(B)
=35%
ANSWER D 35%
Question: Three unbiased coin are tossed. What is the probability of getting atmost
one head?
A.1/2
B.1/4
C.7/8
D.3/5
Answer: C.7/8
Explanation: Here n(S)= 2^3
Let E=event of getting atmost one head =
n(E)= 7
P(E)=n(E)/n(S)=7/8
Answer option C)
Question: In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 1 ounces of corn syrup, how many ounces of water does it contain?
A.15
B.30
C.45
D.60
Answer: A.15
Explanation: Standard:
Fl: Corn S: Water = 1:12:30
Sport:
Fl: Corn S: Water = 3:12:180
This simplifies to 1:4:60
If the large bottle has a capacity of x ounces, then
4x / 65 = 1.
So, x =65 / 4 ounces.
Water = (60 / 65) * (65 / 4) = 15 ounces.
Ans A
Question: A box contains four dimes, of which two dimes have heads on both their faces, one dime has tail on both its faces and the fourth dime is a normal one. A dime is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the dime tossed is also a head.
A.3/5
B.4/5
C.2/5
D.3/4
Answer: B.4/5
Explanation: There are four ways (2 heads in one two-headed dime and 2 heads in the other two-headed dime)
How many ways can you get heads from this entire set of dimes? There are five ways (four as identified above and one from the normal coin)
Therefore probability = 4/5
Option B
Question: Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?
A.10
B.12
C.14
D.16
Answer: B.12
Explanation: Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+26
3x + 6 = x + 26
2x = 20
\inline \therefore x = 10
\inline \therefore Middle number = x + 2 = 10+2 = 12
B
Question: A shoe merchant has declared a 10% rebate in prices. How much rebate would one get if he purchases 5 pairs of shoes at Rs.28 each?
A.11
B.12
C.13
D.14
Answer: D.14
Explanation: Explanation:
5 shirts * Rs.28 = Rs.140
Rebate = 10% * 140 = 14
Correct Option : D
Question: Let f(x,y) be defined as the remainder when (x–y)! is divided by x. If x=16, what is the maximum value of y for which f(x,y)=0?
A.5
B.10
C.15
D.20
Answer: B.10
Explanation: The question is finding y such that (16-y)! is a multiple of 16. That means we need to have 2^4 in (16-y)!
6! is the smallest factorial number with 2^4 as a factor.
16-y = 6
y = 10
The answer is B.
Question: Obra drove 180π meters along a circular track. If the area enclosed by the circular track on which she drove is 57,600π square meters, what percentage of the circular track did Obra drive?
A.37.5%
B.12.5%
C.18.75%
D.25%
Answer: A.37.5%
Explanation: area enclosed by the circular track on which she drove is 57,600π square meters
So, π(r^2) = 57,600π ---> (r^2)=57,600 ---> r=240
Circumference of the circular track = 2πr = 480π
Therefore, part of circumference covered = 180π/480π =37.5%
Hence, answer is A.
Question: Find the area of a rhombus one side of which measures 20 cm and one diagonal is 28 cm.
A.200cm2
B.300cm2
C.400cm2
D.448cm2
Answer: D.448cm2
Explanation: Explanation: Let other diagonal = 2x cm.
Since diagonals of a rhombus bisect each other at right angles, we have:
(20)2 = (12)2 + (x)2 =>x =√(20)2 – (12)2= √256= 16 cm. _I
So, other diagonal = 32 cm.
Area of rhombus = (1/2) x (Product of diagonals) =(1/2× 28 x 32) cm2 = 448 cm2
Answer: Option D
Question: The period of 2 sin x cos x is
A.4 pi 2
B.2 pi
C.4 pi
D.pi
Answer: D.pi
Explanation: Solution
According to trigonometric identities, 2 sin x cos x = sin(2x) and the period is given by.
2 pi / 2 = pi
Answer D
Question: Score Interval Number of Scores
50-59 2
60-69 10
70-79 16
80-89 27
90-99 17
The table shows a distribution of test scores. Which score interval contains the median of the 72 scores?
A.a) 60-69
B.b) 70-79
C.c) 80-89
D.d) 90-99
Answer: C.c) 80-89
Explanation: 36th person
80-89 C
Question: Find the least number when successively divided by 2, 3 and 7 leaves remainders 1, 2 and 3 respectively?
A.67
B.65
C.75
D.61
Answer: B.65
Explanation: 2) 65 (32 3) 32 (10 7) 10 (1
64 30 7
-------- -------- - -----
1 2 3
=> 65
ANSWER:B
Question: Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,600 nuts and 1,600 bolts?
A.1,250 seconds
B.1,500 seconds
C.1,750 seconds
D.2,400 seconds
Answer: D.2,400 seconds
Explanation: I used the Rate formula (R=\frac{1}{T})
Rate of 1st machine = Rate of making 1 bolt + Rate of making 1 nut = 1 + \frac{1}{2}
Rate of 1st machine = Rate of 2nd machine
After this I got lost.
Please can you help how to approach using algebra?
I wouldn't complicate:
1 machine needs 1,600*1 seconds to produce 1,600 bolts, so 2 need half of that, so 1,600/2 seconds.=800
1 machine needs 1,600*2 seconds to produce 1,600 nuts, so 2 need half of that, so 1,600*2/2 seconds.=1600
total = 2400
D
Question: At a certain store, the price of a pair of shoes is twenty dollars more than three times the price of a pair of jeans and the price of a sweater is seventy percent more than the price of a pair of shoes. If the price of a pair of jeans is j dollars at this store, then what is the price, in dollars, of a pair of shoes, a sweater and a pair of jeans, in terms of j ?
A.9.1j + 54
B.3j + 20
C.4.5j + 30
D.5.5j + 30
Answer: A.9.1j + 54
Explanation: Ans A
Given
Price of Jeans = J
Price of shoes = 20+3J
Price of Sweater = 1.7(20+3J)
Total Price of all three items = J+20+3J+1.7(20+3J) = 54+9.1J
Question: A certain rectangular crate measures 8 feet by 14 feet by 16 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?
A.4
B.5
C.6
D.8
Answer: C.6
Explanation: Ans is "B".
For max volume of cylinder (pi*r^2*h) we need to max out r^2*h. We don't know what the dimensions of the crate refer to. . Therefore for max vol base should be 14x20 i.e. of radius 12/2 = 6
C
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 1 : 3?
A. 48 kmph
A.33
B.480/9
C.28
D.27/8
Answer: B.480/9
Explanation: Let the distances between city A to B and B to C be x km and 3x km respectively.
Total time taken to cover from A to C
= (x)/40 + (3x)/60 = (3x + 6x)/120 = 9x/120 Average speed = (x + 3x)/(9x/120) = 480/9 kmph.
Answer: B
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 1000 more than D, what is B's share?
A.Rs.2008
B.Rs.2039
C.Rs.2000
D.Rs.2039
Answer: C.Rs.2000
Explanation: Let the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively.
Then, 4x - 3x = 1000 => x = 1000.
B's share = Rs. 2x = 2 * 1000 = Rs.2000.
Answer: C
Question: A qualified worker digs a well in 5 hours. He invites 2 apprentices, both capable of working 3/5 as fast and 2 trainees both working 1/5 as fast as he. If the five-person team digs the same well, how much time does the team need to finish the job?
A.1:42
B.1:34
C.1:44
D.1:54
Answer: A.1:42
Explanation: and answer is correct as you have calculated : 100/59 hrs that is 1.71 hrs - 1 hr and 42minutes, so 1:42, hence,A.
Question: Which of the following options is the possible total number of people in a hall given that the number of people is a multiple of both 8 and 14.?
A.64
B.72
C.56
D.80
Answer: C.56
Explanation: the number of people are a multiple of both 8 and 14, so it must be divisible by 8 and 14.
using the elimination method look for a number that is both divisible by 8 and 14,
of all the options only 56 is divisible by 8 and 14.
[ 56/8=1 and 56/14=4]
answer :C
Question: Jill works as a waitress at the local diner where she earns an hourly wage of $4.00 per hour and a standard tip rate of 15% of the cost of the orders she serves. If she worked two 8-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?
A.280
B.300
C.160
D.350
Answer: C.160
Explanation: Jill earns 4 dollars/hour and the hourly tip is (3/20)*40.
Jill thus earns 4*8+8*2*3 per day(or 4(8)+6(8)=10(8)=80).
Jill has worked for 2 days -> 80*2=160.
This matches answer choice C.
Question: James took a 3-hour bike ride. In the second hour he travlled 18 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride?
A.54.0
B.54.9
C.55.5
D.57.0
Answer: C.55.5
Explanation: Let the distance travelled in the first hour be x. Thus, 1.2x = 18 , x = 15. Now, the distance travelled in the 3rd hour = 18+1/4∗18= The only option ending with a 0.5 in the decimal place is C.
ANSWER:C
Question: Donovan and Michael are racing around a circular 600-meter track. If Donovan runs each lap in 45 seconds and Michael runs each lap in 40 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time?
A.8
B.7
C.9
D.6
Answer: C.9
Explanation: One way of approaching this question is by Relative speed method
1. Speed/ Rate of Donovan = Distance/ time => 600/45 =>40/3
2. Speed/ Rate of Michael = Distance/ time => 600/40 => 15
Relative Speed between them = 15 - 40/3 => 5/3 (We subtract the Rates if moving in the same direction and add the rates if moving in the opposite direction)
In order to pass Donovan-
Distance to be covered = 600, Relative Rate = 5/3
Total Time taken by Micheal to surpass Donovan = Distance / rate => 600*3/5 => 360
No. of laps taken by Michael = Total time / Michael's rate => 360/40 => 9
Hence correct answer is 9 Laps.
C
Question: The profits of QRS company rose 30% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June?
A.15%
B.32%
C.56%
D.62%
Answer: C.56%
Explanation: Assume 100 in march , then 130 in April as 30% increase , Then 104 in may as 20% decrease from April , and then 156 in june which is 150% of 104 .
So overall increase is from 100 to 156 is 56%
Answer C
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides?
A.3
B.5
C.6
D.87
Answer: A.3
Explanation: S = (1 + 2 + 3)/2 = 3
=> No triangle exists
Answer: A
Question: Every month a man consumes 25 kg rice and 9 kg wheat. The price of rice is 20% of the price of wheat and thus he spends total Rs. 350 on the rice and wheat per month. If the price of wheat is increased by 20% then what is the percentage reduction of rice consumption for the same expenditure of Rs. 350? Given that the price of rice and consumption of wheat is constant :
A.40%
B.25%
C.36%
D.24%
Answer: C.36%
Explanation: Solution: Let the price of wheat is x per kg. Then price of wheat will be 5x per kg.
Expenditure on rice = 25*x = 25x.
Expenditure of wheat = 9*5x = 45x.
Total cost,
25x + 45x = 350.
70x = 350.
x = 5.
Hence, price of Rice = Rs. 5 per kg.
Price of wheat = 25 per kg.
Now, price of wheat = 25 ---- 20% ↑----> Rs. 30 per kg.
Let the new amount of rice is N kg, then
N*5 + 9*30 = 350.
N = 16 kg.
%decrease in the amount of rice = [(25-16)*100]/25 = 36%
Answer: Option C
Question: How much water must be added to 52 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre?
A.10 litres
B.13 litres
C.15 litres
D.18 litres
Answer: B.13 litres
Explanation: C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3
∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4
∴ Quantity of water to be added to 52 litres of milk
= (1⁄4 × 52) litres = 13 litres.
Answer B
Question: Look at this series: 53, 53, 43, 43, 33, 33, ... What number should come next?
A.50
B.40
C.23
D.13
Answer: C.23
Explanation: In this series, each number is repeated, then 10 is subtracted to arrive at the next number.
Answer is C
Question: In how much time will a train of length 100 m, moving at 34 kmph cross an electric pole?
A.15.59 sec
B.12.59 sec
C.10.59 sec
D.11.59 sec
Answer: C.10.59 sec
Explanation: Convert kmph to mps. 34 kmph = 34 * 5/18 = 9.44 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 100/9.44 = 10.59 sec.
ANSWER:C
Question: The savings of employee equals income minus expenditure.If the income of A,B,C are in the ratio 1:2:3 and their expense ratio 3:2:1 then what is the order of the employees in increasing order of their size of their savings?
A.22
B.281
C.A<B<C
D.28
Answer: B.281
Explanation: As the the ratio of their incomes are in ascending order, and their expenses are in descending order, their savings also in their incomes order.
So savings order = A < B < C
Answer:B
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 36 kilometers, Maxwell's walking speed is 3 km/h, and Brad's running speed is 6 km/h. What is the distance traveled by Maxwell when they meet in the middle?
A.12
B.14
C.15
D.13
Answer: A.12
Explanation: Consider Max starts from Point A and Brad Starts from Point B and move towards each other.
Assume they shall meet at point O after Time 'T'. The question asks us to find OA.
From the question stem we can make out :- Distance OA = 50km - Distance OB
=> 3xT = 36 - 6xT (i.e distance =Speed x Time)
=> 9T = 36
Hence T = 4
OA = 3 x 4 = 12 Km
Answer : A
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. What are the marks obtained by them?
A.42, 33
B.42, 31
C.40, 33
D.39, 33
Answer: A.42, 33
Explanation: Let the marks secured by them be x and (x + 9)
Then sum of their marks = x + (x + 9) = 2x + 9
Given that (x + 9) was 56% of the sum of their marks
=>(x+9) = 56/100(2x+9)
=>(x+9) = 14/25(2x+9)
=> 25x + 225 = 28x + 126
=> 3x = 99
=> x = 33
Then (x + 9) = 33 + 9 = 42
Hence their marks are 33 and 42
A)
Question: There are three prizes to be distributed among ten students. If no students gets more than one prize, then this can be done in?
A.10
B.45
C.95
D.120
Answer: D.120
Explanation: Explanation :
3 prize among 10 students can be distributed in 10C3 ways = 120 ways.
Answer : D
Question: Difference between two numbers is 5, six times of the smaller lacks by 10 from the four times of the greater. Find the numbers?
A.10,5
B.9,7
C.11,9
D.13,11
Answer: A.10,5
Explanation: Explanation:
x – y = 5
4x – 6y = 10
x = 10 y = 5
A)
Question: Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is?
A.36
B.76
C.98
D.27
Answer: A.36
Explanation: (3x-9):(5x-9)
= 9:17
x = 12 => 3x
= 36
Answer:A
Question: An urn contains 10 balls, numbered from 1 to 10. If 2 balls are selected at random with replacement from the urn, what is the probability F that the sum of the 2 numbers on the balls will be even?
A.25%
B.37.5%
C.50%
D.62.5%
Answer: C.50%
Explanation: Correct Answer: C
Since there are 5 even numbered balls and 5 odd numbered balls, the probability F of selecting either an even or an odd is 5/10= 1/2. In order for the sum of the numbers on the two balls to be even, either both numbers must be even or both numbers must be odd; one even and one odd number would add to an odd number. The probability of selecting two even numbers is:
1/2 * 1/2= 1/4
The probability of selecting two odd numbers is also:
1/2 * 1/2= 1/4
Adding both probabilities gives 1/4+1/4= 1/2 , or 50%, as the probability that the sum of the numbers will be even. Thus, the correct answer is (C).
Question: If (z + 3)/5 is an integer, what is remainder when z is divided by 5?
A.2
B.3
C.4
D.5
Answer: A.2
Explanation: Assume the answer choices as the value of z
A) 2; (2+3)/5 = 1 satisfies the equation
B) 3; (3+3)/5 = 1.2 Not an integer
C) 4; (4+3)/5 = 1.4 Not an integer
D) 5; (5+3)/5 = 1.6 Not an integer
E) 6; (6+3)/5 = 1.8 Not an integer
Answer: A
Question: A round table conference to be held between 20 delegates of 20 countries. In how many ways can they seated if two particular delegates are always to sit together?
A.14!*5!
B.22!*7!
C.18!*2!
D.28!*1!
Answer: C.18!*2!
Explanation: Regarding two particular delegates who are to sit together as on one person, we have only 18+1=19 persons.these 19 persons can be seated at the round table in 18! ways.
But two particular persons can be arranged among themselves in 2! ways.
Required number =18!*2!
Answer is C
Question: Dany bought a total of 24 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?
A.4
B.10
C.7
D.18
Answer: D.18
Explanation: Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 24. Hence
X + Y = 24
If X is the number of cards at $0.25, then the X cards cost
0.25 X
If Y is the number of cards at $0.15, then the Y cards cost
0.15 Y
The total cost of the X cards and the the Y cards is known to be $4.2 and also given by
0.25 X + 0.15 Y = 4.2
We now need to solve the system of equations
X + Y = 24
0.25 X + 0.15 Y = 4.2
The first equation gives Y = 24 - X. Substitute y by 24 - x in the second equation and solve
0.25 X + 0.15 (24 - X) = 4.2
X(0.25 - 0.15) + 3.6 = 4.2
0.1 X = 0.6
X = 6 and Y = 24 - 6 = 18
correct answer D
Question: Find the amount on Rs.5000 in 2 years, the rate of interest being 20% per first year and 25% for the second year?
A.3377
B.2678
C.5460
D.7500
Answer: D.7500
Explanation: 5000 * 120/100 * 125/100 => 7500
Answer: D
Question: five children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Children AB must sit next to each other, and child C must be somewhere to the right of AB. How many possible configurations are there for the children?
A.600
B.560
C.1440
D.4320
Answer: B.560
Explanation: A, B, C, D, E, F, G- seven children, of which AB must sit next to each other. Considering them as one X (A, B), we have X, C, D, E, F, G. These can be arranged in 6! ways. But A,B can arrange themselves in 2! ways. So a total of 6!*2! ways = 1440. Since in exactly half of them, C will be to the right of AB, and exactly half, C will be to the left of AB, therefore 1440/2 = 560.
B is the right answer.
Question: The present age of a father is 3 years more than three times the age of his son.Three years hence,father as age will be 13 years more than twice the age of the son.Find the present age of the father.
A.88
B.77
C.33
D.42
Answer: D.42
Explanation: Explanation:
Let the present age be 'x' years. Then father's present age is 3x+3 years. Three years hence (3x+3)+3=2(x+3)+13 x=13 Hence father's present age = 3x+3 =[ (3 x 13) + 3] = 42 years.
Answer: D
Question: 20 throws of a die produces following results
SCORE -- NUMBER OF OCCURRENCES
---1-------------------4
---2-------------------3
---3-------------------5
---4-------------------2
---5-------------------2
---6-------------------4
What is the probability P that one more throw to this series will increase the mean score?
A.1/6
B.1/3
C.1/2
D.2/3
Answer: C.1/2
Explanation: I get the mean as 67/20 --> 3.35. Thus in order to raise this mean we would need a 4,5,or 6.
Thus probability P is 1/2.C
Question: In how many ways can an answer key for a quiz be written if the quiz contains 5 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?
A.160
B.320
C.480
D.600
Answer: C.480
Explanation: There are 2^5 = 32 possibilities for the true-false answers.
However we need to remove two cases for TTTTT and FFFFF.
There are 4*4 = 16 possibilities for the multiple choice questions.
The total number of possibilities is 30*16 = 480.
The answer is C.
Question: A square is drawn inside a right-angled triangle with the two perpendicular sides as 12 cm and 8 cm. what is the side of the largest possible square that can be drawn?
A.4 cm
B.4.8 cm
C.4.5 cm
D.4.4 cm
Answer: B.4.8 cm
Explanation: consider the origin as the point of right angle thus (8,0)and (0,12) are the 2 vertices. equation of hypotenuse : 8y+12x=96.
now solve this with y=x(the diagonal of the largest square)
x=4.8, y=4.8 .
ANSWER:B
Question: A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
A.2777
B.3120
C.6877
D.1699
Answer: B.3120
Explanation: Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120
Answer: B
Question: By selling an article for $90, a person gains $15. What is the gain %?
A.25%
B.30%
C.50%
D.20%
Answer: D.20%
Explanation: S.P. = $90
Gain = $15
C.P. = 90-15 = 75
Gain% = 15/75 * 100 = 20%
Answer is D