RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Two cars cover the same distance at the speed of 50 and 66 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
A.212 km
B.214 km
C.188 km
D.216 km
Answer: C.188 km
Explanation: 50(x + 1) = 66x
X = 3.125
60 * 3.125 = 188 km
ANSWER:C
Question: Suppose 7 students are staying in a hall in a hostel and they are allotted 7 beds. Among them, Parvin does not want a bed next to Anju because Anju snores. Then, in how many ways can you allot the beds?
A.2388
B.2088
C.3600
D.2028
Answer: C.3600
Explanation: Let the beds be numbered 1 to 7.Case 1 : Suppose Anju is allotted bed number 1.
Then, Parvin cannot be allotted bed number 2.
So Parvin can be allotted a bed in 5 ways.
After alloting a bed to Parvin, the remaining 5 students can be allotted beds in 5! ways.
So, in this case the beds can be allotted in 5´5!ways = 600 ways.
Case 2 : Anju is allotted bed number 7.
Then, Parvin cannot be allotted bed number 6
As in Case 1, the beds can be allotted in 600 ways.
Case 3 : Anju is allotted one of the beds numbered 2,3,4,5 or 6.
Parvin cannot be allotted the beds on the right hand side and left hand side of Anju’s bed. For example, if Anju is allotted bed number 2, beds numbered 1 or 3 cannot be allotted to Parvin.
Therefore, Parvin can be allotted a bed in 4 ways in all these cases.
After allotting a bed to Parvin, the other 5 can be allotted a bed in 5! ways.
Therefore, in each of these cases, the beds can be allotted in 4´ 5! = 480 ways.
The beds can be allotted in (2x 600 + 5 x 480)ways = (1200 + 2400)ways = 3600 ways
Answer: C
Question: Weights of two friends Ram and Shyam are in the ratio 1:5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased?
A.19%
B.10%
C.21%
D.16%
Answer: D.16%
Explanation: Solution:
given ratio of Ram and Shayam's weight = 1:5
Hence, (x-15)/(15-10) = 1/5
Or, x = 16%.
Answer: Option D
Question: The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.80 per metre.
A.2399
B.6336
C.2999
D.5808
Answer: B.6336
Explanation: Explanation:
Area = (13.86 x 10000) sq.m = 138600 sq.m
Circumference =
Cost of fencing = Rs. (1320 x 4.80) = Rs. 6336.
Answer: B) 6336
Question: How long will a boy take to run round a square field of side 50 meters, if he runs at the rate of 10km/hr?
A.52sec
B.45sec
C.72sec
D.25sec
Answer: C.72sec
Explanation: Speed = 10 km/hr = 10*5/18 = 25/9 m/sec
Distance = 50*4 = 200m
Time taken = 200*9/25 = 72sec
Answer is C
Question: A firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009?
A.700
B.1000
C.1300
D.1600
Answer: C.1300
Explanation: Profit=Revenue-Cost
2007:
-1000=R1-C1
2008:
0=(1+2X%)R1-(1+X%)C1
2009:
P3=(1+2 X%)^2*R1-(1+X%)^2*C1
we've already known that R3=1.44R1, so (1+2 X%)^2=1.44, X=10
we put X=10 back to the equation of 2008:
0=1.2R1-1.1C1, and we have 1.2R1=1.1C1, which we could combine with the equation of 2007.
Then we have C1=12000, R1-11000
Finally, take C1 and R1 into the equation of 2009 and we got P3=15840-14520=1320 ;Answer: C
Question: The length of the bridge, which a train 140 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
A.235
B.288
C.245
D.776
Answer: A.235
Explanation: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (140 + X)/30 = 25/2 ==> 2(140 + X) = 750 ==> X
= 235 m.
Answer:A
Question: A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?
A.120
B.335
C.784
D.217
Answer: A.120
Explanation: Let x be the number he chose, then
2*x*138=102
2x=240
x=120
correct answer A
Question: The average of five numbers is 27. If one number is excluded, the average becomes 21. The excluded number is?
A.48
B.49
C.50
D.51
Answer: D.51
Explanation: Excluded number = (27 * 5) - (21 * 4)
= 135 - 84
= 51.
Answer: D
Question: A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 539, what was his profit?
A.s. 64
B.s. 99
C.s.72
D.s.75
Answer: B.s. 99
Explanation: C.P. = Rs. (100/122.5)x539
= Rs. (1000/1225)x539
= Rs. 440
Profit = Rs. (539 - 440) = Rs. 99.
Answer:B
Question: A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 24 cm. What is the length of the wire?
A.6 cm
B.4 cm
C.8 cm
D.3 cm
Answer: B.4 cm
Explanation: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(24)^2 * h = (4/3)π (12)^3 => h
= 4 cm
Answer:B
Question: If you graph the lines 3x + 2y = –2 and
5x – y = 14 on a standard xy-graph, at
which point will the lines intersect?
A.(1, –7)
B.(2, –4)
C.(–5, 4)
D.(–9, 3)
Answer: B.(2, –4)
Explanation: Solve the two equations, 3x + 2y = –2 and 5x – y = 14, as a system of equations. To do
this, multiply the second equation by 2 and then add it to the first equation:
3x+2y=-2+10x-2y=28=>13x=26
Now solve for x:
x = 2
Replace x with 2 in either equation and solve for y:
3(2) + 2y = –2
6 + 2y = –2
2y = –8
y = –4
At the point of intersection, x = 2 and y = –4, so this point is (2, –4).
correct answer B) (2, –4).
Question: A person starting with 64 rupees and making 6 bets, wins three times and loses three times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for half the money remaining at the time of the bet, then the final result is :-
A.a gain of Rs 27
B.a loss of Rs 37
C.neither gain nor a loss
D.a gain or a loss depending upon the order in which the wins and losses occur
Answer: B.a loss of Rs 37
Explanation: Explanation :
As the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order).
The overall resultant will remain same.
So final amount with the person will be (in all cases):
=64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)= Rs 27
Hence the final result is:
64−27=37.
Answer : B
Question: T divided by S equals 405.24 what is a possible remainder?
A.54
B.2
C.9
D.40
Answer: A.54
Explanation: With the decimal being 24/100, the simplest form is 6/25. If the divisor is a multiple of 25, the remainder must be a multiple of 6. The only number that is so is 54. Answer A.
Question: A rectangular lawn of dimensions 110 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
A.s.3988
B.s.4800
C.s.3228
D.s.3922
Answer: B.s.4800
Explanation: Area = (l + b – d) d
(110 + 60 – 10)10 => 1600 m2
1600 * 3
= Rs.4800
Answer:B
Question: After his first semester in college, Thomas is applying for a scholarship that has a minimum Grade Point Average (GPA) requirement of 3.5. The point values of pertinent college grades are given in the table below. If Thomas took 7 courses, each with an equal weight for GPA calculations, and received two grades of A-, one grade of B+, and one grade of B, what is the lowest grade that Thomas could receive for his fifth class to qualify for the scholarship?
Point Values of Select Grades
Grade: A | A- | B+ | B | B- | C+ | C | C-
Value: 4 | 3.7 | 3.3 | 3 | 2.7 | 2.3 | 2 | 1.7
A. A
B. B+
C. B
D. B-
Answer: D. B-
Explanation: Grade: A | A- | B+ | B | B- | C+ | C | C-
Value: 4 |3.7|3.3|3| 2.7 | 2.3 | 2 | 1.7
7.4 + 3.3 + 3 + x = 3.5 * 5
x = 17.5 - 13.7 = 3.8
Grade A is required to qualify
Answer = B-
D
Question: A man buys a cycle for Rs. 1600 and sells it at a loss of 10%. What is the selling price of the cycle?
A.1410
B.1420
C.1430
D.1440
Answer: D.1440
Explanation: S.P. = 90% of Rs. 1600 = 90/100 x1600= Rs. 1440
answer : D
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.299
B.277
C.240
D.88
Answer: C.240
Explanation: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer:C
Question: A boy has fourteen trousers and 13 shirts. In how many different ways can he select a trouser and a shirt?
A.182 ways
B.287 ways
C.266 ways
D.108 ways
Answer: A.182 ways
Explanation: Explanation:
The boy can select one trouser in 14 ways.
The boy can select one shirt in 13 ways.
The number of ways in which he can select one trouser and one shirt is 14 * 13 = 182 ways.
Answer: A
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 34 kmph. Of how many minutes does the train stop per hour?
A.E982
B.27
C.12
D.14.6
Answer: D.14.6
Explanation: Explanation:
T = 11/45 * 60 = 14.6
Answer: Option D
Question: In a certain pet shop, the ratio of dogs to cats to bunnies in stock is 3 : 7 : 13. If the shop carries 352 dogs and bunnies total in stock, how many dogs are there?
A.42
B.66
C.98
D.112
Answer: B.66
Explanation: Let us assume the number of dogs, cats and bunnies to be 3x, 7x and 13x
Total dogs and bunnies = 16x.
And we are given that 16x = 352.
Hence x = 22.
Dogs = 3x = 3*22 = 66 (Option B)
Question: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.30 per glass on the first day, what was the price per glass on the second day?
A.$0.15
B.$0.20
C.$0.30
D.$0.40
Answer: B.$0.20
Explanation: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;
So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.
We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.
Say the price of the glass of the orangeade on the second day was $x then 2*0.3=3*x --> x=$0.2.
Answer: B.
Question: What is x if x + 3y = 33 and y = 10?
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: Substitute y by 10 in x + 3y = 33
x + 3(10) = 33
x + 30 = 33
If we substitute x by 3 in x + 30 = 33, we have 3 + 30 = 33. Hence
x = 3 correct answer C
Question: If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 10, respectively, what is the probability that b/a will not be an integer?
A.1/2
B.1/3
C.1/4
D.1/6
Answer: B.1/3
Explanation: a is from the following set {1,2,3,4}
b is from the following set {10,12,14}
The total number of ways of choosing 2 integers, one from each set is 4*3 = 12 ways.
The possibilities where b/a is not an integer is for the following outcomes:
{b,a} = {10,3},{10,4},{14,3},{14,4} = 4 ways
Thus the probability is 4/12 = 1/3
The answer is B.
Question: Company P had 15 percent more employees in December than it had in January. If Company P had 480 employees in December, how many employees did it have in January?
A. 391
B. 417
C. 410
D. 423
Answer: B. 417
Explanation: D = number of employees in December
J = number of employees in January
J x 1.15 = D
J x 1.15 = 480
J = 480/1.15
J = 48,000/115 = 417
Thus B is the correct answer.
Question: A jogger running at 9 km/hr along side a railway track is 360 m ahead of the engine of a 90 m long train running at 63 km/hr in the same direction. In how much time will the train pass the jogger?
A.76 sec
B.67 sec
C.30 sec
D.36 sec
Answer: C.30 sec
Explanation: Speed of train relative to jogger = 63 - 9 = 54 km/hr.
= 54 * 5/18 = 15 m/sec.
Distance to be covered = 360 + 90 = 450 m.
Time taken = 450/15 =30 sec.
Answer:C
Question: If a: b = 19: 3, b: c = 17: 13, find a: b: c?
A.323: 51: 39
B.333: 61: 49
C.343: 71: 59
D.353: 81: 69
Answer: A.323: 51: 39
Explanation: a: b = 19: 3
b: c = 17: 13
a: b: c = 323: 51: 39
ANSWER:A
Question: If you have 6 New Year greeting cards and you want to send them to 4 of your friends, in how many ways can this be done?
A.360
B.720
C.920
D.670
Answer: A.360
Explanation: Solution
We have to find number of permutations of 4 objects out of 6 objects. This number is 6P4=6(6-1)(6-2)(6-3)=6*5*4*3=360
Answer A
Question: Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 36 miles per hour. How many miles from the station was train A overtaken by train B?
A.320
B.360
C.400
D.440
Answer: B.360
Explanation: After two hours, Train A is ahead by 60 miles.
Train B can catch up at a rate of 6 miles per hour.
The time to catch up is 60/6 = 10 hours.
In 10 hours, train A travels another 30*10 = 300 miles for a total of 360 miles.
The answer is B.
Question: A vessel of capacity 75 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?
A.23.89
B.72.9
C.58.08
D.78.3
Answer: C.58.08
Explanation: Explanation:
Let the initial quantity of milk in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of milk finally in the vessel is then given by [(T - y)/T]n * T
For the given problem, T = 75, y = 9 and n = 2.
Hence, quantity of milk finally in the vessel
= [(75 - 9)/75]^2 (75) = 58.08 litres.
Answer: Option C
Question: if cost of an apple is equal to cost of 4 oranges and he has 100$ with him. Cost of an orange is 1$. He want to buy same number of orange and apples. So how many apple and orange he would be able to buy in 100$?
A.10 apple an 10 oranges
B.20 apple and 20 oranges
C.27 apples and 27 oranges
D.30 apple and 30 oranges
Answer: B.20 apple and 20 oranges
Explanation: Since cost of an orange is 1$ and apple is 4 times costlier than orange so the cost of apple is 4$. Now if we add cost of an apple and orange it comes to be 5$ and hence if we divide 100 by 5 we get answer 20. So he will be able to buy 20 apple and 20 oranges. So option B is correct.
Question: Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?
A.7 3/8 km
B.5 7/8 km
C.17 7/8 km
D.7 7/8 km
Answer: D.7 7/8 km
Explanation: RS = 6 ¾ - 4 ½ = 2 ¼
T = 3 ½ h.
D = 9/4 * 7/2 = 63/8 = 7 7/8 km
ANSWER:D
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5%?
A.228
B.299
C.266
D.500
Answer: D.500
Explanation: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 85
5x/100 + 90 – 6x/100 = 85
x/100 = 5
=> x = 500
Answer:D
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
A.230
B.387
C.277
D.299
Answer: A.230
Explanation: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.Answer:A
Question: (51+ 52 + 53 + ... + 100) = ?
A.2775
B.2785
C.2975
D.3775
Answer: D.3775
Explanation: This is an A.P. in which a = 51, l = 100 and n = 50.
Sum =	n	(a + l)	=	50	x (51 + 100) = (25 x 151) = 3775.
2	2
D)
Question: A right triangle has sides of a, b, and 15, respectively, where a and b are both integers. What is the value of (a + b)?
A.220
B.221
C.225
D.224
Answer: C.225
Explanation: LET a= hypotenuse , b =base ,15 = perpendicular . therefore a^2 -b^2 =15^2 or (a+b)(a-b) = 225
a+b =225/a-b ' a-b cannot be zero ..therefore a+ b =225 where a-b is equal to 1
C
Question: Find the area of circle whose radius is 8.2m?
A.138
B.154
C.288
D.211.3
Answer: D.211.3
Explanation: 22/7 * 8.2 * 8.2
= 211.3
Answer:D
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
A.10.9 sec
B.13.8 sec
C.53.8 sec
D.10.8 sec
Answer: D.10.8 sec
Explanation: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec.
Answer: D:
Question: 5358 x 51 = ?
A.273762
B.283758
C.273298
D.273258
Answer: D.273258
Explanation: D
273258
5358 x 51 = 5358 x (50 + 1)
= 5358 x 50 + 5358 x 1
= 267900 + 5358
= 273258.
Question: 30 men take 20 days to complete a job working 9 hours a day. how many hour a day should 40 men work to complete the job?
A.6.79
B.6.75
C.6.71
D.6.74
Answer: B.6.75
Explanation: Explanation:
Let the capacity of man in hour is 1 unit. Then total work = 30 × 20 × 9
40 men in 20 days working t hours a day can complete = 40 × 20 × t
⇒ 40 × 20 × t = 30 × 20 × 9
⇒ t = 6.75 hours.
Answer: B
Question: A computer can perform c calculations in s seconds. How many minutes will it take the computer to perform A calculations?
A.60as/c
B.as/c
C.as/60c
D.60c/as
Answer: C.as/60c
Explanation: As 'thick' as this question might look, it's actually a fairly straight-forward Rate question and can be solved by TESTing VALUES.
We're told that a computer can perform a calculations in S seconds.
Let's TEST....
a = 2
S = 3
2 calculations every 3 seconds =
40 calculations every 1 minute
We're asked how many MINUTES it will take to perform K calculations.
Since we already know that the computer can perform 40 calculations in 1 minute, let's TEST...
K = 80
So we're looking for an answer that = 2 when C = 2, S = 3 and K = 80
Answer A: 60KS/a = 60(80)(3)/2 = 7200 This is NOT a match
Answer B: KS/a = (80)(3)/2 = 120 This is NOT a match
Answer C: KS/60a = (80)(3)/(60)(2) = 2 This IS a match
Answer D: 60a/KS = 60(2)/(80)(3) = 1/2 This is NOT a match
Answer E: K/60aS = 80/(60)(2)(3) = a fraction. This is NOT a match
C
Question: The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A ?
A.12
B.13
C.14
D.15
Answer: A.12
Explanation: Explanation:
(A+B) - (B-C) = 12 <=> A - C = 12. Answer: A
Question: It is currently 7:05 PM. What time was it in the morning exactly 51,132 minutes ago?
A.6:53
B.6:55
C.6:59
D.7:03
Answer: A.6:53
Explanation: Convert 51,132 minutes to hours by dividing by 60: 51,132/60 = 852 R12. That is 852 hours, 12 minutes. Convert 852 hours to days by dividing by 24: 852/24 = 35 R12. That is 35 days, 12 hours. Thus 852 hours before 7:05 PM is 12 hours before 7:05 PM which is 7:05 AM. 12 minutes before that is 6:53 AM. A
Question: If a is a positive integer then 1^(2a) + (1^a)/(1^(2a)) =
A.3
B.4
C.2
D.5
Answer: C.2
Explanation: 1^(2a) + 1^a/ 1^(2a) = 1^a + 1^a/1^a = 1+ 1 =2
Answer : C
Question: If the product of two positive integers is 120, which of the following could be the LCM and HCF of the two numbers? a. LCM 60 : HCF 2 b. LCM 30 : HCF 4 c. LCM 12 : HCF 10
A.b only
B.c only
C.b,c only
D.a only
Answer: D.a only
Explanation: The right answer is a.
Answer : D
Question: What is the lowest positive integer that is divisible by 1 through 2, inclusive?
A.2
B.4
C.8
D.6
Answer: A.2
Explanation: The integer should be divisible by: 1 and 2. The least common multiple of these integers is LCM=1*2=2
Answer: A
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 1/8%
B.33 7/3%
C.33 1/3%
D.37 1/3%
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: Howmany three digits odd numbers can be formed using the digits 4,5,6,7,8,9 (repetition of digits allowed)
A.801
B.106
C.216
D.108
Answer: D.108
Explanation: There are 3 ways of filling the unit place of the number. The remaining ten's and 100's place canbe filled in 6 ways each. Required number of numbers =3x6x6=108. Ans: D
Question: The side of a rhombus is 20 m and length of one of its diagonals is 16 m. The area of the rhombus is?
A.223.28
B.293.28
C.293.78
D.291.28
Answer: B.293.28
Explanation: area of the rhombus = 1/2 * p * √4(a)2 - (p)2
a= 20 ; p = 16
A=1/2 * 16 *√4(20)2 - (16)2
=1/2 * 16 *√1600 - 256
=1/2 * 16 *√1344
A =293.28
Answer : B
Question: In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 60 per square m?
A.Rs.43000
B.Rs.50000
C.Rs.57000
D.Rs.60000
Answer: C.Rs.57000
Explanation: Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m
Total area of the hall to be covered with mat = 2(lb + bh + hl)
= 2(20 * 15 + 15 * 5 + 5 * 20)
=2(300 + 75 + 100)
= 2 * 475
= 950 sq. m
Total expenditure = 60 * 950
= Rs.57000
C
Question: In the xy-plane, a triangle has vertices (0,0), (4,0) and (4,7). If a point (a,b) is selected at random from the triangular region, What is the probability that a-b>0?
A.4/7
B.2/3
C.3/5
D.3/7
Answer: A.4/7
Explanation: The area of the right triangle is (1/2)*4*7 = 14.
Only the points (a,b) below the line y=x satisfy a - b > 0.
The part of the triangle which is below the line y=x has an area of (1/2)(4)(4) = 8.
P(a - b > 0) = 8/14 = 4/7
The answer is A.
Question: Given a spinner with four sections of equal size labeled A, B, C, and D, what is the probability of NOT getting an A after spinning the spinner two times?
A.15/16
B.9/16
C.1/2
D.1/4
Answer: B.9/16
Explanation: The probability of NOT getting an A after spinning the spinner two times is 3/4*3/4=9/16 (so getting any of the remaining 3 letters out of 4).
Answer: B.
Question: A collection of books went on sale, and 2/3 of them were sold for $2.00 each. If none of the 36 remaining books were sold, what was the total amount received for the books that were sold?
A.$144
B.$135
C.$90
D.$60
Answer: A.$144
Explanation: Since 2/3 of the books in the collection were sold, 1/3 were not sold. The 36 unsold books represent 1/3 of the total number of books in the collection, and 2/3 of the total number of books equals 2(36) or 72. The total proceeds of the sale was 72($2.00) or $144. The best answer is therefore A.
Answer: A.
Question: A certain fraction has the same ratio to 1/18, as 2/5 does to 2/9. What is this certain fraction?
A.1/5
B.1/7
C.1/10
D.1/12
Answer: C.1/10
Explanation: x / (1/18) = (2/5) / (2/9)
x = 2*9*1 / 18*5*2 = 1/10
The answer is C.
Question: The present worth of a bill due sometime hence is Rs. 1100 and the true discount on the bill is Rs. 110. Find the banker’s discount and the banker’s gain.
A.120
B.121
C.130
D.151
Answer: B.121
Explanation: Sol.
T.D. = √P.W. * B.G.
∴ B.G. = (T.D.)² / T.W. = Rs. [110 * 110 / 1100] = Rs. 11.
∴ B.D. = (T.D. + B.G.) = Rs. (110 + 11) = Rs. 121.
Answer B
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
A.197
B.127
C.189
D.400
Answer: D.400
Explanation: 2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
Answer: D
Question: The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is :
A.123
B.127
C.235
D.305
Answer: B.127
Explanation: Solution
Required number = H.C.F. of (1657 - 6) and (2037 - 5)
= H.C.F. of 1651 and 2032 = 127. Answer B