RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Set A: {1, 3, 4, 6, 9, 12, 15,18}
If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 3?
A.3/14
B.2/7
C.5/14
D.5/7
Answer: C.5/14
Explanation: using probability you can solve: 6/8*5/7*4/6=5/14
Ans C
Question: A train running at 25 km/hr takes 30 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train and that of the platform.
A.a) 200/3m175/3m
B.b) 60m130m
C.c) 50m45m
D.d) 100/3 m200/3
Answer: B.b) 60m130m
Explanation: Hi Math gurus correct me if I am wrong. I wondered i reached the answer mentioned here i.e 100m and 25m
lets solve it
To find out length of train the train, which is must cover the static point of the man as well as the distance covered the man during 12 sec.
The man covered the distance during 12sec is 5*5/30*12=10m so the train covered a distance in 12 sec= 25*5/30*12=50
so the length of the train(Lt) is 10+50=60m
Now crossing the platform means length of train+length of platform(Lt+p)= 30*25*5/30=125m Now the length of platform (Lp) is= 125-60=65m
So answer is 60m and 65m Must beBeven though its mentioned 60m and 130m thinking so typo mistake...........
Question: The sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself?
A.8 years
B.9 years
C.2 years
D.6 years
Answer: D.6 years
Explanation: 100 ---- 300 --- 3
900 --- 3
----
6 years
Answer: D
Question: If (m-8) is a factor of m^2-pm-24, then p=
A.3
B.5
C.6
D.11
Answer: B.5
Explanation: (m-8)(m-a)=m^2-pm-24
A=-3
p=8+a=5=B
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
A.111.12 m
B.111.18 m
C.111.82 m
D.121.12 m
Answer: A.111.12 m
Explanation: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
Answer: A
Question: The number of people who moved to live in a small town per 200 persons is 10.5. if the number of person who leave the town per 200 persons is 5.5 how long will it take for the population of 1000 people to double.
A.25
B.30
C.40
D.10
Answer: C.40
Explanation: Annual increase is (200 + 10.5 - 5.5)*5=1025
Hence every year there is an increase of 25
for the population to double we needs additional 1000
therefore 1000/25=40
correct option is C)
Question: If the number 892,132,26x is divisible by 11, what must be the value of x?
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: Multiplication rule of 11: (Sum of digits at odd places - Sum of digits at even places) should be divisible by 11
Given number: 892,132,24x
Sum of digits at odd places = 8 + 2 + 3 + 2 + x = 15 + x (i)
Sum of digits at even places = 9 + 1 + 2 + 6 = 18(ii)
(i) - (ii) = 15 + x - 18 = x - 3
Hence x should be = 3 to make this a multiple of 11 (0) Option C
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 $0.50 per glass on the first day, what was the price per glass on the second day?
A.$0.15
B.$0.20
C.$0.33
D.$0.40
Answer: C.$0.33
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*0.5=3*x --> x=$0.33.
Answer: 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 year younger than A?
A.10
B.11
C.12
D.13
Answer: C.12
Explanation: Given that, A + B =12+ B + C
⇒ A - C =12
Therefore, C is younger than A by 12 years
Answer is C.
Question: The present average age of a family of five members is 26 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest)
A.30 years
B.76 years
C.20 years
D.15 years
Answer: C.20 years
Explanation: Present total age of the members
= 26(5) = 130 years.
Present age of the youngest member
= 10 years
Present total age of the remaining four members
= 130 -10 = 120 years
Their average age at the time of the birth of the youngest member
= [120 - (4 * 10)] / 4 = 30 - 10 = 20 years.
Answer: C
Question: The Lucknow-Indore Express without its rake can go 24 km an hour, and the speed is diminished by a quantity that varies as the square root of the number of wagon attached. If it is known that with four wagons its speed is 20 km/h, the greatest number of wagons with which the engine can just move is
A.144
B.140
C.143
D.124
Answer: C.143
Explanation: Solution: Speed = 24- k√n;
Putting the value, n = 4;
we get, k = 2.
Now the equation (as k = 2) become, S = 24-2√n;
Thus, it means when n = 144, speed will be zero. Hence, train can just move when 143 wagons are attached.
Answer: Option C
Question: A circular dashboard of radius 1.0 foot is at a distance of 20 feet from you. You throw a dart at it and it hits the dartboard at some point Q in the circle. What is the probability that Q is closer to the center of the circle than the periphery?
A.1.0
B.0.75
C.0.25
D.0.5
Answer: C.0.25
Explanation: .25
because the area of the circle with half radius 'r/2' is 1/4th of the area of circle with radius r
ANSWER:C
Question: A high school has 360 students 1/2 attend the arithmetic club, 5/8 attend the biology club and 3/4 attend the chemistry club. 3/8 attend all 3 clubs. If every student attends at least one club how many students attend exactly 2 clubs.
A.45
B.40
C.35
D.50
Answer: A.45
Explanation: Basically, this question is asking you to figure out how many students are being double-counted.
A-Club has 180 members (1/2 of 360)
B-Club has 225 members (5/8 of 360)
C-Club has 270 members (3/4 of 360)
We can create an equation to solve this:
180+225+270 = n + x + 2y
where n is the number of students, x is the number of students in two clubs, and y is the number of students in three clubs.
The question provides y for us (135).
180+225+270 = 360 + x + 270
x = 405-360 =45
A
Question: Calculate how long it will take a swimmer to swim a distance of 10km against the current of a river which flows at 3km/hr, given that he can swim in still water at 5km/h
A.3
B.4
C.5
D.6
Answer: C.5
Explanation: swim in still water at = 5
speed of river= 3
US = 5 - 3= 2
Distance = 10
T = 10/2 = 5
Answer: C
Question: Out of a group of 10 contestants, 2 are to be selected at random. What is the maximum number of male contestants possible if the probability that both selected contestants are male is less than 50% ?
A. 0
B. 1.46
C. 2
D.1.34
Answer: D.1.34
Explanation: Let x be the number of males.
Total contestants = 10
Probability that the first contestant selected is a male = x/10
Probability that the second contestant selected is also a male = x-1/9
Total probability = x(x-1)/ 90 < 1/50 (this probability is less than 50%)
Solving for x we get, x(x-1)< 9/5. This implies that the maximum value of x can be 1.34.
Answer D!
Question: The average of 10 consecutive integers is 16. Then, 9 is deducted from the first consecutive number, 8 is deducted from the second, 7 is deducted form the third, and so on until the last number which remains unchanged. What is the new average?
A.10.5
B.11
C.11.5
D.12
Answer: C.11.5
Explanation: The total subtracted is (9+8+...+1) = (9*10) / 2 = 45
On average, each number will be reduced by 45/10 = 4.5
Therefore, the overall average will be reduced by 4.5
The answer is C.
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 1320 cm is?
A.A)15
B.B)10
C.C)14
D.D)12
Answer: A.A)15
Explanation: 2 * 22/7 * 14 * x = 1320 => x = 15
ANSWER:A
Question: A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined them after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed amount A, B and C
A.3:7:5
B.6:10:5
C.6:10:7
D.6:7:5
Answer: B.6:10:5
Explanation: Explanation:
Let initial investment of A is 3x and B is 5x, then C investment is also 5x, but most important to note in this question is the time duration of investment
Like, A invested for 12 months, B invested for 12 months and C invested for 6 months.
A:B:C =(3x*12):(5x*12):(5x*6)
= 36:60:30
= 6:10:5
Option B
Question: Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 2 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
A.12 km
B.20 km
C.24 km
D.4 km
Answer: B.20 km
Explanation: Explanation:
Distance = Relative Speed * Time
= (2 + 3) * 4 = 20 km
[ They are travelling in the opposite direction, relative speed = sum of the speeds].
ANSWER IS B
Question: A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
A.81 km/hr
B.80 km/hr
C.90 km/hr
D.99 km/hr
Answer: A.81 km/hr
Explanation: speed x and y
x/8.4 = (y-4.5)*5/18...1)
x/8.5=(y-5.4)*5/18----2)
dividing = y-4.5/y-5.4
8.4y-8.4*4.5=8.5y-8.5*5.4
=>y=81
ANSWER A
Question: in a scheme, a pack of three soaps with mrp rs45 is available for rs42. if it still gives a profit of 5% to the shopkeeper,then the cost price of the pack is:
A.rs40
B.rs37
C.rs41
D.rs35
Answer: A.rs40
Explanation: Price of the pack = 42
x*105/100=42 . 105=100(Price of soap pack) + 5(profit)
x=42*100/105=2*100/5=40
ANSWER:A
Question: A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 11. What could be the ratio of Cats to dogs in the pet store?
A.1:3
B.1:4
C.1:5
D.44:55
Answer: D.44:55
Explanation: Say theratioof cats to dogs is a/b. Then thenumberof cats would be ax and thenumberof dogs bx, for some positive integer x.
We are told that ax - bx = 11 --> x(a - b) = 11. Since 11 is a prime number it could be broken into the product of two positive multiples only in one way: x(a - b) = 1*11.
The above implies that either x = 1 and (a - b) = 11 or x = 11 and (a - b) = 1.
Therefore the correct answer should have the difference between numerator and denominator equal to 1 or 11.
For the original question only option which fits is E, 4:5. Cats = 11*4 = 44 and dogs = 11*5 = 55.
Answer: D.
Question: The present worth of a certain bill due sometime hence is Rs. 1296 and the true discount is Rs. 72. What is the banker's discount?
A.Rs. 76
B.Rs. 72
C.Rs. 74
D.Rs. 4
Answer: A.Rs. 76
Explanation: Explanation :
BG = (TD)2/PW=722/1296 = 72×72/1296 = 12 × 12/36=12/3= Rs. 4
BG = BD – TD
=> 4 = BD - 72
=> BD = 72 + 4 = Rs. 76 Answer : Option A
Question: If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:
A.2.87
B.2.967
C.3.876
D.3.912
Answer: C.3.876
Explanation: Explanation:
log5 512
=	log 512 /log 5
=	log 29 /log (10/2)
=	9 log 2 /log 10 - log 2
=	(9 x 0.3010) /1 - 0.3010
= 2.709 /0.699
=	2709 /699
= 3.876
ANSWER IS C
Question: If P gets 25% more than Q, then by what percent does Q get less than P?
A.33 1/3%
B.30%
C.20%
D.16 2/3%
Answer: C.20%
Explanation: Let Q get 1 unit.
25% of 1 unit = 1/4 = 0.25
P gets (1 + 0.25) i.e., 1.25 units.
Difference = (1.25 - 1) = 0.25
Required percentage = 0.25/1.25 * 100 = 1/5 * 100 = 20%
ANSWER:C
Question: A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
A.29 kmph
B.28 kmph
C.54 kmph
D.37 kmph
Answer: C.54 kmph
Explanation: S = 240/16 * 18/5
= 54 kmph
Answer: C
Question: 45 workers work 8 hours to dig a hole 30 meters deep. How many extra workers should be hired to dig another hole 30 meters deep by working for 6 hours?
A.10
B.15
C.20
D.25
Answer: B.15
Explanation: 45 workers * 8 hours / 30 meters = x * 6 / 30
x = 60 total workers
60 - 45 = 15 new workers
The answer is B.
Question: Beth got a job painting dorm rooms at her
college. At top speed, she could paint 5
identical rooms during one 6-hour shift.
How long did she take to paint each room?
A.50 minutes
B.1 hour and 10 minutes
C.1 hour and 12 minutes
D.1 hour and 15 minutes
Answer: C.1 hour and 12 minutes
Explanation: Six hours equals 360 minutes, so Beth paints 5 rooms in 360 minutes. She paints 1 room
in 360 ÷ 5 = 72 minutes, which equals 1 hour and 12 minutes
correct answer C)1 hour and 12 minutes
Question: If 5 + 7/X = 6 - 5/X, then X =
A.7
B.14
C.12
D.6/7
Answer: C.12
Explanation: We're given the equation 5 + 7/X = 6 - 5/X. We're asked for the value of X.
The common-denominator of these 4 numbers is X, so we need to multiply both sides of the equation by X, giving us...
5X + 7X/X = 6X - 5X/X
We can then eliminate that denominator, which gives us....
5X + 7 = 6X - 5
12 = X
C
Question: In how many ways can 7 boys and 2 girls be arranged a ta table if 2 girls are never together?
A.30240
B.31240
C.32410
D.32540
Answer: A.30240
Explanation: Total ways of arranging 9 person in a circle = 8! = 40320 ways
If we consider two women as one, then we have 7+1=8 persons. Arranging these eight persons in circle will take = 7! = 5040 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 7!*2! = 10080 ways
Total ways in which two women doesn’t sit together in circle = 8! - 7!*2! = 40320 - 10080 = 30240 ways
A
Question: Look at this series: 7.2, 7, 6.8, 6.6, ... What number should come next?
A.6.4
B.6
C.5.8
D.6.3
Answer: A.6.4
Explanation: A
6.4
In this simple subtraction series, each number decreases by 0.2.
Question: A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
A.270
B.288
C.276
D.299
Answer: A.270
Explanation: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 870 = 270
Answer: A
Question: Difficulty:
There are five sales agents in a certain real estate office. One month Andy sold thrice as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold thrice as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?
A.Andy
B.Bob
C.Cary
D.Dora
Answer: C.Cary
Explanation: a= 3e
b =3 +e
c = 3b = 9+ 3e (highest of all)
d = b + e = 3+ e +e = 3 + 2e
Ans. C
Question: In how many ways Chief Minister and Minister be elected from a team of 14 members?
A.182
B.131
C.132
D.143
Answer: A.182
Explanation: To do this, if captain is elected first, then we have 14 ways of doing this.
For election of vice-captain, we have only 13 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 14*13 = 182 ways.
Answer : A
Question: Insert the missing number.
8, 7, 16, 5, 24, 3, 32, 1, 40,-1, (....)
A.48
B.40
C.35
D.-3
Answer: A.48
Explanation: Explanation:
There are two series, beginning respectively with 8 and 7. In one 8 is added and in another 2 is subtracted.
The next number is 40 + 8 = 48.
Answer: A) 48
Question: The sum of 99 consecutive integers is 9999. What is the greatest integer in the set?
A.100
B.120
C.149
D.150
Answer: D.150
Explanation: sum of n numbers = (n(2a+(n-1)d))/2 where n = no of terms a = 1st term , d - difference between two terms (ie d= a2-a1)
here sum = 9999 , n= 99 d = 1 (since consecutive numbers)
9999= (99/2) * (2a+(99-1)1)
from this 'a' (ie the 1st term) = 52
nth term in a sequence : nth term = a + (n-1) d
here a = 52 , n = 99 , d = 1
So nth term = 52 + (99-1)*1
therefore Nth term = 150
ANSWER:D
Question: Roses can be purchased individually for $4.50, one dozen for $36, or two dozen for $50. What is the greatest number of roses that can be purchased for $680?
A. 156
B. 162
C. 318
D. 324
Answer: C. 318
Explanation: Buy as many $50 deals as possible. We can by 650/50=13 two dozen roses, thus total of 13*24 = 312 roses.
We are left with 680 - 650 = $30. We can buy 30/4.5 = ~6 roses for that amount.
Total = 312 + 6 = 318.
Answer: C.
Question: If a 19-cup mixture of powder and water contained 1 cup of powder. How many cups of powder must be added to get a mixture having powder and water in the ratio of 1:2?
A.6
B.8
C.17
D.19
Answer: D.19
Explanation: Concentration of powder in Mix 1 = 1/19
Concentration of powder in Mix 2 = 1 ( i.e. 100% since it is all powder)
Concentration of powder in final mixture = 1/3
w1/w2 = (1 - 1/3)/(1/3 - 1/19) = 19/8
So for every 19 cups of mix1, you need to put 8 cups of powder to make the required mix with ratio 1:2.
ANSWER:D
Question: Pipe B that can fill a tank in an hour and pipe A that can fill the tank in half an hour are opened simultaneously when the tank is empty. Pipe A is shut 15 minutes before the tank overflows. When will the tank overflow?
A.32 mins
B.35 mins
C.40 mins
D.30 mins
Answer: D.30 mins
Explanation: The last 15 minutes only pipe B was open. Since it needs 1 hour to fill the tank, then in 15 minutes it fills 1/4th of the tank, thus 3/4 of the tank is filled with both pipes open.
The combined rate of two pipes is 1 + 2 = 3 tanks/hour, therefore to fill 3/4th of the tank they need (time) = (work)/(rate) = (3/4)/3 = 1/4 hours = 15 minutes.
Total time = 15 + 15 = 30 minutes.
Answer: D
Question: A vessel of capacity 2 litre has 20% of alcohol and another vessel of capacity 6 litre had 55% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
A.37%.
B.71%.
C.49%.
D.29%.
Answer: A.37%.
Explanation: 20% of 2 litres = 0.4 litres
55% of 6 litres = 3.3 litres
Therefore, total quantity of alcohol is 3.7 litres.
This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 37%
A
Question: In a barrel of juice there is 20 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: C.3:1.
Explanation: Juice barrel : beer Barrel = 20:80 i.e. 3:8
price of Juice : Price of Beer = 3 : 4
so for 2/8 costs 3/4, ie 2J / 8B = 3/4.
Solving for J/B, we get 3:1
Answer C.
Question: If a/x = 1/2 and a/y =1/ 4, then (x + y) =
A.A)2a
B.B)a/2
C.C)6a
D.D)7a
Answer: C.C)6a
Explanation: Ratio 1:
2a = x
Ratio 2:
4a = y
x+y = 6a
Answer is C
Question: Each of the cucumbers in 100 pounds of cucumbers is composed of 99% water, by weight. After some of the water evaporates, the cucumbers are now 96% water by weight. What is the new weight of the cucumbers, in pounds?
A.2
B.25
C.92
D.96
Answer: B.25
Explanation: Out of 100 pounds 99% or 99 pounds is water and 1 pound is non-water. After somewaterevaporates the cucumbers become 96% water and 4% of non-water, so now 1 pound of non-water composes 4% of cucucmbers, which means that the new weight of cucumbers is 1/0.04=25 pounds.
Answer: B.
Question: If the annual increase in the population of a town is 10% and the present number of people is 10000, what will the population be in 2 years?
A.12100
B.15240
C.12456
D.11452
Answer: A.12100
Explanation: The required population is = 10000 (1 + 10/100)^2
= 10000 * 11/10 * 11/10
= 12100
Answer is A
Question: In a mixture of 60 liters, the ratio of milk and water is 2:1. What amount of water must be added to make the ratio of milk and water as 1:2?
A.20 liters
B.30 liters
C.60 liters
D.38 liters
Answer: C.60 liters
Explanation: 2:1 --- 60
1:2
2:4
---------------
3
3 ----------- 60
3 ----------- ? => 60 liters
Answer: C
Question: A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.2662 in 3 years. Find the rate percent?
A.20%
B.10%
C.60%
D.70%
Answer: B.10%
Explanation: 2420 --- 242
100 --- ? => 10%
Answer: B
Question: In a fuel station the service costs $1.50 per car, every liter of fuel costs 0.35$. Assuming that you own 3 limos and 2 fleet vans and all fuel tanks are empty. How much will it cost to fuel all cars together if a limo tank is 32 liters and an fleet van tank is 75% bigger?
A.$78.80
B.$79.80
C.$78.90
D.$79.90
Answer: A.$78.80
Explanation: Lots of calculations.
1.50*4 + 3*.35*32+ 2*(7/4)*32 *.35
Answer=$78.80
The correct option is A
Question: 4 letters have to be put into their 4 respective envelopes. If the letters are inserted randomly into the envelopes, what is the probability that all the letters go into their respective envelopes?
A.1/30
B.1/64
C.1/120
D.1/240
Answer: B.1/64
Explanation: A-B-C-D-E (envelopes)
a-b-c-d-e (letters)
4 letters (a, b, c, d, and e) can be assigned to 4 envelopes (arranged) in 4! ways, out of which only one will be correct, thus the probability is 1/4! = 1/64.
Answer: B.
Question: Two trains 200 m and 800 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.10.6
B.10.9
C.36
D.10.8
Answer: C.36
Explanation: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 200 + 800 = 1000 m.
Required time = 1000 * 9/250 = 36 sec.
Answer: C
Question: Three different containers contain 50 litres, 100 litres and 150 litres of mixture of milk and water respectively. What is the biggest measure can measure all the different quantities exactly ?
A.120 litres
B.57 litres
C.60 litres
D.50 litres
Answer: D.50 litres
Explanation: M1 = 50 litres
M2 = 100 litres
M3 = 150 litres
Required measurement = H.C.F. of M1,M2,M3 = 50 litres
Answer is D
Question: Insert the missing number
5, -15, 45, -135, (....)
A.350
B.-405
C.405
D.-350
Answer: C.405
Explanation: 5*-3=-15
-15*-3=45
45*-3=-135
-135*-3=405
ANSWER:C
Question: A fellow borrowed a certain sum of money at 8% per annum at simple interest and in 8 years the interest amounted to Rs.900 less than the sum lent. What was the sum lent?
A.1050
B.1220
C.2500
D.1060
Answer: C.2500
Explanation: P - 900 = (P*8*8)/100
P = 2500
Answer: C
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What isthe probability that first is white and second is black?
A.31/111
B.36/145
C.21/115
D.11/154
Answer: B.36/145
Explanation: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Question: A math teacher has 26 cards, each of which is in the shape of a geometric figure. Half of the cards are rectangles, and a third of the cards are rhombuses. If 8 cards are squares, what is the maximum possible number of cards that re circles.
A.9
B.10
C.11
D.12
Answer: A.9
Explanation: a square is a special kind of rhombus (sides are perpendicular)
a square is a special kind of rectangles (sides with same length)
Among the 26 cards with have:
15 rectangles
10 rhombus
8 squares
Among the 15 rectangles, there could be 8 special ones (with sides of same length) that are squares. That lets at least 7 rectangles that are not square.
Among the 10 rectangles, there could be 8 special ones (with sides perpendicular) that are squares. That lets at least 2 rhombus that are not square.
We have 8 squares.
So the minimum different cards that represent a square, a rhombus or a rectangle is 2 + 7 + 8 = 17
Which means that the maximum number of circles that you could have is 26 - 17 = 9
Answer (A)