RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
A.10
B.8
C.77
D.26
Answer: A.10
Explanation: RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 50 * 100/18 = 2500/9
RS = 60 + 40 = 100 * 5/18
T = 2500/9 * 18/500 = 10 sec.Answer: A
Question: Which of these must the factor W of the product of four consecutive even integers:-
1) 48
2) 64
3) 96
4) 192
5) 80
A.W=1,2 only
B.W=2,3 only
C.W=1,2,3 only
D.W=1,2,3,4 only
Answer: D.W=1,2,3,4 only
Explanation: Let the four variables be a< b< c< d.
Assume a worst case scenario where the a equal to a prime number (hence odd).
therefore
a = divisible by 1
b = a + 1 (divisible by 2)
c = a + 3 (divisible by 3)
d = a + 4 (divisible by 4)
therefore
each answer choice must be divisible by 2 x 3 x 4 = 24
only 80 is not divisible. Therefore answer = D
Question: There are 2 available positions and 50 candidates, one half of whom are democrats and another half are republicans. If it was decided that the positions would be filled at random, then what is the probability Q that the both positions will be taken by members of just one party?
A.1/25
B.12/49
C.1/4
D.24/49
Answer: D.24/49
Explanation: Q probability of one party having both spots:
(1/2) * (24/49) = 12/49
(1/2) or (25/50) because it does not matter which party or which person gets the first spot. (24/49) because after one person from a particular party is chosen, there are 24 members of the same party left out of 49 total candidates.
Since this result can happen for both parties, (12/49) + (12/49) = (24/49)
Answer: D
Question: If there are 4 peanuts in a box and Mary puts 12 more peanuts inside, how many peanuts are in the box?
A.8
B.16
C.10
D.11
Answer: B.16
Explanation: 12+4=16
correct answer is B)16
Question: A qualified worker digs a well in 4 hours. He invites 2 apprentices, both capable of working 3/4 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.1:24
B.1:34
C.1:44
D.1:36
Answer: D.1:36
Explanation: and answer is correct as you have calculated : 100/72 hrs that is 1.64 hrs - 1 hr and 36 minutes, so 1:36, hence, D.
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 90 kmph. Find the speed of the boat in still water and the speed of the stream?
A.10 kmph.
B.15 kmph.
C.18 kmph.
D.11 kmph.
Answer: B.15 kmph.
Explanation: Speed of the boat in still water = (60+90)/2 = 75 kmph. Speed of the stream = (90-60)/2
= 15 kmph.
Answer:B
Question: A coin has two sides. One side has the number 1 on it and the other side has the number 2 on it. If the coin is flipped three times what is the probability that the sum of the numbers on the landing side of the coin will be greater than 4?
A.3/8
B.1/16
C.1/8
D.1/2
Answer: D.1/2
Explanation: Cases for sum to be greater than 4 are as mentioned below
Case 1: (1, 2, 2)
Case 2: (2, 1, 2)
Case 3: (2, 2, 1)
Case 4: (2, 2, 2)
Total Outcomes = 2 x 2 x 2 = 8
Probability = Favorable Outcomes / Total Outcomes
I.e. Probability = 4/8 = 1/2
Answer: Option D
Question: Vijay lent out an amount Rs. 10000 into two parts, one at 8% p.a. and the remaining at 10% p.a. both on simple interest. At the end of the year he received Rs. 850 as total interest. What was the amount he lent out at 8% pa.a?
A.Rs. 15000
B.Rs. 6000
C.Rs. 25000
D.Rs. 10000
Answer: A.Rs. 15000
Explanation: Let the amount lent out at 8% p.a. be Rs. A
=> (A * 8)/100 + [(10000 - A) * 10]/100 = 850
=> A = Rs. 15000.
ANSWER:A
Question: What is the next number of the following sequence
3^2,27,3^4,243
A.3^6
B.3^5
C.3^4
D.3^2
Answer: A.3^6
Explanation: 3^2,27,3^4,243,x
3^2,3^3,3^4,3^5,3^6
x=3^6
ANSWER:A
Question: Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is?
A.1/8
B.1/7
C.1/9
D.1/2
Answer: B.1/7
Explanation: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer: B
Question: The number of sequences in which 10 players can throw a ball, so that the youngest player may not be the last is ?
A.4300028
B.3265920
C.4320201
D.3786220
Answer: B.3265920
Explanation: x Not younger
The last ball can be thrown by any of the remaining 10 players. The first 6 players can throw the ball in 9P9 ways.
The required number of ways = 9(9!)
= 3265920
Answer:B
Question: A and B are two partially filled buckets of water. If 5 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 3 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?
A.11
B.13
C.17
D.49/5
Answer: D.49/5
Explanation: Let A contains A, B contains B liters
so, (A-5)/(B+5)= 1/3.......(1)
again, (B-3)/(A+3)= 1/2..........(2)
from (1)(2) we find A= 49/5
ans: (D)
Question: Two bullet trains of equal lengths take 10 seconds and 12 seconds respectively to cross a telegraph post. If the length of each bullet train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
A.11 sec.
B.15 sec.
C.12 sec.
D.17 sec.
Answer: A.11 sec.
Explanation: Speed of the first bullet train = 120/10 m/sec = 12 m/sec.
Speed of the second bullet train = 120/12 m/sec = 10 m/sec.
Relative speed = (12 + 10) = 22 m/sec.
Required time = (120 + 120)/22 sec = 11 sec.
A
Question: A batsman scored 120 runs which included 10 boundaries and 6 sixes. What % of his total score did he make by running between the wickets
A.40%
B.50%
C.36.67%
D.70%
Answer: C.36.67%
Explanation: Number of runs made by running = 120 - (10 x 4 + 6 x 6)
= 120 - (76)
= 44
Now, we need to calculate 60 is what percent of 120.
=> 44/120 * 100 = 36.67 %
C
Question: In the interior of a forest, a certain number of apes equal to the square of one-sixth of the total number are playing and having great fun. The remaining five apes are on a hill and the echo of their shrieks by the adjoining hills frightens them. They came and join the apes in the forest and play with enthusiasm. What is the total number of apes?
A.48
B.16
C.64
D.6 or 30
Answer: D.6 or 30
Explanation: Let total number be x
No in the interior = (x/6)^2
No outside = 5
So : x - (x/6)^2=5
x^2-36x+180=0
x^2-30x-6x+180=0
(x-6)(x-30)=0
So either x=6 or x=30
D
Question: Ajay and Vijay have some marbles with them. Ajay told Vijay "if you give me 'x' marbles, both of us will have equal number of marbles". Vijay then told Ajay "if you give me twice as many marbles, I will have 30 more marbles than you would". Find 'x'?
A.6
B.5
C.8
D.7
Answer: B.5
Explanation: Explanation:
If Vijay gives 'x' marbles to Ajay then Vijay and Ajay would have V - x and A + x marbles.
V - x = A + x --- (1)
If Ajay gives 2x marbles to Vijay then Ajay and Vijay would have A - 2x and V + 2x marbles.
V + 2x - (A - 2x) = 30 => V - A + 4x = 30 --- (2)
From (1) we have V - A = 2x
Substituting V - A = 2x in (2)
6x = 30 => x = 5.
Answer: B
Question: If x and y are integers and x^2*y is a negative odd integer, which of the following must be true?
I. xy^2 is odd.
II. xy is negative.
III. x + y is even.
A.I only
B.III only
C.I and II only
D.I and III only
Answer: D.I and III only
Explanation: x^2*y = negative odd integer
inference:
1. Odd * Odd = Odd
2. y is negative odd integer
3. x is odd (since its squared, the result is positive - so x could be either positive or negative).
Statement I - xy is odd, so is its sqaure - statement must be true
Statement II - xy may or may not be negative - statement may be true but NOT must
Statement III - x and y are odd, so Odd + Odd = Even - statement must be true
Answer is D
Question: Three friends-whose walking rates are 1 ft./sec., 3ft./sec.,and 6ft./sec. start together walking in the same direction around a circular track that is 240 feet in circumference.After how many minutes are the three of them together again?
A.4 mins
B.10 mins
C.15 mins
D.3 mins
Answer: A.4 mins
Explanation: Answer will be A
The time they take will be what the 1st friend takes to complete one circumference as he is the slowest and that is the point all 3 of them will be together at the end of 4 mins.
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
A.1 min
B.9 min
C.4 min
D.3 min
Answer: C.4 min
Explanation: C
4 min
S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min
Question: P is three times as fast as Q and working together, they can complete a work in 16 days. In how many days can Q alone complete the work?
A.11 days
B.16 days
C.13 days
D.64 days
Answer: D.64 days
Explanation: P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 16 days,
which means Q can alone do the work in 4*16=64 days.
Answer : D
Question: Set A: {1, 3, 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.9/14
D.4/7
Answer: D.4/7
Explanation: probability : 6/7*5/6*4/5=4/7.
Ans D
Question: The numbers of pizza slices that are sold in Joey's Pizza are only in quantities of 5 and 8 slices per customer. How many slices cannot be bought?
A.42.
B.38.
C.33.
D.22.
Answer: D.22.
Explanation: Let X pizzas of 5 slices and Y pizzas of 8 slices.
5X + 8Y.
Lets check options wise.
A. 42 => 5(2) + 8(4)
B. 38 => 5(6) + 8(1)
C. 33 => 5(5) + 8(1)
D. 22 = we can't write anything with 5 and 8 series..Lets try 5(1) + 8(2) = 21 , 5(3) + 8(1) = 23 , nothing works out.
E. 20 = 5(4) + 8(0)
Answer: correct option is D
Question: A room contains 240 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
A.02
B.04
C.06
D.08
Answer: C.06
Explanation: Say group of x people left the room.
# of women in the room was 0.15*240=36;
# of women in the group that left 0.3x;
# of women in the room after the group left it is 0.1(240-x);
So, 36-0.3x= 0.1(240-x) --> x=6.
Answer: C.
Question: If a and b are positive integers such that a/b = 9.32, which of the following must be a divisor of a
A.4
B.3
C.11
D.10
Answer: A.4
Explanation: a/b = 9.32
a/b = 932/100
a/b = 466/50
a = 466/50*b
We require to find from the available 5 options that must be a divisor of a"
This also means which of the following 5 options can divide 466 evenly
(Ignore b as its value unknown; Ignore 50 as in denominator)
Only option A = 4 best fits in
Answer = 4
ANSWER:A
Question: The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 12%?
A.37.5%
B.37.8%
C.38.5%
D.27.5%
Answer: A.37.5%
Explanation: Explanation:
Let marked price = Rs. 100.
Then, C.P. = RS. 64, S.P. = Rs. 88
Gain % = 24/64 * 100 = 37.5%.
Answer:A
Question: The average of 11numbers is 50. Out of 11numbers the average of first 6no. is 58, and last 6numbers is 65 then find 6th number?
A.A)188
B.B)65
C.C)58
D.D)62
Answer: A.A)188
Explanation: 6th number = sum of 1st 6no.s + sum of last 6no.s - sum of 11no.s
answer = 6*58+6*65-11*50= 188
Answer is A
Question: Points X, Y, and Z lie, in that order, on a straight railroad track. The distance from point X to point Y is twice the distance from point Y to point Z. A train traveled from point X to point Z without stopping. The train's average speed when traveling from point X to point Y was 300 miles per hour and the train's average speed when traveling from point Y to point Z was 100 miles per hour. What was the train's average speed, in miles per hour, when traveling from point X to point Z?
A.200
B.220
C.240
D.180
Answer: D.180
Explanation: Average speed = distance/time
Because we are looking for average speed we can pick a distance for the variable D.
Speed X-Y = 300
Speed Y-Z = 100
Average Speed = total distance/total rate
rate = distance/time
X====================Y==========Z
If X-Y is twice the length of Y-Z then let X-Y = 2d and let Y-Z= d
Average speed = 3d/(2d/300) + (d/100)
3d/(2d/300) + (3d/300)
3d/(5d/300)
900d/5d
Average speed = 180
ANSWER: D
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 80 metres?
A.16 seconds
B.76 seconds
C.26 seconds
D.12 seconds
Answer: A.16 seconds
Explanation: Speed of the boat downstream = 15 + 3
= 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 80 m
= 80/5
= 16 seconds.
Answer: A
Question: Average between two sets of numbers is closer to the set withmore numbers?
A.70
B.80
C.90
D.95
Answer: B.80
Explanation: If on a test three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group is not 85% but rather 3×90+2×805=4305=86.3×90+2×805=4305=86.
Here, 90 has a weight of 3 => it occurs 3 times.
Whereas 80 has a weight of 2 => it occurs 2 times.
So the average is closer to 90 than to 80 as we have just calculated.
B
Question: Exactly one side of a certain 10-sided die are red. What is the probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll?
A.0.09
B.0.1
C.0.081
D.0.091
Answer: C.0.081
Explanation: Total no. of sides = 10
Side that are red = 1
Probability that the die lands with red side up = 1/10
Therefore, Probability that the die does not land with red side up = 1 - 1/10 = 9/10
Probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll
= (1st roll - non red face) X (2nd roll - non red face) X (3rd roll - red face)
= (9/10) X (9/10) X (1/10)
= 81/1000
= 0.081
C
Question: With out any halt a train travels a certain distance with an average speed of 75 km ph , and with halts it covers the same distance at an average speed of 60 kmph. When it is traveling with halts, how many minutes/per hour does the train halt on an average ?
A.48 min.
B.12min.
C.15min.
D.18min.
Answer: B.12min.
Explanation: With halt in 1 hour the train travels 60km
With out halt for traveling same distance it take 60/75 = 4/5 = 48 minutes
:. 12 minutes is the halting time per hour
ANSWER:B
Question: 20 percent of Andrea's living room floor is covered by a carpet that is 4 feet by 9 feet. What is the area of her living room floor?
A.14.4
B.180
C.50.4
D.60
Answer: B.180
Explanation: 20% of Area of the floor = 4*9 square feet = 36 square feet
i.e. 100% Area of Floor = (36/20)*100 = 180 square feet
Answer: Option B
Question: In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?
A.50
B.60
C.10
D.20
Answer: C.10
Explanation: Let us write the fraction for each group of students
Group A: younger than 10: 50% = 50/100 = 1/2
Group B: 10 years old: 1/20
Group C: older that 10 but younger than 12: 1/10
Group D: 12 years or older: 70 students
The fraction for group A, B and C together is given by
1 / 2 + 1 / 20 + 1 / 10 = 10 / 20 + 1 / 20 + 2 / 20 , common denominator
= 13 / 20 , add numerators
The fraction for group D is given by
20 / 20 - 13 / 20 = 7 / 20 and corresponds to 70 students
If X is the total number of students, then
7 / 20 of X = 70
or (7 / 20) * X = 70
Solve for X
X = 70 * (20 / 7) = 200
Students who are 10 years old have a fraction of 1 / 20 of the total X and their number is equal to
(1 / 20) of 200 = 10 students
correct answer C
Question: A cricketer has certain average for 5 innings. In the 6 inning he scored 90 runs, there by increasing his average by 8 runs. His new average is
A.42
B.52
C.60
D.48
Answer: A.42
Explanation: Let the average for 5 innings be x
Then, (5x+90)/6 = x+8
x = 42
Answer is A
Question: The average salary of Raj and Roshan is Rs. 4000 but the average salary of Raj, Roshan and Thomas is Rs. 5000. What is the salary of Thomas?
A.4000
B.5000
C.6000
D.7000
Answer: D.7000
Explanation: Total salary of Raj and Roshan= 2x4000=8000
Total salary of Raj Roshan and Thomas= 3x5000=15000
Salary of Thomas= 15000-8000= Rs. 7000
Answer: D
Question: The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20 per cent. The two reductions together are equal to a single reduction of
A.45%
B.40%
C.35%
D.32.5%
Answer: B.40%
Explanation: Price = p
initially price reduced by 25% which means new price is 3/4P
Now on this new price further 20 percent is reduced which means the new price is merely 80 percent of 3/4P
==> (3/4)x(4/5)P = 12/20P is the new price after both deduction which is 60 percent of the original value P. This implies this entire series of deduction is worth having discounted 40% of P. So answer is B = 40%
ANSWER:B
Question: In a certain mathematical activity, we have five cards with five different prime numbers on them. We will distribute these five cards among three envelope: all could go in any envelope, or they could be broken up in any way among the envelopes. Then in each envelop, we find the product of all the cards in that envelope: that is the “number” of the envelope. An envelope containing no cards has the number 1. We then put the three envelope numbers in order, from lowest to highest, and that is our set. How many different Q sets can be produced by this process?
A. 41
B. 89
C. 125
D. 243
Answer: A. 41
Explanation: Case 1: 1 used envelope => 1 way
Case 2: 2 used envelopes
- 4-1-0: Choose 4 from 5 cards: 5 ways
- 3-2-0: Choose 3 from 5 cards: 10 ways
Case 3: All envelopes used
- 3-1-1: Choose 3 from 5 andno need to choose 1 from 2: 10 ways
- 2-2-1: Choose 2 from 5 and choose 2 from 3, but two groups are the same => (10X3):2 = 15
Total Q: 1+5+10+10+15=41 => Answer: A
Question: It takes Avery 3 hours to build a brick wall while Tom can do it in 2.5 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?
A.25 minutes.
B.30 minutes.
C.40 minutes.
D.55 minutes
Answer: C.40 minutes.
Explanation: Avery's efficiency is 100/3 = 33%
tom's = 100/2.5= 40%
they worked together for 1 hour and finished 73% of the job
remaining = 27 %
tom will complete 40% in 60 minutes , 20% in 30 minutes and ,
7% in 60*7/40 minutes = 10.5 minutes
time taken by tom to finish the remaining on his own = 30+10.5 = 40.5 minutes (adjusting for the 0.333) ~ 40 minutes
ANSWER:C
Question: A and B together have $1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
A.$310
B.$395
C.$484
D.$512
Answer: C.$484
Explanation: 4/15 A = 2/5 B
A = 2/5 * 15/4 B
A = 3/2 B
A/B = 3/2
A:B = 3:2
B's share = 1210*2/5 = $484
Answer is C
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
A.44 years
B.40 years
C.50 years
D.60 years
Answer: B.40 years
Explanation: Lets assume fathers,mothers and child's age before 3 years is x,y,z respe.
therefore (x+y+z)/3=27
now x+y+z=27*3=81
and (y-2+z-2)/2=20
y+z=40
on calculating both equations x=37
hence present age x+3=40
ANSWER:B
Question: Tough and Tricky questions: Word Problems.
AC Car Company wants to manufacture a new car known as Model X, and it is trying to determine how many cars it needs to sell in order to make an annual profit of $30,500,000. The annual fixed costs for Model X total $50,200,000. In addition, each Model X car has an average cost of $5,000 per vehicle to manufacture. If the Company forecasts it will sell 20,000 Model X cars this year, at what price must the Company sell the car to achieve the desired annual profit?
A.$4,035
B.$4,036
C.$9,035
D.$16,140
Answer: C.$9,035
Explanation: The AC company plans to make a profit of $30,500,000 and it needs to earn the fixed costs of $50,200,000, so it needs to earn $80,700,000 on top of the costs for the production of the 20,000 cars.
Therefore, price of each car needs to be the unit costs plus $80,700,000/20,000. After removing the 0's, we end with the unit costs plus $8,070/2, which is $5,000 plus $4,035. Therefore, Answer C is correct.
Question: A goods train leaves a station at a certain time and at a fixed speed. After 6 hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train.
A.36 kmph
B.40 kmph
C.30 kmph
D.42 kmph
Answer: A.36 kmph
Explanation: Let the speed of the goods train be x kmph.
Distance covered by goods train in 10 hours
= Distance covered by express train in 4 hours.
∴ 10x = 4 × 90 or x = 36.
So, speed of goods train = 36 kmph.
Answer A
Question: What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
A.4%
B.13%
C.20%
D.23%
Answer: C.20%
Explanation: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number =14
Required % = (14/70)x100 % =20%
answer :C
Question: Find the value of X: 2a^2-7a+10 = 14
A.7
B.5
C.6
D.4
Answer: D.4
Explanation: Using the elimination method substitute options for x and find the correct option.
Answer: D
Question: If one type of tobacco costs Re.1/- per kg and other type costs Rs. 5/- per kg. What quantity of first type and second type are mixed so that 100 kg of mixture costs Rs. 100/-?
A.50 kg
B.100 kg
C.150 kg
D.200 kg
Answer: B.100 kg
Explanation: 100 kg of first type.
ANSWER:B
Question: The moon revolves around the earth at a speed of approximately 0.2 kilometers per second. This approximate speed is how many kilometers per hour?
A.60
B.720
C.62.5
D.3,600
Answer: B.720
Explanation: moon revolves around the earth at a speed of 1.02kilometers per second.
one hour equal to 60 minutes.
one minute equals to 60 seconds. so one hour equals to 3600seconds.
so one hour, speed= 0.2*3600=720kilometers per hour.
Option B is correct
Question: Find the odd man out. 1, 16, 81, 255, 625, 1296
A.255
B.1296
C.81
D.1
Answer: A.255
Explanation: Explanation :
The pattern is 1^4, 2^4, 3^4, 4^4, 5^4, 6^4
Hence, in place of 255, the right digit is 44 = 256
Answer : Option A
Question: Two trains for Delhi leave Jaipur at 8:30 am and 9:00 am and travel at 60 km/hr and 75 km/hr respectively. How many km from Jaipur will the two trains meet?
A.150 km
B.127 km
C.1717 km
D.166 km
Answer: A.150 km
Explanation: ANSWER: A
Question: How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?
A.20
B.150
C.225
D.300
Answer: D.300
Explanation: 4 options for the first digit: 2, 4, 6, 8;
5 options for the second digit: 1, 3, 5, 7, 9;
4 options for the third digit: 2, 3, 5, 7;
4 options for the fourth digit: 0, 3, 6, 9.
Four digit # possible without the restriction (about the digit 2): 4*5*4*4=320
Numbers with two 2-s, 2X2X 1*5*1*4=20.
Thus there are 320-20=300 such numbers.
Answer: D.
Question: There are two positive numbers in the ratio 3:11. If the larger number exceeds the smaller by 32, then what is the smaller number?
A.8
B.11
C.12
D.15
Answer: C.12
Explanation: Let the two positive numbers be 3x and 11x respectively.
11x - 3x = 32
8x = 32 => x = 4
Thus, the smaller number = 3x = 12.
Answer: C
Question: If two dice are thrown together, the probability of getting an even prime number on the dice is
A.1/36
B.1/18
C.1/13
D.1/9
Answer: A.1/36
Explanation: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number prime number on the dice.
P(E) = 1/36
A)
Question: A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 30%, what should be the sale price of the mixed tea?
A.23.75
B.22
C.20.8
D.19.2
Answer: C.20.8
Explanation: C.P. of mixture = 80×15+20×20 /80+20=16
∴ S.P. = (100+30)/100×16=20.8
Answer C