RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: What is the area of square field whose side of length 15 m?
A.225 sq m
B.220 sq m
C.100 sq m
D.30 sq m
Answer: A.225 sq m
Explanation: Explanation:
15 * 15 = 225 sq m
ANSWER IS A
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 4 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.52/5
C.17
D.21
Answer: B.52/5
Explanation: Let A contains A, B contains B liters
so, (A-5)/(B+5)= 1/3.......(1)
again, (B-4)/(A+4)= 1/2..........(2)
from (1)(2) we find A= 52/5
ans: (B)
Question: Three boys, two girls, and two women are to be seated on a bench. If one specific boy must be seated on one of the end seats, and one specific girl must me seated exactly in the middle, find the number of possible arrangements.
A.48
B.144
C.240
D.288
Answer: C.240
Explanation: "One specific boy is seated to either of end seat", lets call him b1
"One specific girl is seated in the middle", lets call her g1
Note the question says *specific girl* and *specific boy*, so we do not consider for example the other girl , g2, being seated on seat #4. Same goes with the specific boy, b1.
b1 can be seated 2 different seats : 2!
g1 is seated on the seat #4, fixed (no other alternative) : 1
the remaining 5 seats can be filled with the remaining people b2,b3,g2,w1,w2: 5!
2! x 1 x 5! = 240
Answer C
Question: In a race of 200 m, A can beat B by 21 m and C by 15 m. In a race of 425 m, C will beat B by ?
A.30 m
B.75 m
C.85 m
D.25 m
Answer: A.30 m
Explanation: Explanation:
A:B = 100 : 79
A:C = 100 : 85
=> B:C = 79:85
When C covers 85 m , B Covers 79 m
When C covers 425 m , B Covers
=> 395 m
So C beats B by (425 - 395) = 30 m.
Answer: A
Question: How many positive integers less than 1000 are multiples of 5 but NOT of 4 or 7?
A.114
B.121
C.122
D.129
Answer: C.122
Explanation: There are 1000/5=200 multiples of 5 . now we have to find the number of multiples of 5 and 4 that is 20 between 0 to 1000 and 5 and 7 that is 35 between 0 to 1000.
multiples of 20=1000/20=50 multiples. and multiples of 35= 1000/35 =28.5 so 28 multiples of 35.
So multiples of 5 between o to 1000 not including multiples of 20 and 35 are equal to 200-78 = 122 multiples.
So the answer is C.
Question: If k^3 is divisible by 168, what is the least possible value of integer k?
A.36
B.42
C.48
D.54
Answer: B.42
Explanation: k^3 = 168*x = 2^3*3*7*x
The factors of k must at minimum include 2*3*7 = 42.
The answer is B.
Question: At a certain supplier, a machine of type A costs $22,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
A.$7,920
B.$11,200
C.$12,000
D.$12,800
Answer: A.$7,920
Explanation: Total Cost of 2 Machines of Type A
= 20% of (Cost of 2 machine A) + remainder + 40 % remainder
= 20% of 44000 + (44000 - 20% of 44000) + 40% of (44000 - 20% of 44000)
= 58080
Total Cost of 1 Machine of Type B
= 20% of (Cost of 1 machine B) + remainder + 40 % remainder
= 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000)
= 66000
Diff = 66000 - 58080 = 7900
Hence, A.
Question: The average age of father and his two sons is 24 Years. Five years ago, the average age of the two sons was 15 Years. If the difference between the ages of the two sons is four years, what is the present age of the father?
A.45
B.32
C.47
D.48
Answer: B.32
Explanation: The total present age of father and two sons is 3x24 = 72 yrs
The total present age of sons is (15+5) X 2 = 40Years
so, present age of father is 72 â€“ 40 = 32 yrs
Answer B
Question: What is the cost of leveling the field in the form of parallelogram at the rate of Rs.30/10 sq.metre, whose base & perpendicular distance from the other side being 64m & 74m respectively?
A.s. 6000
B.s. 6300
C.s.4736
D.s. 6480
Answer: C.s.4736
Explanation: Area of the parallelogram = Length of the base * Perpendicular height
= 64 * 74 = 4736 m.
Total cost of levelling = Rs. 4736
C
Question: Due to construction, the speed limit along an 9-mile section of highway is reduced from 55 miles per hour to 20 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
A.A) 5.61
B.B) 8
C.C) 10
D.D) 17.19
Answer: D.D) 17.19
Explanation: Old time in minutes to cross 9 miles stretch = 9*60/55 = 9*12/11 = 9.81
New time in minutes to cross 9 miles stretch = 9*60/20 = 9*3/1 = 27
Time difference = 17.19
Ans:D
Question: Find the odd man out
2, 5, 11, 23, 48, 95
A.5
B.11
C.23
D.48
Answer: D.48
Explanation: 2*2+1 = 5
5*2+1 = 11
11*2+1 = 23
23*2+1 = 47
47*2+1 = 95
ANSWER:D
Question: If 0 < a < 1, what is the median of the values a, x^-1, a^2, a^1/2 and a^3?
A.a
B.a^-1
C.a^2
D.a^1/2
Answer: A.a
Explanation: A. To make the problem less confusing, I picked a number between 0 and 1 such as a = 1/4 and calculate:
a = 1/4
a^-1 = 4
a^2 = 1/16
a^(1/2) = 1/2
a^3 = 1/8.
From this, rearrange the number and the median is 1/4, which is a. Answer A
Question: Rahim and his uncle differ in their ages by 30 years. After 7 years, if the sum of their ages is 66, what will be the age of the uncle ?
A.41 years
B.36
C.48
D.33
Answer: A.41 years
Explanation: A
41
Let uncle’s present age = x
Rahim's present age = y
y– x= 30 ...(i)
After 7 year
(x + 7) + (y+ 7) = 66
x + y + 14 = 66
x + y = 52 ...(ii)
combining (i) and (ii) we get
(x + y = 52) + (x – y = 30)
2x= 82
x= 41
Uncle's age is 41
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
A.1/115
B.3/113
C.1/216
D.3/119
Answer: C.1/216
Explanation: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Question: Find the value of x if the mean of the series 245,564,458,125,36,x is 250
A.50
B.72
C.36
D.45
Answer: B.72
Explanation: mean = 245+564+458+125+36+x / 6 = 250
1428+x = 1500
x = 72
Answer is B
Question: If 6 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?
A. -7
B. -4
C. -3
D. -9
Answer: D. -9
Explanation: The phrase “6 is one solution of the equation” means that one value of x is 6. Thus, we first must plug 6 for x into the given equation to determine the value of k. So we have
6^2 + (3)(6) + k = 10
36 + 18 + k = 10
54 + k = 10
k = -44
Next we plug -44 into the given equation for k and then solve for x.
x^2 + 3x – 44 = 10
x^2 + 3x – 54 = 0
(x+9)(x-6) = 0
x = -9 or x = 6
Thus, -9 is the other solution. Answer D.
Question: A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1990 on her 32nd birthday first be eligible to retire under this provision?
A.2003
B.2009
C.2005
D.2006
Answer: B.2009
Explanation: She must gain at least 70 points, now she has 31 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2*(# of years) = 70 --> (# of years) = 19 --> 1990+19=2009.
Answer: B.
Question: The concentration of spirit in three different vessels A, B and C are 45%, 30% and 12% respectively. If 4 litres from vessel A, 5 litres from vessel B and 6 litres from vessel C are mixed, find the concentration of spirit in the resultant solution.
A.32.80%
B.26.80%
C.34%
D.24.62%
Answer: B.26.80%
Explanation: Quantity of spirit in new solution=(4*45/100)+(5*30/100)+(6*12/100)=1.8+1.5+0.72=4.02 liters
So % concentration of spirit=100*4.02/(4+5+6)=26.80%
ANSWER:B
Question: Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has traveled 100 km more than the second. The distance between P and Q is?
A.237
B.278
C.277
D.900
Answer: D.900
Explanation: At the time of meeting, let the distance traveled by the second train be x km. Then, distance covered by the first train is (x + 100) km.
x/40 = (x + 100)/50
50x = 40x + 4000 => x = 400
So, distance between P and Q = (x + x + 100)km = 900 km.
Answer: D
Question: What is the length of the longest pole which can be kept in a room 10 m long, 4 m broad and 3 m high?
A.7
B.9
C.11.18
D.13
Answer: C.11.18
Explanation: Explanation:
d2 = 102 + 42 + 32 = 11.18
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.0 sq m
B.3 sq m
C.2 sq m
D.6 sq m
Answer: A.0 sq m
Explanation: Explanation:
S = (1 + 2 + 3)/2 = 3
=> No triangle exists
ANSWER IS A
Question: The set S consists of 5 numbers: {1,2,3,4,5}. If all possible subsets including the null set are created and one subset is chosen at random, what is the probability that the subset has 2 as its largest number?
A.1/2
B.1/4
C.1/8
D.1/16
Answer: D.1/16
Explanation: The set S has 2^5 = 32 subsets.
The number 2 is the largest number in the subset {1,2} and the subset {2}.
Thus 2 is the largest number in 2 subsets of S.
The probability that 2 is the largest number is 2/32 = 1/16.
The answer is D.
Question: Andy solves problems 80 to 125 inclusive in a Math exercise. How many problems does he solve?
A.53
B.52
C.51
D.46
Answer: D.46
Explanation: 125-80+1= 52
'D' is the answer
Question: Kamal was 4 times as old as his son 8 years ago. After 8 years, Kamal will be twice as old as his son. Find out the present age of Kamal.
A.30
B.35
C.40
D.45
Answer: C.40
Explanation: Let age of the son before 8 years =x
Then, age of Kamal before 8 years ago =4x
After 8 years, Kamal will be twice as old as his son
⇒4x+16=2(x+16)⇒x=8
Present age of Kamal
=4x+8=4×8+8=40
Answer is C.
Question: Pipe A can fill a tank in 4 hours. Due to a leak at the bottom, it takes 8 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
A.13
B.17
C.18
D.8
Answer: D.8
Explanation: Let the leak can empty the full tank in x hours 1/4 - 1/x = 1/8
=> 1/x = 1/4 - 1/8 = (2 - 1)/8 = 1/8
=> x = 8.
Answer: D
Question: Train A travelling at 63 kmph takes 27 to sec to cross Train B when travelling in opposite direction whereas it takes 162 seconds to overtake it when travelling in the same direction. If the length of train B is 500 meters, find the length of Train A.
A.400 m
B.810 m
C.500 m
D.310 m
Answer: D.310 m
Explanation: DETAILED SOLUTION
Let the length of Train A be x meters
Let speed of Train B be y kmph
Relative distance = Relative speed * time taken to cross/overtake
Crossing scenario:
Relative speed of 2 trains = 63 + y
Time taken to cross = 27 sec or 27/3600 hrs
Relative distance between 2 trains = Length of Train A + length of train B = (x + 0.5) km
Therefore, x + 0.5 = (63 + y) * 27 / 3600 ----- (1)
Overtaking scenario:
Relative speed of 2 trains = 63 – y
Time taken to overtake = 162 sec or 162/3600 hrs
Relative distance between 2 trains = x + 0.5
Therefore, x + 0.5 = (63 – y) * 162/3600 --- (2)
From (1) and (2), solve for y.
(63 + y) * 27 = (63 – y) * 162
27y + 162 y = 63*162 – 63 *27
189y = 63 * 135 or y = 45 kmph
Substitute in (2) to get x.
x + 0.5 = (63 – 45) * 162/3600
Or x = 0.31 km or 310 meters
CORRECT ANSWER D
Question: What is the total number of integers between 200 and 500 that are divisible by 25?
A.20
B.25
C.14
D.15
Answer: D.15
Explanation: 125, 150, 175, ..., 450,475
This is an equally spaced list; you can use the formula:
n = (largest - smallest) / ('space') + 1 = (475- 125) / (25) + 1 = 350/25 + 1 = 14+ 1 = 15
Answer is D
Question: If Rs.400 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
A.s.575
B.s.595
C.s.590
D.s.610
Answer: D.s.610
Explanation: 80 = (400*4*R)/100
R = 8.75%
I = (400*6*8.75)/100 = 210
400 + 210 = 610
ANSWER:D
Question: A car runs 10,000 miles using 5 tyres interchangeably. to have equal worn out by all tyres,how many miles each tyre should have run?
A.5000
B.8000
C.4000
D.3000
Answer: B.8000
Explanation: for 5 tyres running interchangeably 10,000 miles the car runs
for 1 tyre=10000/5=2000
as you all know i suppose the car has 4 tyre
to have equal worn out by 4 tyres we need=2000*4=8000
ANSWER:B
Question: The salaries of A, B, C are in the ratio 2:3:5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries?
A.23:33:62
B.23:33:68
C.23:33:60
D.23:32:60
Answer: C.23:33:60
Explanation: Let A = 2k, B = 3k and C = 5k
A's new salary = 115/100 of 2k = 23/10 k
B's new salary = 110/100 of 3k = 33/10 k
C's new salary = 120/100 of 5k = 6k
New ratio = 23k/10 : 33k/10 : 6k = 23:33:60
Answer:C
Question: Robert is traveling from one end of a forest to the other. In order to find his way back, he is leaving morsels of bread in the following pattern: 2 morsels of milk, 3 morsels of white, and 1 morsel of rye. The pattern repeats after he leaves the morsel of rye. If Robert drops 2,000 morsels of bread, what are the last 3 morsels of bread that he drops?
A.rye − milk − milk
B.milk − milk − white
C.white − rye − milk
D.white − white − white
Answer: A.rye − milk − milk
Explanation: In a single round Robert drops 6 morsels.
Remainder (2000/6) = 2
Final action = 2 drops of milk --> Options B, C, D and E can be eliminated
Answer: A
Question: Over a three-week period, the price of an ounce of gold increased by 25% in the first week, decreased by 40% in the following week, and increased by 20% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price at the end of the three weeks?
A.0.75G
B.0.8G
C.0.85G
D.0.9G
Answer: D.0.9G
Explanation: After 3 weeks, the price was 1.2*0.6*1.25*G=0.9G
The answer is D.
Question: Ashok and Pyarelal invested money together in a business and share a capital of Ashok is 1/9 of that of Pyarelal.if the incur a loss of Rs 2000 then loss of Pyarelal?
A.1600
B.1700
C.1800
D.1900
Answer: C.1800
Explanation: Let the capital of Pyarelal be x, then capital of Ashok=x/9
So ratio of investment of Pyarelal and Ashok = x : x/9 =9x : x
Hence out of the total loss of 2000, loss of Pyarelal= 2000*9x/10x=1800
ANSWER:C
Question: 2,300 has how many positive divisors?
A.12
B.15
C.18
D.24
Answer: C.18
Explanation: By factorization, we can write 2300 as 2300=2^2*5^2*23.
The number of factors is (2+1)(2+1)(1+1) = 18
The answer is C.
Question: If x = 3p, where p is a prime number greater than 2, how many different positive even divisors does x have, including x?
A.0
B.1
C.2
D.3
Answer: A.0
Explanation: p is prime greater than 2 thus p is odd
3p is odd
Thus no even factors
Ans:A
Question: Three bells commence tolling together and toll at intervals of 2, 4, 6 seconds respectively. In 10 minutes, how many times do they toll together ?
A.51
B.52
C.53
D.54
Answer: A.51
Explanation: LCM of 2, 4, 6 is 12.
So, after each 12 seconds, they would toll together.
Hence, in 10 minutes, they would toll 10*60 seconds / 12 seconds = 50 times
But then the question says they commence tolling together. So, they basically also toll at thebeginning(0second).
So, total tolls together = 50+1 = 51
Answer: A
Question: One-third of Ramani’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has 150000 as total savings, how much he saved in Public Provident Fund?
A.60000
B.50000
C.90000
D.30000
Answer: A.60000
Explanation: Ratio of Ramani’s savings in NSC and PPF = 3: 2
His savings in PPF = 2⁄5 × 150000 = 60000
Answer A
Question: Stock / Number of shares
V ------------ 68
W ---------- 112
X ------------ 56
Y ------------ 94
Z ------------ 45
The table shows the number of shares of each of the 5 stocks owned by Mr Sami. If Mr. Sami was to sell 20 shares of Stock X and buy 27 shares of stock Y, what would be the increase in the range of the numbers of shares of the 5 stocks owned by Mr. Sami?
A.4
B.6
C.9
D.18
Answer: D.18
Explanation: Based on the original number of shares, the range would be: 112 - 45 = 67
However, the prompt tells us that two of the values in the table are going to change. After the changes, the values will be:
V 68
W 112
X 36
Y 121
Z 45
Now the range is 121 - 36 = 85
The INCREASE in the range requires us to compare thenewrange to theoldrange: 85 - 67 = 18
D
Question: Swetha takes a trip and drives 8 hours from Town A to Town C at a rate of 40 miles per hour. On her way back, Swetha drives 30 miles per hour and stops in Town Y which is midway between Town A and Town C. How many hours does it take Swetha to drive from Town C to Town B?
A.1.01
B.1.25
C.1.53
D.5.33
Answer: D.5.33
Explanation: distance from A to C =8 hr* 40 mph= 320 miles
hence distance from B to C= 1/2*320=160
time=160/30=5.33 hrs
IMO: D
Question: The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 22,000 is made?
A.328897
B.120000
C.118000
D.277768
Answer: C.118000
Explanation: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 22,000 is made = 96,000 + 24,000 = Rs. 1,18,000
Answer: C
Question: In each term of a sequence, 12 is added to get the next term. If the first term is 5, what is the forty-fifth term?
A. 533
B. 595
C. 513
D. 562
Answer: A. 533
Explanation: 1rst term + 44 terms = 5 + 12+12+12+12+12+12+12+...+12 (44 times)
5 + (12 x 44) = 5 + 528 = 533
Answer A
Question: A two digit number is 18 less than the sum of the squares of its digits. How many such numbers are there?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: suppose the digit 10x+y.
so, 10x+y=x^2+y^2-18
=>(x-6)(x-4)=(y-7)(-y-6)
so conddition satisfied for x=6,4 and y=7 so no of digit 2. 67,47.
ANSWER:B
Question: City A and City B are 140 miles apart. Train C departs City A, heading towards City B, at 4:00 and travels at 40 miles per hour. Train D departs City B, heading towards City A, at 5:30 and travels at 20 miles per hour. The trains travel on parallel tracks. At what time do the two trains meet?
A.5:00
B.7:30
C.6:00
D.6:30
Answer: B.7:30
Explanation: Train C has traveled 20 mi in the half hour before Train D has started its journey.
140-20=120
40+20 =60 mph
120 mi/ 60 mph = 2 hrs
5:30pm + 2 hrs = 7:30pm
Answer:
B. 7:30
Question: A and B can do a piece of work in 6 days, B and C in 8 days, C and A in 12 days. How long will C take to do it?
A.48 days
B.55 days
C.24 days
D.33 days
Answer: A.48 days
Explanation: 2c = 1/8 + 1/12 – 1/6= 1/24
c = 1/48 => 48 days
Answer: A
Question: If x^2 + 9/x^2 = 10, what is the value of x - 3/x
A.36
B.25
C.2
D.5
Answer: C.2
Explanation: To find : x-3/x. Let it be t.
=> x-3/x = t
=> (x^2 + 9/x^2) - 2*x*3/x = t^2 (Squaring both sides).
=> (10) - 2*3 = 4
=> t^2 = 4. Thus t=2 or t=-2.
Answer C
Question: When asked what the time is,a person answered that the amount of time left is 3/5 of the time already completed.what is the time.
A.2 PM
B.9 PM
C.3 PM
D.8 PM
Answer: C.3 PM
Explanation: A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x)
24−x=3/5x⇒x=15
Time is 3 PM
Answer:C
Question: Four people need to cross a dark river at night.
* They have only one torch and the river is too risky to cross without the torch.
* If all people cross simultaneously then torch light wont be sufficient.
* Speed of each person of crossing the river is different.cross time for each person is 1 min, 2 minutes, 7 minutes and 10 minutes.
What is the shortest time needed for all four of them to cross the river ?
A.16 minutes
B.17 minutes
C.18 minutes
D.19 minutes
Answer: B.17 minutes
Explanation: Solution:
17 min
The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 minutes. Is that it? No. That would make this question too simple even as a warm up question.
Let's brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let's put all this together.
1 and 2 go cross
2 comes back
7 and 10 go across
1 comes back
1 and 2 go across (done)
Total time = 2 + 2 + 10 + 1 + 2 = 17 minutes
Answer B
Question: Dana borrows 6000 pounds annually for her college education. If Dana gives her parents 2% of that amount back each month, how much will she still owe her parents after three years of college?
A.13680
B.13885
C.14005
D.14280
Answer: A.13680
Explanation: dana borrows 6000 and returns 2% per month.
so returns 120 per month. and 1440 per year.
so dana owes 6000-1440=4560 per year.
after 3 years she will owe 13680.
Ans (A)
Question: The 4 sticks in a complete bag of Pick-Up Sticks are all straight-line segments of negligible width, but each has a different length: 1 inch, 2 inches, 3 inches, and 4 inches, respectively. If Tommy picks a stick at random from each of 3 different complete bags of Pick-Up Sticks, what is the probability A that Tommy CANNOT form a triangle from the 3 sticks?
A.11/32
B.13/32
C.15/32
D.17/32
Answer: C.15/32
Explanation: In order to form a triangle, the sum of two sides must be greater than the third side.
So we can choose the combination of numbers which will NOT result in a triangle.
Favorable outcomes:
1,1,4 (4>1+1): 3 ways of arriving at this (1,1,4), (1,4,1), (4,1,1) or
1,2,4 (4>1+2): 6 ways of arriving at this (1,2,4), (1,4,2), (2,1,4), (2,4,1), (4,1,2), (4,2,1) which is same as 3!
1,3,4 (4=1+3): 6 ways of arriving at this
2,2,4 (4=2+2): 3 ways of arriving at this
1,1,3 (3>1+1): 3 ways of arriving at this
1,2,3 (3=1+2): 6 ways of arriving at this
1,1,2 (2+1+1): 3 ways of arriving at this
Overall favourable outcomes: 30
Total outcomes: 4*4*4 = 64 (4 ways of choosing a stick from each of the 3 bags)
Probability A that a triangle is not formed = 30/64 = 15/32
C is the correct option here.
Question: The average of marks obtained by 120 boys was 40. If the average of marks of passed boys was 39 and that of failed boys was 15, the number of boys who passed the examination is?
A.100
B.110
C.125
D.130
Answer: C.125
Explanation: Let the number of boys who passed = X.
Then, 39 x X + 15 x (120 - X) = 120 x 40
24X = 4800 - 1800
=> X = 3000/24
X = 125
Hence, the number of boys passed = 125.
ANSWER:C
Question: (A% of 2B + B% of A) is equal to ?
A.A% of B
B.B% of A
C.3% of AB
D.AB% of 3
Answer: C.3% of AB
Explanation: Answer
A% of 2B + B% of A =2AB/100 + AB/100
= 23AB/100 = 3% of AB
Correct Option: C
Question: if x+y+z =1. then xy+yz+zx is
A.1/2
B.1/3
C.1/4
D.1/5
Answer: C.1/4
Explanation: 1/2+1/2+0=1
xy=1/2*1/2=1/4
ANSWER:C
Question: If HARD is coded as 1357
and SOFT is coded as 2468
what will 21448 stand for?
A.SHOOR
B.SHOOA
C.SHOOT
D.SHEOT
Answer: C.SHOOT
Explanation: HARD = 1357 => 1=H, 3=A , 5=R , 7=D
SOFT = 2468 => 2=S, 4=O , 6=F , 8=T
so, 21448 = SHOOT
ANSWER:C
Question: A circular rim 14 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?
A.48pi/x
B.75x
C.48x
D.24x
Answer: D.24x
Explanation: The larger rim must circulate for the same number of inches the smaller rim does.
C = (pi)d
C(small): (pi)*14
C(large): (pi)*35
Lets say the time horizon is 60 seconds, so during that time the smaller rim covers a distance of (pi)*14*60 = (pi)*(840) inches
(pi)*(840) = (pi)*(35)(x)
pi*(24) = pi*(x)
24=x
Answer: D