RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Which of the following is closest in value to (9^8)-(9^2)?
A.9^9
B.9^8
C.9^7
D.9^6
Answer: B.9^8
Explanation: 9^8 is much larger number than 9^2 and as we need approximate value then it's pretty much negligible in this case, so: (9^8)-(9^2) = ~9^8.
Answer: B.
Similar questions to practice:
Hope it helps.
Question: A certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 10^5, then what was the number in the population 80 minutes later?
A.2(10^5)
B.8(10^5)
C.(2^8)(10^5)
D.(10^8)(10^5)
Answer: C.(2^8)(10^5)
Explanation: Every 10 minutes, the population is double the previous population.
In 80 minutes, the population doubles 8 times.
The population then is 2^8*10^5.
The answer is C.
Question: three men invested sum. and their ratio is 5:7:6. profit is 900.then b's share
A.2000
B.2100
C.2200
D.350
Answer: D.350
Explanation: b's share =7/18*900=350
ANSWER:D
Question: ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all equal. What is the perimeter of the parallelogram?
A.12
B.9√3
C.9
D.8
Answer: D.8
Explanation: So, BC = BD = CD = BA = AD = 2
The parallelogram has 4 equal sides
BC = CD = BA = AD = 2
So The perimeter of the parallelogram will be 2*4 =8
Hence answer will be (D) 2
Question: What is 35% of 4/13 of 585?
A.52
B.63
C.74
D.85
Answer: B.63
Explanation: This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 585, or 1/9 of 585. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate.
The number 585 is between 540 and 630, so (1/9)*585 will be about 65.
Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently.
The closest answer is 63, so this is the answer to choose.
The answer is B.
Question: A travel agent offers a vacation plan which costs 'a' dollars for the first day, and a/8 for each additional day. How much does a vacation of b days cost, where b > 1.
A.(ab+7a)/4
B.(ab+8a)/8
C.(ab+a)/8
D.(ab+7a)/8
Answer: D.(ab+7a)/8
Explanation: Cost = a + (b-1)*a/8 = (8a + (b - 1)*a)/8 = (ab+7a)/8
Answer is D
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
A.11
B.77
C.30
D.88
Answer: C.30
Explanation: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer:C
Question: a pole rests against a wall, and the tip of the pole is at a height of 8m. after sometime the pole slips back by 4m and falls on the ground.what is the length of the pole?
A.10
B.12
C.15
D.18
Answer: A.10
Explanation: let the distance from of the ladder from the pole be x meter. A/c to Pythagoras th., ladder= root_under( x^2 + 64).
In the second case, when the ladder moves 4 m , i.e distance from the pole = x+4, it touches the ground, means the length of ladder = x+4.
Now, equating the both lengths we get x=6, length = x+4 =10
ANSWER:A
Question: A shopkeeper forced to sell at cost price, uses a 800 grams weight for a kilogram. What is his gain percent?
A.10%
B.25%
C.11.11%
D.12 %
Answer: B.25%
Explanation: Shopkeeper sells 800g instead of 1000g.
So, his gain = 1000 - 800 = 200g.
Thus, %Gain = 200 *100)/800 = 25%.
answer : OPTION B
Question: 60 is increased by 50%. Find the final number.
A.100
B.110
C.90
D.30
Answer: C.90
Explanation: Final number = Initial number + 50%(original number) = 60 + 50%(60) = 60 + 30 = 90.
Answer C
Question: (p/q-q/p)=21/10. Then find 4p/q+4q/p?
A.58/9
B.58/5
C.58/7
D.58/2
Answer: B.58/5
Explanation: Let p/q = a, then (a - 1/a) = 21/10
⇒a2−1=a.2110⇒a2−1=a.2110
⇒10a2−21a−10⇒10a2−21a−10 = 0
Roots of the equation = −b±b2−4ac−−−−−−−√2a−b±b2−4ac2a
a = 21±441+400−−−−−−−−√2021±441+40020
a = 21±292021±2920 = 5/2 or -2/5
For a = 5/2, 4p/q+4q/p = 58/5
For a = -2/5, 4p/q+4q/p = -58/5
Answer:B
Question: Ravi can do a piece of work in 25 days while Prakash can do it in 35 days. In how many days will they finish it together?
A.15 7/9 days
B.16 17/9 days
C.15 1/19 days
D.14 7/12 days
Answer: D.14 7/12 days
Explanation: 1/25 + 1/35 = 12/175
175/12 = 14 7/12 days
ANSWER:D
Question: Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 500 square feet. How many feet offence does Frank use?
A.14
B.47
C.70
D.180
Answer: C.70
Explanation: Area = Length x Breadth
500 = 40 x Breadth
So, Breadth = 15 Units
Fencing required is -
Breadth + Breadth + Length
15 + 15 + 40 => 70 feet
Answer must be (C) 70
Question: Kevin sold an item for Rs.5000/- and incurred a loss of 50%. At what price should he have sold the item to have gained a profit of 50%?
A.15000
B.14000
C.13000
D.12000
Answer: A.15000
Explanation: Explanation:
50% loss means SP = 50% of CP
:. CP = Rs.5000x100/50 = Rs.10000.
The SP for a gain of 50% = 10000+50% of 10000 = 10000+5000 =Rs15000.
Answer: Option A
Question: A train passes a station platform in 38 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.180 m
B.270 m
C.260 m
D.280 m
Answer: B.270 m
Explanation: Speed = 54 x 5/18 = 15 m/s
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then, (x + 300)/38 = 15
--> x + 300 = 570
x = 270m.
Answer : B.
Question: In a forest 120 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
A.1,200
B.750
C.1,250
D.1,500
Answer: A.1,200
Explanation: The percentage of tagged deer in the second sample = 5/50*100=10%.
So, 120 tagged deers comprise 10% of total # of deers --> total # of deers = 120*10 = 1,200
Answer: A
Question: When 1/10 percent of 3,000 is subtracted from 1/10 of 3,000, the difference is
A. 0
B. 50
C. 450
D. 397
Answer: D. 397
Explanation: We can break this problem into two parts:
1) What is 1/10 percent of 3,000?
2) What is 1/10 of 3,000?
To calculate 1/10 percent of 3,000 we must first remember to DIVIDE 1/10 BY 100.
So we have: (1/10)/(100)
To divide a number by 100 means to multiply it by 1/100, so we have:
1/10 x 1/100 = 1/1,000
Thus, 1/10 percent of 3,000 = 1/1,000 x 3,000 = 3.
Now let's concentrate on part 2. We need to calculate 1/10 of 3,000. To do this we simply multiply 1/10 by 3,000.
1/10 x 3,000 = 300
The answer to part 1 is 3, and the answer to part 2 is 300. Their difference is 300 – 3 = 397.
Answer D.
Question: A work as fast as B. If B can complete a work in 8days independently,the number of days in which A and B can together finish the work in?
A.2days
B.2 2/3days
C.4days
D.5days
Answer: B.2 2/3days
Explanation: Ratio of rates of working of A and B = 2:1
ratio of times taken = 1:2
A's 1day work = 1/4
B's 1day work = 1/8
A+B 1day work = 1/4 + 1/8 = 3/8 => 8/3 = 2 2/3
A and B can finish the work in 2 2/3days
Answer is B
Question: Three taps A,B and C can fill a tank in 12,15 and 20. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in?
A.5hours
B.7hours
C.6hours
D.8hours
Answer: B.7hours
Explanation: A+B 1 hour work = 1/12 + 1/15 = 9/60 = 3/20
A+C 1 hour work = 1/12 + 1/20 = 8/60 = 2/15
Part filled in 2 hours = 3/20 + 2/15 = 17/60
Part filled in 6 hours = 3* 17/60 = 17/20
Remaining part = 1 - 17/20 = 3/20
Now it is the turn of A and B and 3/20 part is filled by A and B in 1hour
Total time taken to fill the tank = 6+1 = 7 hours
Answer is B
Question: Seven consecutive traffic signals each show either red or green. How many different arrangements of the seven signals are possible?
A.40
B.69
C.88
D.128
Answer: D.128
Explanation: Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly.
We're told that 7 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 7 signals are possible.
Total Options: 128
Final Answer:
D
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is?
A.50 km
B.76 km
C.18 km
D.16 km
Answer: A.50 km
Explanation: Let the actual distance traveled be x km. Then,
x/10 = (x + 20)/14
4x - 200 =>x = 50 km.
Answer: A
Question: A straight line in the xy- plane has y-intercept of 20 . On this line the x-coordinate of the point is 150 and y-coordinate is 600 then what is the slope of the line?
A.3.9
B.4.6
C.5.2
D.6
Answer: A.3.9
Explanation: Eq of line = Y = MX +C
C= 20
X=150
Y=150M + 20,
Substitute Y by 600 as given in question.
600=150M+20 , M =3.9
correct option is A
Question: The population of a town increased from 1,75,000 to 2,27,500 in a decade. The average percent increase of population per year is
A.4.37%
B.5%
C.3%
D.8.75%
Answer: C.3%
Explanation: Solution
Increase in 10 years	= (227500 - 175000)
= 52500.
Increase%	= (52500/175000Ã—100)%
= 30%.
Required average	= (30/10)%
= 3%.
Answer C
Question: Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 51 years. What will be the age of the B ten years hence?
A.39
B.23
C.28
D.102
Answer: D.102
Explanation: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 51 => b + c = 102 --- (2)
Answer: D
Question: If 170!/10^n is an integer, what is the largest possible value of n?
A.47
B.46
C.41
D.48
Answer: C.41
Explanation: The question actually asks the highest power of 10 which divides 300! ( For a number to be an integer - Without any remainder all the trailing zeroe's must be divided by the denominator)
10 = 2 x 5
170 factorial will have 41 as -
170/5 = 34
34/5 = 6
6/5 =1
So answer will be (C) 41
Question: By the how much is two-fifth of 300 greater than three -fifths of 125?
A.15
B.3
C.5
D.45
Answer: D.45
Explanation: Reqd no. = 2â„5 Ã— 300 - 3â„5 Ã— 125
= 120 - 75 = 45
Answer D
Question: An 80-liter solution of cool-drink is made from 10% jasmine water. If 5 liters of jasmine and 15 liters of water were added to the solution, what percent of the solution is jasmine?
A.11%
B.13%
C.15%
D.17%
Answer: B.13%
Explanation: The percent of jasmine in the resulting solution is: (amount of jasmine) / (total volume)
(0.1(80) + 5) / 100 = 13/100 = 13%
The answer is B.
Question: If you have 8 New Year greeting cards and you want to send them to 6 of your friends, in how many ways can this be done?
A.20160
B.22100
C.23000
D.24500
Answer: A.20160
Explanation: Solution
We have to find number of permutations of 6 objects out of 8 objects. This number is 8P6=8(8-1)(8-2)(8-3)(8-4)(8-5)=8*7*6*5*4*3=20160
Answer A
Question: The diameter of a cylindrical tin is 6cm and height is 5 cm. Find the volume of the cylinder?
A.33
B.45
C.66
D.77
Answer: B.45
Explanation: r = 3 h = 5
π * 3 * 3 * 5 = 45 π cc
Answer:B
Question: How many words can be formed by taking 4 letters at a time out of the letters of the word MATHEMATICS.
A.2154
B.2454.
C.2254
D.2354
Answer: B.2454.
Explanation: There are 8 distinct letters: M-A-T-H-E-I-C-S. 3 letters M, A, and T are represented twice (double letter).
Selected 4 letters can have following 3 patterns:
1. abcd - all 4 letters are different:
8P4=16808 (choosing 4 distinct letters out of 8, when order matters) or 8C4∗4!=16808 (choosing 4 distinct letters out of 8 when order does not matter and multiplying by 4! to get different arrangement of these 4 distinct letters);
2. aabb - from 4 letters 2 are the same and other 2 are also the same:
3C2∗4!/2!2!=18 choosing which two double letter will provide two letters (out of 3 double letter - MAT), multiplying by 4!/2!2! to get different arrangements (for example MMAA can be arranged in 4!/2!2! # of ways);
3. aabc - from 4 letters 2 are the same and other 2 are different:
3C1∗7C2∗4!/2!=756 choosing which letter will proved with 2 letters (out of 3 double letter - MAT), 7C2 choosing third and fourth letters out of 7 distinct letters left and multiplying by 4!/2!to get different arrangements (for example MMIC can be arranged in 4!/2!# of ways).
1680+18+756=2454
Answer: B
Question: If the weight of 13 meters long rod is 13.4 kg. What is the weight of 6 meters long rod ?
A.7.2 kg.
B.10.8 kg.
C.12.4 kg.
D.6.18 kg
Answer: D.6.18 kg
Explanation: Answer
∵Weight of 13 m long rod = 13.4 kg
∴ Weight of 1 m long rod = 13.4 / 13 kg
∴ Weight of 6 m long rod = 13.4 x 6 / 13
= 6.18 kg
Option: D
Question: A salt manufacturing company produced a total of 4000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its ave66rage daily production for that year?
A.140
B.149
C.156
D.195
Answer: B.149
Explanation: Total production of salt by the company in that year = 4000 + 4100 + 4200 + .... + 5100 = 54600.
Average monthly production of salt for that year = 54600/365 â‰ˆ 149
ANSWER:B
Question: Arun's Ice Cream Shop sells ice cream at x cents a scoop. For an additional y cents, a customer can add 4 toppings to his or her sundae. How much would a sundae with 4 scoops and 4 toppings cost, in terms of x and y?
A.3x+y
B.5x+y
C.6x+y
D.4x+y
Answer: A.3x+y
Explanation: Answer A 4x+y
Question: A certain university will select 1 of 5 candidates eligible to fill a position in the mathematics department and 2 of 8 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
A.138
B.140
C.142
D.145
Answer: B.140
Explanation: 1C5*2C8 = 5*28 = 140
the answer is (B)
Question: If cost of sugar increases by 15%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed?
A.13%
B.50%
C.20%
D.80%
Answer: A.13%
Explanation: 100
115
-----
115 ----- 15
100 ------ ? => 13%
Answer: A
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 66 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?
A. 16%
B. 32%
C. 83%
D. 84%
Answer: C. 83%
Explanation: This is easiest to solve with a bell-curve histogram. m here is equal to µ in the Gaussian normal distribution and thus m = 50% of the total population.
So, if 66% is one st.Dev, then on either side of m we have 66/2 = 33%. So, 33% are to the right and left of m (= 50%). In other words, our value m + d = 50 + 33 = 83% goingfrom the mean m, to the right of the distributionin the bell shaped histogram.. This means that 83% of the values are below m + d.
Like I said, doing it on a bell-curve histogram is much easier to fullygethow this works, or you could apply GMAT percentile jargon/theory to it
C
Question: In an examination, questions were asked in five sections. Out of the total students, 5% candidates cleared the cut-off in all the sections and 5% cleared none. Of the rest, 25% cleared only one section and 20% cleared four sections. If 24.5% of the entire candidates cleared two sections and 300 candidates cleared three sections. Find out how many candidates appeared at the examination?
A.1000
B.1200
C.1500
D.2000
Answer: B.1200
Explanation: Solution: Passed in none = 5%
Passed in all = 5%
Passed in four = 20% 0f 90% = 18%
Passed in three = 24.5%
Passed in three =(100-5-5-22.5-24.5-18) = 25%.
But given 300 students passed in three.
Hence, 25% = 300.
So, 100% = 1200.
1200 students must have appeared.
Answer: Option B
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
A.3
B.6
C.7
D.4
Answer: D.4
Explanation: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4.
Answer:D
Question: In a certain candy store, 22% of the customers are caught sampling the candy and are charged a small fine, but 15% of the customers who sample the candy are not caught. What is the total percent of all customers who sample candy?
A.22%
B.23%
C.24%
D.26%
Answer: D.26%
Explanation: Since 15% of the customers who sample the candyare notcaught, then 88% of the customers who sample the candyarecaught:
{% of customers who sample candy}*0.85 = 0.22;
{% of customers who sample candy} = 0.259
Answer: D.
Question: The ratio of the ages of Anil and his son at present is 7:3. Six years hence, the ratio of the ages of the Anil's wife and the son will be 2:1. Find the ratio of the present ages of Anil and his wife?
A.5:4
B.6:5
C.4:3
D.Cannot be determined
Answer: D.Cannot be determined
Explanation: Let the present ages of Anil and his son be 7x and 3x years respectively.
Let the present age of the son's mother be m years.
(m + 6)/(3x + 6) = 2/1
m = 6x + 6
Ratio of the present ages of Anil and his son's mother = 7x/(6x + 6).
This cannot be found uniquely.
Answer: D
Question: A water tank is one-third full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
A.5 min. to empty
B.6 min. to full
C.9 min. to empty
D.9 min. to full
Answer: A.5 min. to empty
Explanation: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.
Part to be emptied = 1/3
Part emptied by (A + B) in 1 minute = (1/6 - 1/10) = 1/15
1/15 : 1/3 :: 1 : x
x = (1/3 * 1 * 15) = 5 min.
So, the tank will be emptied in 5 min.
ANSWER:A
Question: Last year, a certain public transportation system sold an average (arithmetic mean) of 40,000 tickets per day on weekdays (Monday through Friday) and an average of 18,000 tickets per day on Saturday and Sunday. Which of the following is closest to the total number of tickets sold last year?
A.1 million
B.1.25 million
C.10 million
D.12.2 million
Answer: D.12.2 million
Explanation: If you type that into the calculator, it results in 12.3 mil
[D], 12.2 mil, is the correct answer... see 2 posts above for quick approx method
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time?
A.Rs.51.25
B.Rs.51.27
C.Rs.51.79
D.Rs.51.8
Answer: A.Rs.51.25
Explanation: Sum = (50 * 100) / (2 * 5) = Rs. 500
Amount = [500 * (1 + 5/100)2] = Rs. 551.25
C.I. = (551.25 - 500)
= Rs.51.25.
Answer: A
Question: If A is to be chosen at random from the set {14, 7, 25, 6} and B is to be chosen at random from the set {2, 5, 8}, what is the probability that AB will be even?
A.2/3
B.8/3
C.5/6
D.1/3
Answer: B.8/3
Explanation: Method-1
AB will be even when
1) A is even and B is odd, Probability of A even is (2/4) and Probability of B odd is (1/3), so Probability of Case(1) = (2/4)*(1/3) = (2/12)
2) A is Odd and B is Even, Probability of A Odd is (2/4) and Probability of B Even is (2/3), so Probability of Case(2) = (2/4)*(2/3) = (4/12)
3) A is even and B is Even, Probability of A even is (2/4) and Probability of B Even is (2/3), so Probability of Case(1) = (2/4)*(2/3) = (4/12)
Total Favorable Probability = (2/12)+(4/12)+(4/12) = (32/12) = 8/3
Answer: option B
Question: A pack of 52 playing cards, 2cards are drawn together at random. Find the probability of both the cards being king?
A.1/113
B.2/213
C.1/221
D.3/341
Answer: C.1/221
Explanation: Two cards can be drawn from a pack of 52 playing cards in 52C2 ways. i,e., 52 x 51 / 2 = 1326 ways. The event that two kings appear in a single drawn of cards is 4C2 ways, i.e 6 ways.
∴ The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221
C
Question: A man sells an article at 15% loss. Had he sold it for Rs. 210/- more he could have gained 20%. What is the cost price of the article?
A.Rs.420/-
B.Rs.400/-
C.Rs.600/-
D.Rs.680/-
Answer: C.Rs.600/-
Explanation: Explanation:
Short cut method:
Loss =====> 15 %
Profit ====> 20 %
~
----------------
35 % ---------> Rs. 210/-
100 % --------> Rs. 600/-
Answer: Option C
Question: The banker's discount on $1600 at 15% per annum is the same as true discount on $1680 for the same time and at the same rate. The time is:
A.2 months
B.1 months
C.4 months
D.8 months
Answer: C.4 months
Explanation: S.I. on $1600 = T.D. on $1680.
THEREFORE $1600 is the P.W. of $1680, i.e., $80 is on $1600 at 15%.
Time =(100 x 80/ 1600 x 15) year	=	1/3	year = 4 months.
ANSWER:C
Question: The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
A.20.9
B.28.9
C.28.6
D.11.5
Answer: D.11.5
Explanation: 1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 119.9 = 11.5
6th number = 11.5
Answer: D
Question: Find the average of all the numbers between 6 and 34 which are divisible by 5?
A.32
B.20
C.28
D.11
Answer: B.20
Explanation: Average = (10 + 15 + 20 + 25 + 30)/5
= 100/5
= 20.
Answer: B
Question: 6 pints of a 20 percent solution of alcohol in water are mixed with 4 pints of a 10 percent alcohol in water solution. The percentage alcohol in the new solution is
A.16
B.15
C.14
D.13
Answer: A.16
Explanation: Percentage of alcohol in new solution
=( 6*.2 + 4 * .1) / 10
=(1.2 + .4 ) / 10
= 1.6/10
=.16
Percentage of alcohol in new solution = 16 %
Answer :A
Question: If x is divisible by 10, 14, and 70, which of the following must be the least multiple of x?
A.70
B.140
C.210
D.350
Answer: A.70
Explanation: We are looking for the LCM (which is not 0) of 10 = 2*5, 70 = 2*7*5, 14 = 2*7:
2 * 5 * 7 = 70
The answer is A.
Question: Five children, Anaxagoras, Beatrice, Childeric, Desdemona, and Ethelred, sit randomly in five chairs in a row. What is the probability that Childeric and Ethelred sit next to each other?
A.1/30
B.1/15
C.1/5
D.2/5
Answer: D.2/5
Explanation: Total no of empty space is 5 so total no of ways A B C D and E can sit is 5 !
Solution 1:
Now condition is C&E will sit together
If they sit at 1st and 2nd place . # of ways will be 1*3! but C&E can be either at 1 or at 2 so # of ways will be 1*3!*2!
Similarly they can sit together at position 2 and 3 or 3 and 4 or 4 and 5
So total # ways will be 1*3!*2! + 1*3!*2! + 1*3!*2! + 1*3!*2! = 4 *1*3! *2 !
So probability is (4! * 2! ) / 5! = 2/5
Solution 2:
Consider C*E as 1 person . So we have 4 ppl and 4 places . # of ways they can sit is 4!
C&E can sit as C&E or E&C so total # of ways is 4! * 2!
So probability will be 2/5
Answer:D
Question: A 4 digit number is formed by repeating a 2 digit number such as 2525, 3232 etc. Any number of this form is exactly divisible by
A.7
B.11
C.13
D.Smallest 3 digit prime number
Answer: D.Smallest 3 digit prime number
Explanation: Sol.
Smallest 3 digit prime number is 101.
Clearly, 2525 = 25 x 101;
3232 = 32 x 101, etc.
∴ Each such number is divisible by 101.
Answer D
Question: If 12 men and 16 boys can do a piece of work in 5 days and 13 men together will 24 boys can do it in 4 days. Compare the daily work done by a man with that of a boy.
A.2:9
B.2:1
C.2:7
D.2:5
Answer: B.2:1
Explanation: 12M + 16B ----- 5 days
13M + 24B ------- 4 days
60M + 80B = 52M + 96B
8M = 16B => 1M = 2B
M: B = 2:1
Answer:B
Question: In a covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay double his speed, then he would take 1 hour less than Sammer. Abhay's speed is?
A.5 km/hr
B.7 km/hr
C.1 km/hr
D.9 km/hr
Answer: A.5 km/hr
Explanation: Let Abhay's speed be x km//hr.
Then, 30/x - 30/2x = 3
x = 5 km/hr.
Answer:A