RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Which one of the given numbers is divisible by 11?
A.4823718
B.8423718
C.8432718
D.4832817
Answer: D.4832817
Explanation: Explanation:
4832817 = (4+3+8+7) – (8+2+1) = 11
So, the given number is divisible by 11
Answer:D
Question: (500 + 200) × 4 × (3 + 2) = ?
A.2902
B.14000
C.8402
D.16800
Answer: B.14000
Explanation: (500 + 200) × 4 × (3 + 2) = ?
or, ? = 700 × 4 × 5 = 14000
Answer B
Question: What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 11, 60 and 61?
A.6.5
B.12.5
C.28
D.30.5
Answer: D.30.5
Explanation: Some of pyhtagron triplets we need to keep it in mind.
Like {( 2,3,5) , ( 5,12,13) ,( 7, 24,25), ( 11, 60,61).
So now we know the triangle is an right angle triangle. The circle circumscribes the triangle.
The circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 61 / 2 = 30.5
Ans. D
Question: January 1, 2008 is Monday. What day of the week lies on Jan 1, 2009?
A.Saturday
B.Wednesday
C.Thursday
D.Tuesday
Answer: B.Wednesday
Explanation: Explanation:
Number of odd days in 2008 = 2 (since it is a leap year)
(we have taken the complete year 2008 because we need to find out the odd days from 01-Jan-2008 to 31-Dec-2008, that is the whole year 2008)
Given that January 1, 2008 is Monday.
Hence January 1, 2009 = (Monday+ 2 odd days) = Wednesday
Answer: Option B
Question: Which of the following points is closest to line y=x
A.(2, -1)
B.(-2, -4)
C.(-1, 1)
D.(-2, 1)
Answer: B.(-2, -4)
Explanation: Attachment:
m12-20.pngAs you can see point (-2, -4) is the closest to line y=x.
Answer: B.
Question: Two containers of equal capacity are full of a mixture of oil and water . In the first, the ratio of oil to water is 4:7 and in the second it is 7:11. Now both the mixtures are mixed in a bigger container. What is the resulting ratio of oil to water.
A.149 : 247
B.247 : 149
C.143 : 241
D.241 : 143
Answer: A.149 : 247
Explanation: Two Container C1, C2 of equal capacity x.
For C1:
Oil= 4/11 x
Water= 7/11 x
For C2
Oil= 7/18 x
Water = 7/11 x
Mix C1 and C2.
Total Oil= 4/11 x + 7/18 x = 149/198 x
Total Water= 7/11 x + 7/11 x = 247/198 x
resulting ratio of oil to water = (149/198 x) / (247/198 x)
= 149:247.
ANSWER:A
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
A.16 2/3% loss
B.22 2/3% loss
C.88 2/3% loss
D.66 2/3% loss
Answer: A.16 2/3% loss
Explanation: 15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer: A
Question: If log 27 = 1.431, then the value of log 9 is:
A.0.934
B.0.945
C.0.954
D.0.958
Answer: C.0.954
Explanation: log 27 = 1.431
log (33 ) = 1.431
3 log 3 = 1.431
log 3 = 0.477
log 9 = log(32 ) = 2 log 3 = (2 x 0.477) = 0.954.
Answer: Option C
Question: The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 1 year?
A.14300
B.12000
C.14500
D.14600
Answer: B.12000
Explanation: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 × 120/100 = 12000
B)
Question: A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 9:00 am and some time later the drain that empties the pool was also opened. If the pool was filled by 9:00 pm and not earlier, when was the drain opened?
A.at 10:00 am
B.at 11:00 am
C.at 12:00 pm
D.at 1:00 pm
Answer: B.at 11:00 am
Explanation: The filling rate is 1/4 and the draining rate is 1/5.
The combined rate of filling and draining is 1/4 - 1/5 = 1/20.
Let x be the number of hours before the drain was opened.
x/4 + (12-x)/20 = 1
5x + 12 - x = 20
4x = 8
x = 2
The answer is 11:00 am.
The answer is B.
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 25 seconds. The ratio of their speeds is?
A.3/7
B.3/2
C.3/5
D.8/1
Answer: D.8/1
Explanation: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 25
==> 27 x + 17 y = 25 x + 25 y ==> 2x = 8 y ==> x/y
= 8/1.
Answer: D
Question: Rice weighing 29/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each container? (Note that 1 pound = 16 ounces)
A.21
B.25
C.29
D.33
Answer: C.29
Explanation: 29/4 ÷ 4 = 29/16 pounds in each container
29/16 pounds * 16 ounces / pound = 29 ounces in each container
The answer is C.
Question: A man rows downstream 32 km and 14 km upstream. If he takes 6 hours to cover each distance, then the velocity (in kmph) of the current is:
A.1.5 kmph
B.1.75 kmph
C.2 kmph
D.3 kmph
Answer: A.1.5 kmph
Explanation: Sol.
Rate downstream = [32/6] kmph; Rate upstream = [14/6] kmph.
∴ Velocity of current = 1/2[32/6 - 14/6] kmph = 3/2 kmph = 1.5 kmph.
Answer A
Question: What day of the week was 11th January 1801
A.Monday
B.Sunday
C.Friday
D.Thursday
Answer: B.Sunday
Explanation: Explanation:
11th Jan 1801 = (1800 years + 11th Jan 1801)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 1600 years = 0 (Since 1600 is a perfect multiple of 400)
Number of odd days in the period 1601-1800
= Number of odd days in 200 years
= 5 x 2 = 10 = 3
(As we can reduce perfect multiples of 7 from odd days without affecting anything)
11th Jan 1801 = 4 odd day
Total number of odd days = (0 + 3 + 4) = 7 =0
0 odd days = Sunday
Hence 11th January 1801 is Sunday.
Answer: Option B
Question: The food in a camp lasts for 30 men for 40 days. If ten more men join, how many days will the food last?
A.40 days
B.20 days
C.30 days
D.50 days
Answer: C.30 days
Explanation: one man can consume the same food in 30*40 = 1200 days.
10 more men join, the total number of men = 40
The number of days the food will last = 1200/40 = 30 days.
ANSWER:C
Question: Find the value of (875 233/899) × 899
A.786858
B.786900
C.786920
D.786913
Answer: A.786858
Explanation: (875 233/899) × 899
(786625 + 233)/899 × 899
786858/899 × 899
786858
A
Question: A money lender finds that due to a fall in the annual rate of interest from 8% to 7 1/5 % his yearly income diminishes by Rs.61.50. his capital is
A.22.378
B.37.78
C.76.88
D.27.888
Answer: C.76.88
Explanation: Explanation:
Capital = Rs.x , then
4/5 x =61.5
x = 76.88
Answer: C) Rs.76.88
Question: Leona bought a 1-year, $10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
A.$10,464
B.$ 864
C.$ 816
D.$ 800
Answer: C.$ 816
Explanation: Approach #1:
8 percent compounded semiannually --> 4% in 6 moths.
For the first 6 moths interest was 4% of $10,000, so $400;
For the next 6 moths interest was 4% of $10,000, plus 4% earned on previous interest of $400, so $400+$16=$416;
Total interest for 1 year was $400+$416=$816.
Answer: C.
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 50 minutes later?
A.2(10^5)
B.5(10^5)
C.(2^5)(10^5)
D.(10^5)(10^5)
Answer: C.(2^5)(10^5)
Explanation: Every 10 minutes, the population is double the previous population.
In 50 minutes, the population doubles 5 times.
The population then is 2^5*10^5.
The answer is C.
Question: Of the 70 electronics components that a factory must manufacture, 90 percent would be most e¢ ciently manufactured by Machine A and the remaining 10 percent would be most efficiently manufactured by Machine B, though either machine could manufacture any of the 70 components. If 50 percent of the components were manufactured by Machine A and the remainder were manufactured by Machine B, what is thehighest possible number of components that were manufactured by the machine that would manufacture them the most efficiently?
A. 30
B. 32
C. 42
D. 35
Answer: C. 42
Explanation: A can manufacture 90 % of 70 efficiently, which is 63.
B can manufacure 10 % of 70 efficiently, which is 7.
Now 50 % of 70 are produced by A. This means 35 parts. Since A can produce 63 efficiently, all 35 are produced efficiently. Rest (35) is produced by B, which can produce max. 7 parts efficiently.
Hence parts that were produced efficiently = 7+35 = 42. (C).
Question: Of 70 players on a football team, 40 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
A.54
B.59
C.60
D.71
Answer: C.60
Explanation: Total = 70
Thrower = 40
Rest = 70 - 40 = 30
Left Handed = 30/3 = 10
Right handed = 20
If all Throwe0r are right handed then total right handed is 40 + 20 = 60
so C. 60 is the right answer
Question: S is the set of all fractions defined by the formula n/(n + 1), where n is a positive integer less than 20. What is the product X of all the fractions that are in S?
A.1) 1/20
B.2) 1/21
C.3) 1/2
D.4) 19/40
Answer: A.1) 1/20
Explanation: 1/2 * 2/3 * 3/4 * ... 19/20
= 1/20
Answer - A
Question: Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 15 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
A.40
B.48
C.80
D.192
Answer: D.192
Explanation: Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.
But we are told that one of these individual works is 30hrs. hence, possible scenarios, if
(1)2x =15 => 16x = 120 (2) 3x =15 => 16x = 80 (3) 5x =15 => 16x = 48 (4) 6x =15 => 16x = 40
Hence Answer is D 192 which can not be any of these.
Question: In a race of 800 mtr gives Mary a start of 200 mtr and then loses the race by 20 seconds. What is the speed of Mary & Rose respectively ? If the ratio of respective speeds be 3:2?
A.10 m/s
B.12 m/s
C.16 m/s
D.20 m/s
Answer: D.20 m/s
Explanation: Let the speed of Kaushik be and speed of Piyush be and let the time taken by Piyush be t second then,
t = 20 s
Speed of Priya = 30 m/s
and Speed of Kala = 20 m/s
D
Question: There are 720 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?
A.320
B.345
C.450
D.380
Answer: C.450
Explanation: In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 720. Hence
3x + 5x = 720
Solve for x
8x = 720
x = 90
Number of boys
3x = 3 × 90 = 270
Number of girls
5x = 5 × 90 = 450
C
Question: Find the last non-zero digit of 30^2345
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: 30^2345=(3*10)^2345=3^2345*10^2345
so 30^2345 has 2345 zeroes,the last non-zero digit of 30^2345 will be same as unit digit of 3^2345
3^2345=3^(4*586+1)=> 3^1=3
last non-zero digit of 30^2345= 3
ANSWER:C
Question: The labelled price of a cupboard is Rs. 6500. The shopkeeper sold it by giving 5% discount on the labelled price and earned a profit of 15%. What approximately is the cost price of the cupboard?
A.5350
B.5450
C.5500
D.5700
Answer: A.5350
Explanation: Sol.
S.P. = 95% of Rs. 6500 = Rs. [95 / 100 * 6500] = Rs. 6175.
Profit = 15%.
∴ C.P. = Rs. [110 / 115 * 6175] = Rs. 5369.56 = Rs. 5350.
Answer A
Question: If the true discount on s sum due 2 years hence at 14% per annum be Rs. 196, the sum due is:
A.s. 768
B.s. 968
C.s. 896
D.s. 2400
Answer: C.s. 896
Explanation: td=pw*r*t/100 so 196=pw*14*2/100 so pw=700
sum=pw+td..
sum=700+196=896
ANSWER:C
Question: The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 576 feet squared, what is the difference between the length and the width of the roof?
A.38.
B.40.
C.36.
D.44.
Answer: C.36.
Explanation: Let the width= x
x*4x=576
x^2= 144
x= 12
Length= 4*12= 48
difference= 48-12= 36
C is the answer
Question: A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 3 students left over. What is the sum of the two smallest possible values of n?
A.54
B.58
C.62
D.66
Answer: C.62
Explanation: n = 4k+1 = 7j+3
Let's start at 1 = 4(0)+1 and keep adding 4 until we find a number in the form 7j+3.
1, 5, 9, 13, 17 = 7(2)+ 3
The next such number is 17 + 4*7 = 45.
17+45 = 62
The answer is C.
Question: Two pumps are connected to an empty tank. Pump X fills the tank with water at a constant rate, while pump Y drains water out of the tank at a constant rate. The two pumps finish filling the tank in five times the duration it would take pump X alone to fill the tank. If pump Y alone can empty a whole tank in 45 minutes, then how many minutes does it take pump X alone to fill the tank?
A.27
B.30
C.33
D.36
Answer: D.36
Explanation: Let V be the volume of the tank.
Let R be the rate per minute that pump X fills the tank.
Let T be the time it takes pump X to fill the tank.
The rate at which pump Y empties the tank is V/45 per minute.
(R - V/45)*5T=V=RT.
(R-V/45)*5=R
4R=V/9.
R=V/36.
It takes pump X 36 minutes to fill the tank.
The answer is D.
Question: In what time will a railway train 30 m long moving at the rate of 36 kmph pass a telegraph post on its way?
A.6 sec
B.7 sec
C.3 sec
D.9 sec
Answer: C.3 sec
Explanation: T = 30/36 * 18/5
= 3 sec
Answer:C
Question: Share Rs.5400 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John?
A.1800
B.980
C.1200
D.1240
Answer: A.1800
Explanation: Amount received by sanjay.
4 / 12 X 5400 = 1800= ( related ratio / sum of ratio ) x Total amount
So, the Amount received by sanjay is 1800.
A
Question: For every positive integer n, the nth term of sequence is given by an= 1/n - 1/(n+1). What is the sum of the first 70 terms?
A.3/5
B.7/15
C.35/36
D.70/71
Answer: D.70/71
Explanation: a1 = 1 - 1/2
a2 = 1/2 - 1/3
a3 = 1/3 - 1/4
etc...
a70 = 1/70 - 1/71
The sum of these terms is 1-1/71 = 70/71
The answer is D.
Question: The diagonal of a rhombus are 80 m and 120m. Its area is:
A.4500
B.4000
C.4800
D.4600
Answer: C.4800
Explanation: Area of the rhombus = 1/2 d1d2 = ( 1/2 Ã— 80 Ã— 120) Cm(power)2
= 80Ã— 60= 4800 Cm(power)2
Answer is C.
Question: The average age of a group of persons going for picnic is years. Seventeen new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is
A.5
B.10
C.17
D.23
Answer: C.17
Explanation: Solution
Let the initial number of persons be x. Then
16x + 17 x 15 = 15.5(x+20)
= 0.5x = 8.5
x = 17.
Answer C
Question: A box contains 14 mangoes out of which 6 are spoilt. If six mangoes are chosen at random, find the probability that A number is selected at random from first fifty natural numbers. What is the chance that it is a multiple of either 5 or 12?
A.15/25
B.2/25
C.14/25
D.7/25
Answer: D.7/25
Explanation: The probability that the number is a multiple of 5 is 10/50. (Since 5*10 = 50).
Similarly the probability that the number is a multiple of 12 is 4/50. {Since 14*4 =
48).
Neither 5 nor 12 has common multiple from 1 to 50. Hence these events are mutually exclusive events. Therefore chance that the selected number is a multiple of 5 or 12 is (10+4)/50 = 7/25.
ANSWER:D
Question: David has $1,800 at the beginning of his trip, after spending money, he still has exactly $800 less than he spent on the trip. How much money does John still have?
A.$200
B.$500
C.$600
D.$800
Answer: B.$500
Explanation: Suppose total money spent = x
Not spend (Money he still has)= x-800
x+x-800 = 1800
x= 1300
Money not spend= 1300-800= 500
Answer : B
Question: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jackets for her business trip. If an outfit consists of one of each item of clothing except shirts, of which she will wear 2, how many different outfits F can does Grace have available during her trip?
A. 2,520
B. 1,260
C. 620
D. 360
Answer: B. 1,260
Explanation: The idea is to multiply the number of possibilities for each item of clothing with the different items. For the shirts you essentially choose 2 out of 8 so you should use the combination forumla (don't know how to use math symbols here).
This gives you F=5 x 3 x 28 x 3 = 1'260. Hence, solution B is correct.
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 3 or 4 as its largest number?
A.3/4
B.3/8
C.3/16
D.5/16
Answer: B.3/8
Explanation: The set S has 2^5 = 32 subsets.
The number 5 is in half of these subsets.
Of the remaining 16 subsets, 4 is an element in 8 of them.
Thus 4 is the largest number in 8 subsets of S.
Of the remaining 8 subsets, 3 is an element in 4 of them.
Thus 3 is the largest number in 4 subsets of S.
The probability that 3 or 4 is the largest number is 12/32 = 3/8.
The answer is C.
Question: There are 60 slots around a circle,numbered 1 to 60. A man starts from the first slot and jumps to the 5th slot.From there he jumps to the 9th slot and so on. In which slot will he land in his
2200th jump?
A.1
B.5
C.41
D.45
Answer: C.41
Explanation: every 15th jump, he comes back to 1st position
so, 2200/15 = Remainder 10
Hence 10th position is 41st slot
ANSWER:C
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 10-meter platform and caught it after it had traveled 29.65 meters. How many times did the ball bounce?
A.5
B.6
C.7
D.8
Answer: B.6
Explanation: Ans: 6
Division of total diatance travelled will be 10+10+5+2.5+1.25+0.6+0.3 ANS B
Question: If the units digit of n^43 is 7, which of the following could be the value of n?
I. n = 41
II. n = 43
III. n = 47
A.Only I
B.Only II
C.Only III
D.I and II
Answer: A.Only I
Explanation: I tried in this way.
Given n^43 units digit is 7.
If at all we have to get 7 as units digits only 3 and 7 series has 7
3^! = 3 , 3^2 = 9 , 3^3 = 27 , 3^4 = 81
7^1 = 7, 7^2 = 49 , 7^3 = 3 (units ) , 7^4 = 1 (units)
We have n^43 - then divide 43 by 4 = reminder 3.
Then we have for only 7^3 - we have units digit as 7.
Hence 47^43 = 7 (units).
Option A is correct answer , and with 41^43 we always get 1 as units digit and 43^43 - we get units as 3.
Question: The sale price of a trolley bag including the sale tax is Rs. 1190. The rate of sale tax is 12% . If the shopkeeper has made a profit of 25%, the cost price of the trolley bag is:
A.Rs 800
B.Rs 820
C.Rs 860
D.Rs 850
Answer: D.Rs 850
Explanation: Explanation :
112% of S.P. = 1190
S.P. = Rs.(1190 x 100/112) = Rs.1062.50.
C.P. = Rs (100/125x 1062.50) = Rs 850
Answer : D
Question: On his first 3 tests, Rajeev received an average score of N points. If on his fourth test, he exceeds his previous average score by 20 points, what is his average score for his first 4 tests?
A.N
B.N + 4
C.N + 5
D.N + 10
Answer: C.N + 5
Explanation: Total points from first three tests: 3N
Points on fourth test: N + 20
Total points on all four tests: 3N + (N + 20) = 4N + 20
Average score for first four tests: (4N + 20)/4 = N + 5
Answer is C.
Question: The triangle ABC has sides of the following lengths: AB = 24, BC = 7, and AC = 25.
Let M be the midpoint of AB. What is the length of CM?
A.1
B.root139
C.12
D.root193
Answer: D.root193
Explanation: Since 242 + 72 = 252, triangle ABC is a right triangle. Thus, MBC is also a right
triangle and CM2 = BM2 + BC2 = 122 + 72 = 193.
correct answer D
Question: Due to flooding, vendors increased the cost of sandbags by 30% to keep customers from buying out all the sandbags. Government officials declared an emergency and would only pay 60% of total price for sandbags. What is the difference between the new cost of the sandbags and the amount government officials paid?
A.12.0%
B.15.0%
C.20.0%
D.22.0%
Answer: D.22.0%
Explanation: Quantity X Rate = Price
1 X 1 = 1
0.60 X 1.30 = 0.780
Decrease in price = (0.22/1) Ã— 100 = 22.0%
Answer = Option D
Question: The 7th grade French and Spanish classes each have 21 students in them, and there are six students in the 7th grade taking both languages. If everyone in the 7th grade is in at least one of the two language classes, how many students are taking just one of the two classes?
A.24
B.28
C.30
D.32
Answer: C.30
Explanation: French class + Spanish class = 42 students.
Six students are in both classes so they were counted twice.
The number of students taking just one class is 42 - 2(6) = 30.
The answer is C.
Question: A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?
A.175/256
B.451/365
C.312/456
D.156/754
Answer: A.175/256
Explanation: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.
So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.
The event of not hitting the target even once is the complement of the event of hitting the target at least once.
The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾
Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256
The probability that he will hit the target at least in one of the four shots=1-81/256
=175/256
Ans:A
Question: x, a, z, and b are single digit positive integers. x = 1/3a. z = ¼3b. (10a + b) – (10x + z) could NOT equal
A.31
B.32
C.46
D.64
Answer: A.31
Explanation: a=3x , b =3z therefore(3x.10+3z) - (10x +z) = (3-1) (10x+z) =2.(10x+Z)
number should be divisible by 2
A
Question: The area of a triangle is 615 m2. If one of its sides is 123 metre, find the length of the perpendicular dropped on that side from opposite vertex.
A.15 metres
B.12 metres
C.10 metres
D.9 metres
Answer: C.10 metres
Explanation: In a triangle,
Area = 1⁄2 × length of perpendicular × base
or 615 = 1⁄2 × length of perpendicular × 123
∴ Length of perpendicular = 615×2/123=10m
Answer C
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
A.4
B.7
C.9
D.14
Answer: B.7
Explanation: 1 woman's 1 day's work = 1/70
1 Child's 1 day's work = 1/140
5 Women and 10 children 1 day work = (5/70+10/140)=1/7
So 5 women and 10 children will finish the work in 7 days.
Answer: B
Question: What is the remainder when 1014*1047*1050*1053 is divided by 33?
A.3
B.6
C.30
D.21
Answer: B.6
Explanation: OA is 'C'.
OE:
take the remainder from each of 1044/33, 1047/33 and so on..
1014/33 gives remainder = 24
1047/33 gives remainder = 24
1050/33 gives remainder = 27
1053/33 gives remainder = 30
the net remainder is the product of above individual remainders. i.e = 24*24*27*30
break them into pairs 24*24/33 gives remainder 15
and 27*30/33 gives remainder 18
so 15*18/33 gives remainder 6.
B
Question: Alice and Bob will throw three dice each. The score is the sum of points on all three dice. If Alice scores 17 in her attempt what is the probability that Bob will outscore Alice in his attempt?
A.1/216
B.5/216
C.7/216
D.1/36
Answer: A.1/216
Explanation: The total number of ways the dice can land is 6*6*6=216.
Bob must get a score of 18=6+6+6.
There is only 1 way to do this.
P(Bob wins)=1/216
The answer is A.