RikoteMaster/aqua-rat-mcqa huggingface dataset:
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 W 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: W 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: The average of seven results is 156 and that of the first six is 169. The fifth result is?
A.120
B.160
C.89
D.78
Answer: D.78
Explanation: 7 * 156 â€“ 6 * 169 = 78
Answer: D
Question: A man complete a journey in 1010 hours. He travels first half of the journey at the rate of 2121 km/hr and second half at the rate of 2424 km/hr. Find the total journey in km.
A.121 km
B.242 km
C.224 km
D.112 km
Answer: C.224 km
Explanation: Solution 1
Average Speed =2Ã—21Ã—2421+24=22.4 km/hr=2Ã—21Ã—2421+24=22.4 km/hr
Total distance =22.4Ã—10=224 km
ANSWER IS C
Question: Points A, B, and C lie, in that order, on a straight railroad track. The distance from point A to point B is twice the distance from point B to point C. A train traveled from point A to point C without stopping. The train's average speed when traveling from point A to point B was 150 miles per hour and the train's average speed when traveling from point B to point C was 100 miles per hour. What was the train's average speed, in miles per hour, when traveling from point A to point C?
A.22.5
B.21.43
C.25.5
D.26.5
Answer: B.21.43
Explanation: Average speed = distance/time
Because we are looking for average speed we can pick a distance for the variable d.
Speed A-B = 150
Speed B-C = 100
Average Speed = total distance/total rate
rate = distance/time
A====================B==========C
If A-B is twice the length of B-C then let A-B = 2d and let B-C = d
Average speed = 3d/(2d/150) + (d/100)
3d/(4d/300 + (3d/300)
3d/(7d/50)
150d/7d
Average speed = 21.43
ANSWER: B
Question: A father is now three times as old as his son. Six years back, he was four times as old as his son. The age of the son (in years) is
A.12
B.15
C.18
D.20
Answer: C.18
Explanation: If father's age is F and son's age is S, then
F=3S
and
F-6 = 4*(S-6)
3S-6 =4S-24
S=18
F=54 years
ANSWER:C
Question: A fruit juice company earns $150 per 100 gallons of apple juice sold, $170 per 100 gallons of guava juice sold, $130 per 100 gallons of grape juice sold, $100 per 100 gallons of orange juice. If the company manages to sell 230 gallons of apple, 210 gallons of guava, 310 gallons of grape, 270 gallons of orange on a particular day. What is the average earning of the company per 100 gallon of the juice sold?
A.134.8
B.141.2
C.147.2
D.152.3
Answer: A.134.8
Explanation: Earning of the company from apple=150/100x230=345
Earning of the company from guava=170/100x210=357
Earning of the company from grape=130/100x310=403
Earning of the company from orange=100/100x270=270
Total earning of the company=345+357+403+270=1375
Total juice sold=1020
Average earning per 100 gallon of juice sold=(1375/1020)x100
=$134.8
Answer: A
Question: A biker covered half the distance between two towns in 2 hr 30 min. After that he increased his speed by 2 km/hr. He covered the second half of the distance in 2 hr 20 min. Find the distance between the two towns and the initial speed of the biker.
A.140
B.260
C.320
D.480
Answer: A.140
Explanation: Let x km/hr be the initial speed of the biker, then his speed during the second part of the trip is x + 2 km/hr. Half the distance between two cities equals 2*30/60⋅x km and 2*20/60⋅(x+2) km. From the equation: 2*30/60⋅x=2*20/60⋅(x+2) we get x=28 km/hr.
The intial speed of the biker is 28 km/h.
Half the distance between the two towns is
2h30min×28=2.5×28=70.
So the distance is 2×70=140 km
Question: A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet?
A.287
B.279
C.200
D.278
Answer: C.200
Explanation: When the second train leaves Mumbai the first train covers 40 * 1 = 40 km
So, the distance between first train and second train is 40 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed = 40 / (50 -40) = 4 hours
So, the two trains meet at 2 p.m. The two trains meet 4 * 50 = 200 km away from Mumbai.
Answer:C
Question: If P = 775 × 778 × 781, what is the remainder when P is divided by 14?
A.6
B.7
C.8
D.9
Answer: A.6
Explanation: P 775/14 leaves a remainder 5
778/14 leaves a remainder 8
781/14 leaves a remainder 11
5*8*11 =440
So the remainder will be the remainder of 440/14 which is 6
Ans A
Question: The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 7 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
A.45
B.65
C.75
D.79
Answer: D.79
Explanation: A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 7 = 75
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 – 316 = 4
A = E +4 = 75 + 4 = 79
D
Question: Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 1 hours, how many minutes did it take Cole to drive to work?
A.35
B.50
C.62
D.75
Answer: A.35
Explanation: First round distance travelled (say) = d
Speed = 75 k/h
Time taken, T2 = d/75 hr
Second round distance traveled = d (same distance)
Speed = 105 k/h
Time taken, T2 = d/105 hr
Total time taken = 1 hrs
Therefore , 1 = d/75 + d/105
LCM of 75 and 105 = 525
1= d/75 + d/105
=> 1 = 7d/525 + 5d/525
=> d = 525 / 12 Km
Therefore, T1= d/75
=> T1 = 525 / (12 x 75)
=> T1 = (7 x 60) / 12 -- in minutes
=> T1 = 35 minutes.
A
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 360 m and they cross each other in 24 sec, then the speed of each train is?
A.78
B.89
C.36
D.54
Answer: D.54
Explanation: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (360 + 360)/24 => x =15
Speed of each train = 15 m/sec.
= 15 * 18/5 =54 km/hr.
Answer: Option D
Question: If Deepesh had walked 20 km/h faster he woulh have saved 1 hour in the distance of 60km. what is the usual speed of Deepesh?
A.100
B.299
C.208
D.273
Answer: A.100
Explanation: Explanation:
Let the original speed be x km/h, then
\inline \frac{600}{x}-\frac{600}{(X+20)}=1
\inline \Rightarrow 600\left ( \frac{x+20-x}{x(x+20)} \right )=1
\inline \Rightarrow \: \: x^{2}+120x-12000=0
\inline \Rightarrow \: \: (x-120)(x-100)=0
\inline \Rightarrow \: \: x=100 \: \: and\: \: x=120
\inline \therefore original speed = 100km/h
Answer: A
Question: A train running at the speed of 60 km/hr crosses a pole in 12 sec. What is the length of the train?
A.356
B.200
C.127
D.279
Answer: B.200
Explanation: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 12 = 200 m
Answer: B
Question: A square mirror has exactly half the area of the rectangular wall on which it is hung. If each side of the mirror is 54 inches and the width of the wall is 68 inches, what is the length of the wall, in inches?
A. 25.7
B. 72.7
C. 70.7
D. 85.7
Answer: D. 85.7
Explanation: Since the mirror is 42 inches in all sides, it must be a square. Area of a square is A=a^2; 54^2=2916.Area of rectangle is double of that 2 *2916=5832.Now A=lw and we need find w so A/l=w ; 5832/68= 85.7 Answer!
Answer is D
Question: The proportion of X’s and Y’s ages is 4:5. If the difference between the current age of X and the age of Y 0.5 decades hence is 3, then what is the sum of current ages of X and Y?
A.83 years
B.39 years
C.72 years
D.48 years
Answer: D.48 years
Explanation: D
72 years
We simplified the most of steps because lack of font prolem.
X = 32 years
and, Y = (5/4) x 32 = 40 years
Therefore X + Y = 40 + 32 = 72 years.
Question: What is the area of a square with perimeter 8P ?
A. 16p^2
B. 4P^2
C. P^2/4
D. P/16
Answer: B. 4P^2
Explanation: Each side is 2p
A = (2p)^2 = 4(p^2)
Answer B
Question: Insert the missing number
121, 112, ..., 97, 91, 86
A.102
B.108
C.99
D.104
Answer: D.104
Explanation: first and second number difference is starting from 9, and further decresed by 1 by each iteration.
121, 112, ..., 97, 91, 86....
Difference between two numbers Will be as 9, 8, 7, 6, 5,...
ANSWER:D
Question: Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3?
A.2/5
B.3/5
C.3/10
D.3/11
Answer: C.3/10
Explanation: Here, S = [1, 2, 3, 4, …., 19, 20]
Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18]
P (E) = n (E) / n (S) = 6 / 20 = 3/10
C
Question: How many seconds will a 700 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
A.22
B.42
C.99
D.77
Answer: B.42
Explanation: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 700 * 3/50 = 42 sec.
Answer: B
Question: If 500 gm of salt solution has 30% salt in it, how much salt must be added to make the concentration of salt 50% in the solution?
A.200 gm
B.280 gm
C.202 gm
D.700 gm
Answer: A.200 gm
Explanation: Explanation:
Amount of water in solution = 100 % - 30 % = 70 % of total
Amount of water = 70 % x 500 = 350 gm
Amount of water remains same for both the solutions. Therefore, let amount of new solution be x gm.
x = 350 x (100/ 50)
x = 700
Salt added = (700 – 500) = 200 gm
Alternate solution:
Quantity of sugar to be added :
= [Solution (Required % value – Present % value)] / (100 – Required % value)
= [500 (50 – 30)] / 100 – 50
= (500 x 20) / 50
= 200 gm
ANSWER: A
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
A.5
B.7
C.3
D.1/2
Answer: C.3
Explanation: Explanation:
M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer: C
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
A.5.29
B.5.2
C.5.76
D.5.12
Answer: C.5.76
Explanation: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
Answer:C
Question: Pipe A can fill a tank in 2 hours. Due to a leak at the bottom, it takes 3 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
A.10
B.9
C.7
D.6
Answer: D.6
Explanation: Let the leak can empty the full tank in x hours 1/2 - 1/x = 1/3
=> 1/x = 1/2 - 1/3 = (3 - 2)/6 = 1/6
=> x = 6.
Answer: D
Question: The perimeter of a rectangular yard is completely surrounded by a fence that measures 12 meters. What is the length of the yard if the area of the yard is 9 meters squared?
A.8
B.1
C.3
D.4
Answer: B.1
Explanation: Perimeter of rectangular yard = 2(l + b) = 12 --> l + b = 6
Area = l * b = 9
b = 6 - l
l(6 - l) = 9
6l - l^2 = 9
l^2 - 6l + 9 = 0
Upon simplifying we get l = 3.
Answer: B
Question: If 5a + 7b = k, where a and b are positive integers, what is the largest possible value of k for which exactly one pair of integers (a, b) makes the equation true?
A.35
B.48
C.69
D.70
Answer: C.69
Explanation: We 'll start putting the values of with a = 10 and b = 1.
Keep decreasing the value of a by 1 and increasing the value of b by 1.
At a = 10 and b = 1, 5a + 7b = 57
At a = 9 and b = 2, 5a + 7b = 59
At a = 8 and b = 3, 5a + 7b = 61
We see a pattern, for every decrease in a and every decrease in b, the result is increasing by 2.
So,
At a = 4 and b = 7, 5a + 7b = 69.
ANSWER:C
Question: Two perpendicular line segments divide a large rectangle
into 4 small rectangles. The areas of 3 of these 4 small
rectangles are shown. What is the area of the other small
rectangle?
A.12
B.13
C.14
D.15
Answer: A.12
Explanation: Label the 4 small rectangles R1, R2, R3, and R4 so that the areas of R1, R2,
and R3 are 8, 6, and 9 respectively and R4 is the rectangle whose area we want to find.
Denote the area of R4 by x. Then 8 · 9 = 6 · x. (Note that R1 and R2 have the same
base and so do R3 and R4. Also, R1 and R4 have the same height and so do R2 and
R3.)
correct answer A
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31750. What percentage of profit did he make?
A.42.7
B.27
C.40
D.26
Answer: A.42.7
Explanation: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31750
Profit(%) = (31750 - 22250)/22250 * 100 = 42.7%.Answer:A
Question: A certain list consists of 21 different numbers. If n is in the list and n is 5 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?
A.1/20
B.1/6
C.1/5
D.4/21
Answer: C.1/5
Explanation: series : a1, a2....a20,n
sum of a1+a2+...+a20 = 20*x (x = average)
so, n = 5*x
Hence, a1+a2+..+a20+n = 25x
So, the fraction asked = 5x/25x = 1/5
Answer C
Question: A sum of Rs.96000 is divided into three parts such that the simple interests accrued on them for Eight, two and four years respectively may be equal. Find the amount deposited for 8 years.
A.14000
B.16000
C.12000
D.20000
Answer: C.12000
Explanation: Let the amounts be x, y, z in ascending order of value. As the interest rate and interest accrued are same for 2 years 4 years and 8 years i.e. 2x = 4y = 8z = k.
L.C.M. of 2,4,8 = 8 So x:y:z: = 48000 : 24000 :12000
The amount deposited for 11 years = 12000
ANSWER:C
Question: In an examination, 30% of total students failed in Hindi, 42% failed in English and 28% in both. The percentage of these who passed in both the subjects is :
A.23
B.37
C.56
D.40
Answer: C.56
Explanation: Explanation:
Formula n(aâˆªb) = n(a) + n(b) âˆ’ n(aâˆ©b)
Fail in Hindi or English = 30 + 42 â€“ 28 = 44
Therefore students who passed = 100 â€“ 44 = 56.
Answer: C
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
A.85 kg
B.87 kg
C.90 kg
D.91 kg
Answer: A.85 kg
Explanation: Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
Answer is A
Question: At a certain university, 66% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?
A.25
B.37.5
C.60
D.62.5
Answer: C.60
Explanation: answer is 75%
total women = 66%
total men = 40%
total tenured = 70% (both men and women)
therefore, women tenured + women professors + men tenured = 90%
men tenured = 24%
but question wants to know the percent of men that are tenured
24%/40% = 60%
C
Question: There are 4 copies of 5 different pencils. In how many ways can they be arranged on a shelf?
A.20!/4!
B.20!/5(4!)
C.20!/(4!)^5
D.20!
Answer: C.20!/(4!)^5
Explanation: There are 4 copies of 5 different pencils.20!/((4!)^5)
Answer - C
Question: 25 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 3:2. How many liters of Liquid Q must be added to make the ratio 5:4?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: Let x be the amount of liquid Q to be added.
(2/5)*25 + x = (4/9)*(25+x)
450 + 45x = 500 + 20x
25x = 50
x = 2
The answer is B.
Question: What is the place value of 7 in the numeral 2734?
A.600
B.650
C.700
D.800
Answer: C.700
Explanation: Option 'C'
7 * 100 = 700
Question: A rope of which a calf is tied is increased from 12 m to 18 m, how much additional grassy ground shall it graze?
A.1217
B.1219
C.1210
D.565.7
Answer: D.565.7
Explanation: π (182 – 122) = 565.7
Answer:D
Question: In a recent election, Ms. Robbins received 7,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 20 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 50 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?
A.0.06N + 3,200
B.0.1N + 7,000
C.0.4N + 7,200
D.0.1N + 8,000
Answer: B.0.1N + 7,000
Explanation: I will go with option B
According to question 50 percent of total votes (N) cas were cast by independent voters. This implies 50 percent of N are voters that belong to political party. And she received 7000 votes from independent voters and 20 percent from registered voters (i.e 0.2 * 0.5 * N = 0.1N). Hence total votes = 7000 + 0.1N ....option B
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
A.5
B.4
C.6
D.7
Answer: D.7
Explanation: 7 * 8 : 9 * x = 8:9 => x= 7
Answer: D
Question: Calculate the amount that an investor needs to be invest to earn $460 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 9% compounded semi-annually?
A.7,000
B.4,000
C.6,000
D.5,000
Answer: D.5,000
Explanation: the approach is substitution,
our interest requirement is 460 after 12 months, 2 compounding period.
calculate the compound interest on each option and find out the one that yields 460 in 12 months
5,000 yielded $460
using the formula
A = P(1 + r/n)nt
hence answer is D
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 15 kmph, then the speed in downstream is?
A.30 kmph
B.5 kmph
C.20 kmph
D.22 kmph
Answer: A.30 kmph
Explanation: M = 15
S = 15
DS = 15 + 15 = 30
ANSWER:A
Question: 562Ã—99=?
A.55684
B.55432
C.55638
D.44530
Answer: C.55638
Explanation: 562Ã—(100-1)
56200-562=55638
answer C
Question: Divide Rs.116000 among three persons A, B and C such that the ratio of the shares of A and B is 3:4 and that of B:C is 5:6.find the share of A?
A.29491
B.28491
C.39491
D.49491
Answer: A.29491
Explanation: Compound ratio of A:B:C
A:B = 3:4
B:C = 5:6
----------
A:B:C = 15:20:24
We can divide Rs.116000 in this ratio.
Share of A = 15/59 * 116000 = 29491
ANSWER:A
Question: What will be the CI on a sum of Rs. 25,000 after 3 years at the rate of 12 per year?
A.Rs. 10110.20
B.Rs. 10120
C.Rs. 10123.20
D.Rs. 10124
Answer: C.Rs. 10123.20
Explanation: Amount
= Rs. 25000 x 1 +	12 3
100
= Rs. 25000 x	28	x	28	x	28
25	25	25
= Rs. 35123.20
C.I. = Rs. (35123.20 - 25000) = Rs. 10123.20
C
Question: The average age of 12 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is
A.22
B.30
C.34
D.38
Answer: C.34
Explanation: total age increased = (12 * 2) years = 24 years.
Sum of ages of two new men = (21 + 23 + 24) years = 68 years
Average age of two new men = (68/2) years = 34 years.
Answer: C
Question: If a survey shows that 50 citizens out of a sample of 200 support a particular Senate bill, what percent of the sample does not support the bill?
A.56%
B.64%
C.75%
D.82%
Answer: C.75%
Explanation: Those who support = 50.
% of those who don't support it is (200-50)/ 200 = 75%
Answer C
Question: What percent is 2 gm of 1 kg?
A.0.5 %
B.0.2%
C.1.5%
D.2%
Answer: B.0.2%
Explanation: 1 kg = 1000 gm
2/1000 × 100 = 200/1000
=1/5 = 0.2 %
B)
Question: what is the value of (2)^-3?
A.1/6
B.1/5
C.1/8
D.1/9
Answer: C.1/8
Explanation: 2^-3= 1/(2)^3= 1/8
ANSWER:C
Question: A man can row upstream at 6km/hr and down stream at 11km/hr find mans rate in still water ?
A.2.9km/hr
B.8.5km/hr
C.7.8km/hr
D.85.4km/hr
Answer: B.8.5km/hr
Explanation: given upstream(u) =6km/hr
down stream (v)= 11km/hr rate in still water =1/2(u+v)=1/2(6+11)=8.5km/hr Answer is (B)
Question: If a card is drawn from a well shuffled deck of cards, what is the probability of drawing a black card or a face card?
A.7/13
B.15/26
C.9/12
D.8/13
Answer: D.8/13
Explanation: P(Bá´œF) = P(B) + P(F) - P(Bâˆ©F), where B denotes black cards and F denotes face cards.
P(Bá´œF) = 26/52 + 12/52 - 6/52
= 8/13
Answer: D
Question: The sum of 3 consecutive numbers is definitely
A.Positive.
B.Divisible by 3.
C.Divisible by 2.
D.Divisible by 4.
Answer: B.Divisible by 3.
Explanation: If 1st term is x:
x+(x+1)+(x+2)=3x+3--->Always divisible by 3
If 2nd term is x:
(x-1)+x+(x+1)=3x--->Always divisible by 3
If 3rd term is x:
(x-2)+(x-1)+x=3x-3--->Always divisible by 3
Answer: B
Question: If w, x, and y are consecutive even positive integers and w < x < y, which of the following could be equal to y - x - w ?
A.-4
B.-2
C.-1
D.0
Answer: D.0
Explanation: Since W, X and Y are CONSECUTIVE EVEN POSITIVE INTEGERS and W < X < Y, we can start with the easiest set of values that comes to mind:
W = 2
X = 4
Y = 6
The question asks for what COULD be the value of Y - X - W.
In this case, the value would be...
6 - 4 - 2 = 0
0 IS among the answer choices, so we're done.
D
Question: If C.P. of 24 books is equal to S.P of 30 books , then your gain or loss is ?
A.23 1/3 gain %
B.30 10/23 loss %
C.20% loss %
D.30 1/3 loss %
Answer: C.20% loss %
Explanation: Say the cost price of 24 books is $24 so $1 for a book.
The cost of 30 books would be $30, and the selling price of 30 books would be 24$, hence the loss = ($30 - $24)/$30 = 20%.
Answer: C.
Question: 75% of a number when added to 75 is equal to the number. The number is ?
A.150
B.200
C.225
D.300
Answer: D.300
Explanation: Answer
75 + 75% of N = N
⇒ N -3N/4 = 75
⇒ N/4 = 75
∴ N = (75 x 4) = 300
Correct Option: D
Question: Given two sets A = {1,1,6,6,7,7} and B = {0,1}, if one number is chosen from each set at random, what is the probability that the sum of both numbers is an even number
A.1/4
B.1/6
C.1/2
D.1/3
Answer: C.1/2
Explanation: One way to look at it:
The number from set A can be ANYTHING.
The number selected from set B will determine whether the sum is odd or even.
For example, if a 6 is selected from set A, we need a 0 from set B to get an even sum.
If a 7 is selected from set A, we need a 1 from set B to get an even sum.
And so on.
So, P(sum is even) = P(select ANY number from set AANDselect the number from set B that makes the sum even)
= P(select ANY number from set A)xP(select the number from set B that makes the sum even)
= 1x1/2
= 1/2
= C
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
A.238
B.288
C.237
D.400
Answer: D.400
Explanation: Explanation:
2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
Answer: D
Question: An outlet pipe empties a tank which is full in 5 hours. If the inlet pipe is kept open, which lets water in at the rate of 4 litres/min then outlet pipe would take 3 hours longer. Find the capacity of the tank.
A.8600 litres
B.3200 litres
C.12800 litres
D.11200 litres
Answer: B.3200 litres
Explanation: Let the rate of outlet pipe be x liters/hour;
Rate of inlet pipe is 8 litres/min, or 4*60 = 240 liters/hour;
Net outflow rate when both pipes operate would be x-240 liters/hour.
Capacity of the tank = x*5 hours = (x-240)*(5+3) hours
5x=(x-240)*8 --> x=640 --> capacity = 5x = 3200 liters.
Answer: B.
Question: Some persons can do a piece of work in 20 days. Two times the number of these people will do half of that work in?
A.3
B.4
C.5
D.6
Answer: C.5
Explanation: 20/ (2 * 2) = 5 days
Answer:C
Question: If log	(a/b)+log(b/a)	= log (a + b), then:
A.a=b
B.a+b=0
C.a-b=1
D.a+b=1
Answer: D.a+b=1
Explanation: log(a/b)+ log(b/a)	= log (a + b)
log (a + b) = log{(a/b)x(b/a)}	= log 1.
So, a + b = 1.
Answer is D
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
A.27
B.27
C.20
D.99
Answer: C.20
Explanation: M = 15
S = 5
DS = 15 + 5 = 20'
Answer:C