RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A local bank that has 15 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 15 codes?
A.3
B.4
C.5
D.6
Answer: B.4
Explanation: Consider the code XY. If there are nn digits available then X can take nn values and Y can also take nn values, thus from nn digits we can form n2n2 different 2-digit codes: this is the same as from 10 digits (0, 1, 2, 3, ..., 9) we can form 10^2=100 different 2-digit numbers (00, 01, 02, ..., 99).
We want # of codes possible from nn digit to be at least 15 --> n2≥15n2≥15 --> n≥4n≥4, hence min 4 digits are required.
Answer: B.
Question: Solution Y is 30 percent liquid P and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid P?
A.30%
B.33 1/3%
C.37 1/2%
D.40%
Answer: C.37 1/2%
Explanation: Answer:C
Took time to solve this one, the statement2 kilograms of solution Y are added to the remaining 6 kilograms of liquidwas confusing to me. After thinking more deeply, it was clear to me that new 2 kg of solution Y will also be 30% liquid P and 70% water, and then I was able to get the answer. That was a bit tricky and nice question=C
Question: Machine T can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
A. 1/2
B. 1/3
C. 4/13
D. 8/29
Answer: C. 4/13
Explanation: Let the following be true:
T makes x in time t
Then the following follows:
N makes x in 4t/3
O makes x in 3/2(4t/3) = 2t
M:N:O = 1:4/3:2=3:4:6
So N=4/(3+4+6)=4/13=C
Question: If all the numbers 2, 3, 4, 5, 6, 7, 8 are arranged, find the number of arrangements in which 2, 3, 4, are together?
A.650
B.680
C.720
D.740
Answer: C.720
Explanation: If (2 3 4) is one.
we must arrange (2 3 4), 5, 6, 7, 8 in
5P5 = 5! = 120 ways
2, 3, 4 can be arranged in 3P3 = 3! = 6
120 × 6 = 720.
C
Question: The average of first 10 natural numbers is?
A.5.9
B.5.5
C.5.4
D.5.1
Answer: B.5.5
Explanation: Sum of 10 natural no. = 110/2 = 55
Average = 55/10 = 5.5
Answer: B
Question: How long will take a leak at the bottom of a tank to empty it if it will take
8 hours to fill it without the leak, but due to the leak it will take 9 hours to be filled?
A.50 hours
B.33 hours
C.72 hours
D.82 hours
Answer: C.72 hours
Explanation: Part filled without leak in 1 hour = 1/8
Part filled with leak in 1 hour = 1/9
Work done by leak in 1 hour
=1/8âˆ’1/9=72 hours
Answer:C
Question: The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
A.3000
B.2802
C.1750
D.2990
Answer: C.1750
Explanation: C.I. = [4000 * (1 + 10/100)2 - 4000]
= (4000 * 11/10 * 11/10 - 4000) = Rs. 840.
Sum = (420 * 100)/(3 * 8)
= Rs.1750
Answer:C
Question: A sum was put at simple interest at a certain rate for 7 years Had it been put at 2% higher rate, it would have fetched 140 more. Find the sum.
A.500
B.750
C.1000
D.1250
Answer: C.1000
Explanation: Difference in S.I. = P×T/100(R1−R2)
⇒ 140 = P×7x2/100(∵ R1 - R2 = 2)
⇒ P = 140×100/7×2=1000
Answer C
Question: The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group?
A.22
B.77
C.23
D.44
Answer: C.23
Explanation: Let the initial number of members in the group be n.
Initial total weight of all the members in the group = n(48)
From the data,
48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23
Therefore there were 23 members in the group initially.
Answer: C
Question: A merchant sells an item at a 20% discount, but still makes a gross profit of 30 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?
A.20%
B.40%
C.50%
D.62.5%
Answer: D.62.5%
Explanation: original SP = X
Cost =C
current selling price = .8x ( 20% discount)
.8x = 1.3C (30% profit)
x= 1.3/.8 *C
x= 13/8 C
Original selling price is 1.625C which is 62.5% profit
Answer D
Question: What was the day of the week on, 18th July, 1776?
A.Thursday
B.Wednesday
C.Monday
D.Saturday
Answer: A.Thursday
Explanation: 16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)
Counting of odd days :
1600 years have 0 odd day.
100 years have 5 odd days.
75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days.
1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day.
Jan Feb Mar Apr May Jun Jul
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 4 days)
Total number of odd days = (0 + 4) = 4.
Required day was 'Thursday'.
Answer:A
Question: If a2 - b2 = 10 and a*b = 8, find a4 + b4.
A.200
B.228
C.182
D.102
Answer: B.228
Explanation: a2 - b2 = 10 : given
a4 + b4 - 2a2b2 = 102 : square both sides and expand.
a*b = 8 : given
a2b2 = 82 : square both sides.
a4 + b4 - 2(64) = 100 : substitute
a4 + b4 = 228
correct answer B
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
A.38 seconds
B.26 seconds
C.88 seconds
D.12 seconds
Answer: D.12 seconds
Explanation: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5 = 12 seconds.
Answer:D
Question: An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/5 %, then the amount invested at 11% was?
A.23777
B.30000
C.29977
D.26777
Answer: B.30000
Explanation: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then,
(x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 48/5 * 1/100)
(9x + 1100000 - 11x) = 960000
x = 70000
Sum invested at 9% = Rs. 70000
Sum invested at 11% = Rs. (100000 - 70000) = Rs. 30000.
Answer: B
Question: Calculate the distance covered by 320 revolutions of a wheel of radius 28.1 cm.
A.465.2 m
B.965.2 m
C.265.2 m
D.565.2 m
Answer: D.565.2 m
Explanation: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 320 * 2 * 22/7 * 28.1 = 56521.14 cm = 565.2 m
ANSWER:D
Question: A rectangular field has to be fenced on three sides leaving a side of 2020 feet uncovered. If the area of the field is 680680 sq. feet, how many feet of fencing will be required?
A.95
B.92
C.88
D.82
Answer: C.88
Explanation: Explanation:
Area of the field =680 sq. feet.
Length of the adjacent sides are
20 feet and 680/20=34 feet.
Required length of the fencing
=20+34+34=88 feet
Answer: Option C
Question: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
A.8 hours
B.10 hours
C.12 hours
D.24 hours
Answer: C.12 hours
Explanation: A's 1 hour's work = 1/4 ;
(B + C)'s 1 hour's work = 1/3 ;
(B + C)'s 1 hour's work = 1/2
(A + B + C)'s 1 hour's work = (1/4 + 1/3) = 7/12
B's 1 hour's work = (7/12 - 1/2) = 1/12
B alone will take 12 hours to do the work.
Answer = C
Question: he total marks obtained by a student in Physics, Chemistry and Mathematics is 130 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
A.55
B.65
C.75
D.85
Answer: B.65
Explanation: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.
P + C + M = 130 + P
C + M = 130
Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 130/2 = 65.
ANSWER:B
Question: A table is bought for Rs.400/- and sold at Rs.300/- find gain or loss percentage
A.25% loss
B.20% gain
C.20% loss
D.15% gain
Answer: A.25% loss
Explanation: Formula = (Selling price ~ Cost price)/Cost price * 100
= (300 - 400)/400 = 25% loss
A
Question: Joseph Paul and his friend went for fishing.
They got six fishes without heads, nine fishes without the tail and eight fishes cut in two halves.
How many fishes did they caught ?
A.0
B.4
C.1
D.7
Answer: A.0
Explanation: A
6 without head => 0
9 without tail => 0
8 in two halves => 0 & 0
Question: Working simultaneously and independently at an identical constant rate, 6 machines of a certain type can produce a total of x units of product P in 10 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 5x units of product P in 6 days?
A.50
B.18
C.16
D.12
Answer: A.50
Explanation: 6 machines do x units in 10 days
we have x/10 => rate of the 6 machines
we know that we need to have 5x units in 6 days
therefore, we need to get to 5x/6 rate of the machines.
rate of one machine is x/10*1/6 = x/60.
now, we need to know how many machines need to work simultaneously, to get 5x done in 6 days.
5x/6 work needs to be done by machines that work at x/60 rate.
let's assign a constant Y for the number of machines:
(x/60)*y = 5x/6
y = 5x/6 * 60/x
cancel 6 with 60, and x with x and get -> 50. Answer choice A
Question: Find the least number must be subtracted from 11070 so that remaining number is divisible by 22.
A.2
B.3
C.4
D.7
Answer: A.2
Explanation: On dividing 11070 by 22 we get the remainder 4, so 4 should be subtracted. Answer is A.
Question: The perimeter of one face of a cube is 28 cm. Its volume will be:
A.125cm3
B.343cm3
C.250cm3
D.625cm3
Answer: B.343cm3
Explanation: Explanation:
Edge of cude = 28/4 = 7 cm
Volume = a*a*a = 7*7*7 = 343 cm cube
Option B
Question: If a2 + b2 + c2 = 213 and ab + bc + ca = 6, then a + b + c is
A.14
B.20
C.15
D.32
Answer: C.15
Explanation: by formula ,
(a + b + c)^2= a^2 + b^2 + c^2 + 2(ab + bc + ca),
since, a^2 + b^2 + c^2 = 213 and ab + bc + ca = 6,
(a + b + c)^2 = 213 + 2(6)
= 225
= 15^2
therefore: a + b + c = 15
ANSWER:C
Question: Two trains, each 100 meters long, moving in opposite directions, completely pass each other in 20 seconds. If one train is moving twice as fast the other, then what is the speed of the faster train (in km/hr)?
A.16 km/hr
B.20 km/hr
C.24 km/hr
D.28 km/hr
Answer: C.24 km/hr
Explanation: Let the speed of the slower train be x m/s
Then, the speed of the faster train is 2x m/s
The relative speed is 3x m/s
(100 + 100)/20 = 3x
x = 10/3 m/s
So, the speed of the faster train is 20/3 = 20/3 * 18/5 = 24 km/hr
The answer is C.
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
A.2:5
B.1:5
C.3:5
D.4:5
Answer: A.2:5
Explanation: The volume of the cone = (1/3)Ï€r2h
Only radius (r) and height (h) are varying.
Hence, (1/3)Ï€ may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2 : 5
ANSWER A
Question: In a series of six consecutive even numbers, the sum of the second and sixth numbers is 24. What is the fourth number?
A.10
B.11
C.12
D.14
Answer: C.12
Explanation: Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10.
Given (x + 2) + (x + 10) = 24
=> 2x + 12 = 24 => x = 6
The fourth number = x + 6 = 6 + 6 = 12.
C
Question: If p^2 = q^2, which of the following must be true?
A.p =q
B.p = −q
C.p = |k|
D.|p| = |q|
Answer: D.|p| = |q|
Explanation: Since p^2=q^2 we have 0=p^2 – q^2 =(p-q)*(p+q). So p=q or p=-q.
So only (A) and only (B) cannot be an answer.
The choice (C) tells us that k should be greater than or equal to 0.
Similarly the choice (E) tells us that k should be less than or equal to 0.
So neither (C) nor (E) cannot be the answer.
The answer is, therefore, (D).
Question: In the manufacture of a certain product, 4 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?
A.0.125%
B.0.2%
C.0.16%
D.1.25%
Answer: C.0.16%
Explanation: Percent of defective produced = 4%
Percent of the defective units that are shipped for sale = 4%
Percent of units produced are defective units that are shipped for sale = (4/100)*(4/100)*100%
= (16/10000)*100%
= (16/100)%
= .16 %
Answer C
Question: In Township K, 1/5 of the housing units are equiped with cable Tv. If 1/10 of the housing units, including 1/4 of those that are equiped with cable tv, are equipped with videocassette recorders, what fraction of the housing units have neither cable tv nor videocassette recorders?
A.3/4
B.11/15
C.7/10
D.1/6
Answer: A.3/4
Explanation: 1/5 -- cable TV (This includes some data from video cassette recorder)
1/10 -- video cassette recorder including 1/4(equiped with cable tv) i.e. 1/4(1/5) = 1/20
therefore only video cassette recorder = 1/10 - 1/20 = 1/20
Total = 1/5+1/20+neither cable tv nor videocassette recorders
1 = 1/4 + neither cable tv nor videocassette recorders
therefore neither cable tv nor videocassette recorders = 1-1/4 = 3/4
Hence A.
Question: The time on a clock is 20 minutes past 7. What is the angle between the hands of the clock?
A.60 degrees
B.100 degrees
C.80 degrees
D.50 degrees
Answer: B.100 degrees
Explanation: The hour hand rotates 360 degrees in twelve hours.
The hour hand rotates 30 degrees in one hour.
The hour hand rotates 5 degrees in ten minutes.
At this time, the hour hand has rotated 220 degrees.
The minute hand rotates 360 degrees in 60 minutes, or 60 degrees in ten minutes.
At this time, the minute hand has rotated 120 degrees.
The difference is 220 - 120 = 100 degrees.
The answer is B.
Question: The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
A.1677
B.1683
C.2523
D.3363
Answer: B.1683
Explanation: L.C.M. of 5, 6, 7, 8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 x 2 + 3) = 1683. Answer: Option B
Question: On a summer camp, 25% of the campers paid $110 each, 35% paid $80 each and the rest paid $65 each. What percentage of the total amount paid came from the campers who paid $80?
A.18%
B.21%
C.33.35
D.33.3%
Answer: C.33.35
Explanation: let the total no of campers be 100
total amount = (25*110)+(35*80)+(40*65) = 2750+2800+2600= $8150
required percentage = (2800/8150)*100=33.35%
C
Question: If there are 8 pairs of twins, and a committee will be formed with 3 members. In how many ways this committee formed in a way that no siblings in a group?
A.32
B.24
C.56
D.448
Answer: D.448
Explanation: Firstly, there are 8 ways to choose 3 groups from the 4 groups. Hence 8C3.
Next, with the 3 groups chosen, there are 2^3 choices of choosing either one of the siblings.
Hence, the total number of ways are 8C3 * (2^3) = 448
D
Question: The length of rectangle is thrice its breadth and its perimeter is 80 m, find the area of the rectangle?
A.432 sq m
B.356 sq m
C.300 sq m
D.428 sq m
Answer: C.300 sq m
Explanation: 2(3x + x) = 80
l = 30 b = 10
lb = 30 * 10 = 300
ANSWER:C
Question: . In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 65 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
A. 50%
B. 47%
C. 54%
D. 55%
Answer: B. 47%
Explanation: Registered voters = 100
D = 60
R = 40
65% of D ( 60) = 39
20% of R ( 40 ) = 8
Total voter% of registered voters = 47 / 100
47% Ans B
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
A.9 1/4 min
B.11 1/4 min
C.7 1/4 min
D.8 1/2 min
Answer: B.11 1/4 min
Explanation: 3/12 + x/15 = 1
x= 11 1/4
ANSWER:B
Question: A furniture manufacturer has two machines, but only one can be used at a time. Machine F is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine F can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?
A.14
B.13
C.11
D.9
Answer: D.9
Explanation: 'Approximately' could actually make such a question ambiguous. Not this one though but a similar question with the answer as 9.2 days. You round off 8.89 days as 9 days and everything is fine in this question. What do you do when you get 9.2 days? Do you need 9 days or 10 days? Can you round off 9.2 as 9 even though that is what you do with numbers? No, because in 9 days your work is not over. You do need 10 days.
To finish a work say Machine F you need to work full 9 days and a part of the 10th day. If I ask you how many days do you need to complete the work, will you say 9 or 10? You will say 10 even if you don't use the 10th day fully=D
Question: There are 30 children in a classroom, each student will get 1 dozen pencils and 2 dozen erasers, there are 6 teachers. how many pencils will each teacher have to give out to each student?
A.6
B.4
C.3
D.2
Answer: D.2
Explanation: Each student is supposed to get 12 pencils and there are 6 teachers. 6 x 2 is 12. With each teacher giving out 2 pencils to each student, each student will then get 12 pencils like they are supposed to. The answer is D.
Question: In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
A.400
B.625
C.1,250
D.2,500
Answer: C.1,250
Explanation: total fish = x
percentage of second catch = (2/50)*100 = 4%
so, x * 4% = 50
x = 1250
ANSWER:C
Question: There are, in a certain league, 20 teams, and each team face another team for a total of 4 times. How many games are played in the season?
A.450
B.760
C.110
D.180
Answer: B.760
Explanation: By using the formula, t[n(n - 1) / 2], where t = no. of games between two teams and n = total no. of teams, we get: 760
Option B.
Question: The average price of 10 oranges is Rs. 12 while the average price of 8 of these oranges is Rs. 11.75. Of the remaining two oranges, if the price of one orange is 40% more than the price of the other, what is the price of each of these two oranges?
A.Rs 5, Rs 7.50
B.Rs 8, Rs 12
C.Rs 10, Rs 16
D.Rs 10.8, Rs 15.2
Answer: D.Rs 10.8, Rs 15.2
Explanation: Explanation :
Total price of the two oranges = Rs. [(12 x 10) (11.75 x 8)]
= Rs. (120 - 94) = Rs. 26.
Let the price of one orange be Rs. x.
Then, the price of other orange = Rs. (x + 40% of x) = Rs. x + x2/5 = Rs. 7x/5
So, x + 7x/5 = 26
12x = 130
x = 10.8
The prices of the two oranges are Rs. 10.8 and Rs. 15.2
Answer : D
Question: On a map, 2 inches represent 30 miles. How many miles approximately is the distance if you measured 38 centimeters assuming that 1-inch is 2.54 centimeters?
A.226
B.228
C.230
D.224
Answer: D.224
Explanation: 1 inch = 2.54 cm
2 inch = 2.54 * 2 cm
5.08 cm = 30 miles
38 cms = 30/5.08*38 = 224 miles
Answer : D
Question: A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
A.Rs. 460
B.Rs. 484
C.Rs. 550
D.Rs. 664
Answer: B.Rs. 484
Explanation: Explanation:
4/15A=2/5B
A=(2/5X15/4)B
A/B=3/2
A:B=3:2
B's share = Rs.(1210X2/5)= Rs. 484.
ANSWER IS B
Question: A Sum at compound interest amounts to Rs.7500 in 2 years and to Rs.9000 in 3 years then rate per annum is
A.11%
B.12%
C.15%
D.20%
Answer: D.20%
Explanation: 1500/7500 *100=20%
ANSWER:D
Question: Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. The area of the space encosed by the four pieces is
A.12
B.32
C.42
D.52
Answer: C.42
Explanation: required area = 14*14 - (4 * 1/4 * 22/7 * 7 *7) sq cm
= 196 - 154 = 42 sq cm. Answer: C
Question: If the price of an article went up by 15%, then by what percent should it be brought down to bring it back to its original price?
A.17.39%
B.2/8%
C.2/1%
D.1/3%
Answer: A.17.39%
Explanation: Let the price of the article be Rs. 100.
15% of 100 = 15
New price = 100 + 15 = Rs. 115
Required percentage = (115 - 100)/115 * 100
= 20/115 * 100 = 17.39 %.
Answer:A
Question: Find k if 24 / k = 4.
A.6
B.7
C.8
D.4
Answer: A.6
Explanation: Since 24 /k = 4 and 24/ 6 = 4, then
k = 6 correct answer A
Question: Average of first five multiples of 3 is
A.9
B.11
C.13
D.15
Answer: A.9
Explanation: Explanation:
Average=3(1+2+3+4+5)5=455=
Answer: Option A
Question: Find a sum for 1st 4 prime number's?
A.25
B.17
C.30
D.34
Answer: B.17
Explanation: Required sum = (2 + 3 + 5 + 7 ) = 17
Note: 1 is not a prime number
Option B
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
A.18
B.17
C.17
D.12
Answer: D.12
Explanation: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5 = 12 seconds.
Answer: D
Question: The population of a city increases by 7% per year but due to migration it decrease by 1% per years. What will be the percentage increase in population in 3 years?
A.9%
B.9.10%
C.27%
D.12%
Answer: B.9.10%
Explanation: Actual increase in population=6%
Let, earlier population=100 then the population after 3 years
=100(1+6/100)^3=119.1016
∴Required percentage=9.1016%
ANSWER:B
Question: A bag contains 9 wool scarves, exactly one of which is red and exactly one of which is green. If Deborah reaches in and draws three scarves, simultaneously and at random, what is the probability that she selects the red scarf but not the green scarf?
A.1/4
B.2/9
C.3/11
D.4/19
Answer: A.1/4
Explanation: Total possible ways to choose three scarves is 9C3 = 84
We need to choose the red scarf and two of 7 other scarves (not the green scarf).
The number of successful possibilities is 7C2 = 21
P(red scarf but not green scarf) = 21/84 = 1/4
The answer is A.
Question: 4 Women & 6 men have to be seated in a row given that no two women can sit together. How many different arrangements are there.
A.6! x 7P4
B.6! x 9P4
C.6! x 5P4
D.6! x 3P4
Answer: A.6! x 7P4
Explanation: Let us first sit all the 6 men in 6 positions in 6! ways. Now there are 7 gaps between them in which 4 women can sit in 7P47P4 ways.
So total ways are 6! x 7P4
Answer:A
Question: n the youth summer village there are 150 people, 75 of them are not working, 50 of them have families and 100 of them like to sing in the shower. What is the largest possible number of people in the village, which are working, that don't have families and that are singing in the shower?
A.25.
B.50.
C.75
D.100
Answer: C.75
Explanation: total =150
not working =75
having family=50
like to sing in shower = 100
working=150-75=75
not having family = 150-50=100
like to sing in shower = 100
largest possible number is the lowest possible among the above
ANSWER:C
Question: A metallic sheet is of rectangular shape with dimensions 46 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:
A.4830
B.5120
C.6420
D.4800
Answer: D.4800
Explanation: l = (46 - 16)m = 30 m,
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (30 x 20 x 8) m3 = 4800 m3.
Answer: Option D
Question: A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
A.3 : 5 : 2
B.3 : 5 : 5
C.6 : 10 : 5
D.6 : 11 : 2
Answer: C.6 : 10 : 5
Explanation: Let the initial investments of A and B be 3x and 5x.
A : B : C = (3x x 12) : (5x x 12) : (5x x 6) = 36 : 60 : 30 = 6 : 10 : 5.
Answer:C