RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The letters in the word ADOPTS are permuted in all possible ways and arranged in alphabetical order then find the word at position 42 in the permuted alphabetical order?
A.AOTDSP
B.AOTPDS
C.AOTDPS
D.AOSTPD
Answer: D.AOSTPD
Explanation: Explanation :
In alphabetical order : A D O P S T
A _ _ _ _ _ : the places filled in 5! ways = 120, But we need a rank less than 120. So the word starts with A.
A D _ _ _ _ : empty places can be filled in 4!=24
A O _ _ _ _ : the places filled with 4! ways = 24. If we add 24 + 24
this total crosses 42. So We should not consider all the words starting with AO.
A O D _ _ _ : 3!= 6
A O P _ _ _ : 3!=6
Till this 36 words are obtained, we need the 42nd word.
AOS _ _ _ : 3!= 6
Exactly we are getting the sum 42. So last 3 letters in the descending order are TPD.
So given word is AOSTPD
Answer : D
Question: The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder F of Y divided by 5?
A.F= 1.
B.F=2.
C.3.
D.4.
Answer: B.F=2.
Explanation: X divided by 10 gives reminder of 2. X can be 2/12/22....
X+Y divided by 5 is 4. X+Y can be 4/ 9/ 19....
If X+Y= 4 and X is 2 then Y = 2 and Y/5 will give a reminder of 2
Similarly, if X+Y= 9 and X = 2, then y/5 will give a reminder of 2
Hence the answer must be 2 (B)
Also....
x+y=5m+4 and x=10K+2
hence 10k+2+y=5m+4 or y=5(m-2k)+2, m-2k being a constant remainder is 2 hence answer is B
Question: In one year, the population, of a village increased by 10% and in the next year, it decreased by 10%. If at the end of 2nd year, the population was 7920, what was it in the beginning?
A.2889
B.8000
C.2777
D.2999
Answer: B.8000
Explanation: x*110/100 * 90/100 = 7920
X*0.99=7920
X=7920/0.99
=> 8000.Answer:B
Question: A, B and C can do a work in 6, 8 and 12 days respectively doing the work together and get a payment of Rs.1800. What is B’s share?
A.600
B.882
C.266
D.288
Answer: A.600
Explanation: WC = 1/6:1/8:1/12 => 4:3:2
3/9 * 1800 = 600
Answer: A
Question: In a simultaneous throw of 2 dice, what is the probability of getting a total of 5?
A.1/7
B.2/3
C.1/9
D.2/7
Answer: C.1/9
Explanation: n(S) = 6*6 = 36
E = event of getting a total of 5 = {(1,4),(2,3),(3,2),(4,1)}
probability = 4/36 = 1/9
Answer is C
Question: In each of the following questions a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the blank spaces.
?, 7, 14, 23, 34, 47
A.31
B.2
C.36
D.31
Answer: B.2
Explanation: B
2
The given sequence is +5, +7, +9, ——
ie. 2+ 5 = 7, 7 + 7 = 14, 14 + 9 = 23
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 52, then how old is B?
A.17 years
B.20 years
C.29 years
D.10 years
Answer: B.20 years
Explanation: Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.
(2x + 2) + 2x + x = 52
5x = 50 => x = 10
Hence, B's age = 2x = 20 years.
Answer: B
Question: If a and b are multiples of 8 then which are all the multiples of 8
1) a*b
2) a-b
3) a+b
4) a/b
5) a^b
A.1,2,5
B.1,3
C.2,3,4,5
D.1,2,3,5
Answer: D.1,2,3,5
Explanation: a*b a^b a+b a-b are multiples of 6 except a/b
ANSWER:D
Question: Two men start together to walk a certain distance, one at 4 kmph and another at 3 kmph.The former arrives half an hour before the latter. Find the distance.
A.6 kilometre
B.61 kilometre
C.8 km
D.9 km
Answer: A.6 kilometre
Explanation: Let the distance be x km. Then,
x/3 - x/4 = 1/2
(4x - 3x)/12 = 1/2
x = 6 km
ANSWER:A
Question: Jane invested $1500 in fund A and $1000 in fund B. Over the next two years, the money in Fund A earned a total interest of 12 percent for the two years combined and the money in fund B earned 30 percent annual interest compounded annually. Two years after Jane made these investments. Jane's investment in fund B was worth how much more than her investment in fund A?
A.1. $200
B.2. $100
C.3. $10
D.4. $150
Answer: C.3. $10
Explanation: interest on fund A will be 180. rate of interest will be 6% per annum simple interest as 12% is for 2 year. this will make investment A 1680 at the end of 2nd year.
interest on fund B will be 690 on 30% interest compounded annually. This will make investment B 1690 at the end of 2nd year.
Difference in investment B and investment A=1690-1680=10
answer is C.
Question: At the A-Street Fish Market a vendor sells fresh caught fish. His store is filled with 2/7 bass, 1/5 tuna, 1/7 trout, and the rest are catfish. If a customer just bought 1/7 of all the tuna and 1/7 of all the catfish, and a fisherman arrived to restock the bass, doubling the number of bass, what proportion of fish now in the store are trout?
A.30/71
B.4/7
C.5/43
D.1/2
Answer: C.5/43
Explanation: Bass = 2/7 = 10/35
Tuna = 1/5 = 7/35
Trout = 1/7 = 5/35
Catfish = 1 - (10/35 +7/35 + 5/35) = 13/35
Purchased: Tuna = 7/35 - (7/35)(1/7) = 6/35, and
Catfish = 13/35 - (13/35)(1/7) = 12/35
Stocked: doubling the number of bass (2)(10/35) = 20/35
Now: 20 + 6 + 5 + 12 = 43
Trout proportion is now 5/43.
Answer: C
Question: In Goshawk-Eurasian nature reserve 30 percent of the birds are Hawks, and 40 percent of the non-Hawks are Paddyfield-Warblers. If there are 25 percent as many Kingfishers as Paddyfield-Warblers in the reserve, then what percent of the birds E in the nature reserve are not Hawks, Paddyfield-Warblers, or Kingfishers?
A.25%
B.35%
C.45%
D.70%
Answer: B.35%
Explanation: 1. We are given the following percentages: 30 (70), 40 (60), 25 (75). There are two threads from here. First starts at 30% and finishes there. Second one starts at 70, then 40, and then 25. We need a value that is divisible by 7, 2, and 5 at least once. lets pick a number now, say 700. So say if Non Hawks are 700 (this is 70% of the total, so total = 1000), then Paddy Warbs are 2/5 x 700 = 1400/5 = 280. Kingfishers, therefore, are 280/4 = 70. Lets add them up. 300 hawks + 280 Peddy Warbs + 70 kingsifhers = 650. So all others are 1000 - 650= 350 or 35% of total birds.
The main job here to to identify the smart number to start the question with. This can be time consuming, but once identified, this question can be solved fairly quickly.
2. Another method: If X is total --> Non Hawks = 0.7X --> Warbs = 0.4(0.7X) --> KFs = 0.25(0.4(0.7X)).
Our job is to find out E: (0.3X + 0.28X + 0.07X)/ X. OR 0.65X/X = 0.65. We need to find 1-0.65 = 0.35 or 35%.B
Question: By selling 11 pencils for a rupee a man loses 10%. How many for a rupee should he sell in order to gain 20%?
A.8.25
B.9.25
C.7.25
D.10.25
Answer: A.8.25
Explanation: 90% --- 11120% --- ?90/120 * 11 = 8.25Answer: A
Question: 24.39 + 562.093 + 35.96 = ?
A.622.441
B.622.243
C.622.233
D.622.443
Answer: D.622.443
Explanation: Explanation :
24.39 + 562.093 + 35.96 = 622.443. Answer : Option D
Question: A trader cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 10% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 50% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage.
A.80%
B.65%
C.28.33%
D.19.109%
Answer: B.65%
Explanation: Anyways, one can infer that he 'steals' 10% from suppliers and then charges 50% extra to customers
So basically 1.1 * 1.5 = 1.65
Given that 1 is start point, we get 65% more
Hence answer is B
Question: Fifty applicants for a job were given scores from 1 to 5 on their interview performance. Their scores are shown in the table above. What was the average score for the group?
A.2.79
B.2.86
C.2.91
D.2.99
Answer: B.2.86
Explanation: Multiply score * number of application = 10+48+63+14+8 = 143.
Number of applications is 50.
143/50 = 2.86.
Answer: option B is correct..
Question: A man traveled a total distance of 900 km. He traveled one-third of the whole trip by plane and the distance traveled by train is one-half of the distance traveled by bus. If he traveled by train, plane and bus, how many kilometers did he travel by bus?
A.400 km
B.450 km
C.500 km
D.550 km
Answer: A.400 km
Explanation: total distance traveled = 900 km.
distance traveled by plane = 300 km.
distance traveled by bus = x
distance traveled by train = x/2
x + x/2 + 300 = 900
3x/2 = 600
x = 400 km
The answer is A.
Question: A certain candy manufacturer reduced the weight of Candy Bar M by 10 percent buy left the price unchanged. What was the resulting percent increase in the price per ounce of Candy Bar M?
A.10
B.11
C.12
D.14
Answer: B.11
Explanation: assume 1oz candy cost $1 before.
now price remain same $1 but weight of candy reduces to 0.9 oz
new price of candy = 1/0.9 =1.11
price increase 11 %
B
Question: The SF Chronicle has a word game where all the letters are scrambled up and you have to figure out what the word is. Imagine that a scrambled word is 5 characters long: How many possible solutions are there? What if we know which 5 letters are being used?
A.120
B.130
C.110
D.125
Answer: A.120
Explanation: There are 26^5 = 1188137 solutions.
If we know the letters, then there are 5! = 120 possible solutions
ANSWER:A
Question: If both 5^3 and 3^3 are factors of n x (2^5) x (12^2) x (7^3) x (10^2), what is the smallest possible positive value of n?
A.15
B.45
C.75
D.125
Answer: A.15
Explanation: (2^5) x (12^2) x (7^3) x (10) has two appearances of 3 (in 12^2) and two appearances of 5 (in 10^2).
Thus n must include at least 3 * 5 = 15
The answer is A.
Question: A can do a work in 12days. When he had worked for 3days, B joinedhim. If they complete the work in 3more days, in how manydays can Balone finish the work?
A.5 days
B.4 days
C.6 days
D.10 days
Answer: C.6 days
Explanation: sax Work done by Afar 3 days : i
J
.. Remzming war — 1
.Work done by (A + B) for 1 day :
. Work done by a for 1 day
6 days
C
Question: On selling 20 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:
A.s. 48
B.s. 50
C.s. 55
D.s. 60
Answer: A.s. 48
Explanation: (C.P. of 20 balls) - (S.P. of 20 balls) = (C.P. of 5 balls)
C.P. of 15 balls = S.P. of 20 balls = Rs.720.
C.P. of 1 ball = Rs.720/15	= Rs. 48.
Answer: Option A
Question: A sum of money at simple interest amounts to Rs. 825 in 3 years and to Rs. 854 in 4 years. The sum is:
A.s. 650
B.s. 690
C.s. 698
D.s. 738
Answer: D.s. 738
Explanation: S.I. for 1 year = Rs. (854 - 825) = Rs. 29.
S.I. for 3 years = Rs.(29 x 3) = Rs. 87.
Principal = Rs. (825 - 87) = Rs. 738.
Answer: Option D
Question: I chose a number and divide it by 12. Then I subtracted 240 from the result and got 8. What was the number I chose?
A.2976
B.2989
C.2789
D.2888
Answer: A.2976
Explanation: Let x be the number I chose, then
x/12−240=8
x/12=248
x=2976
Answer is A.
Question: A worker's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 5 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?
A.2/11
B.3/14
C.5/17
D.7/20
Answer: C.5/17
Explanation: Let x be the fraction of her take-home pay that the worker saved.
Let P be the monthly pay.
12xP = 5(1-x)P
12xP = 5P - 5xP
17xP = 5P
x = 5/17
The answer is C.
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
A.11%
B.25%
C.87%
D.19%
Answer: B.25%
Explanation: 800 --- 200
100 --- ? => 25%
Answer: B
Question: 95 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?
A.75
B.80
C.85
D.90
Answer: C.85
Explanation: Answer = C
Please refer diagram below
95 - 10 = 85
Question: At a certain company, each employee has a salary grade s that is at least 1 and at most 5. Each employee receives an hourly wage p, in dollars, determined by the formula p = 8.50 + 0.25(s – 1). An employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1?
A.$0.50
B.$1.00
C.$1.25
D.$1.50
Answer: A.$0.50
Explanation: OA is definitely wrong. The answer should be A.
Question: Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
A.$ 145.
B.$ 146
C.$ 147
D.$ 148
Answer: A.$ 145.
Explanation: Solution:
Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
Answer A
Question: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 190 m in length?
A.18.9 sec
B.88.9 sec
C.22.9 sec
D.18.0 sec
Answer: D.18.0 sec
Explanation: D = 110 + 190 = 300 m
S = 60 * 5/18 = 50/3
T = 300 * 3/50 = 18.0 sec
Answer: D
Question: A certain truck uses 18 gallons of diesel fuel in traveling 260 miles. In order for the truck to travel the same distance using 10 gallons of diesel fuel, by how many miles per gallon must the truck’s fuel mileage be increased?
A.8
B.9
C.12
D.11
Answer: D.11
Explanation: There are two sets 18G1 gallons and 10G2 gallons details given.
18 gallons covering 260 miles
Then 1 G1 is used to cover 15 miles.
Now for 10 G2 covering 260 miles.
then 1 G2 is used to cover 26 miles.
There must 26- 15 = 11 miles per gallon increment is needed for 10 gallons to improve the mileage to cover 270 miles.
IMO D is correct answer.
Question: The amounts of time that three secretaries worked on a special project are in the ratio of 1 to 2 to 5. If they worked a combined total of 120 hours, how many hours did the secretary who worked the longest spend on the project?
A.80
B.70
C.75
D.16
Answer: C.75
Explanation: 8x = 120
=> x = 15
Therefore the secretary who worked the longest spent 15 x 5 = 75 hours on the project
Option (C)
Question: Sandy buys an old scooter for $900 and spends $300 on its repairs. If Sandy sells the scooter for $1500, what is the gain percent?
A.10%
B.15%
C.20%
D.25%
Answer: D.25%
Explanation: selling price / total cost = 1500/1200 = 1.25
The gain percent is 25%.
The answer is D.
Question: The ratio between x and y is 7/5; x is multiplied by y and y is multiplied by x , what is the ratio between the new values of x and y?
A.7/5
B.5/7
C.1
D.49/25
Answer: C.1
Explanation: Ratio = 7k/5k = 7/5, 14/10, etc.
x is multiplied by y and y is multiplied by x --> (7k*9k)/(9k*7k) = 1
Answer: C
Question: along a yard 225 metres long, 26 trees are planted at equal distances, one tree bring at each end of the yard. What is the distance between two consecutive trees ? long,26 trees
A.8 metres
B.9 metres
C.10 metres
D.15 metres
Answer: B.9 metres
Explanation: Solution
26 trees have 25 gaps between them. Hence, required distance = (225/25)m =9m
Answer B
Question: Working together, printer A and printer B would finish the task in 15 minutes. Printer A alone would finish the task in 45 minutes. How many pages does the task contain if printer B prints 3 pages a minute more than printer A ?
A.125
B.135
C.145
D.155
Answer: B.135
Explanation: 15*A + 15*B = x pages
in 15 mins printer A will print = 15/45 * x pages = 1/3*x pages
thus in 15 mins printer printer B will print x - 1/3*x = 2/3*x pages
Also it is given that printer B prints 3 more pages per min that printer A. In 15 mins printer B will print 45 more pages than printer A
thus 2/3*x - 1/3*x = 45 => x = 135 pages
Answer: B
Question: New town is straight to the north of New york. A high way M runs from newtown making an angle of 61 degree south east. from newyork there is also an high way N which runs Northeast 61 degrees. If high ways M and N are straight then findout the acute angle made at their intersection point.
A.56degree
B.57degree
C.58degree
D.59degree
Answer: C.58degree
Explanation: the acute angle must be 58 degree . taking north-south as reference axis . from center M is at an angle of 61degree near south and N is at an angle of 61degree from north .therefore, 180-61-61 gives 58degree
ANSWER:C
Question: If Rs.1000 be invested at interest rate of 5% & the interest be added to the principal every 10 yrs, then the no. of yrs in which it will amount to Rs.2000 is:
A.14 years
B.15 years
C.16 2/3 years
D.17 years
Answer: C.16 2/3 years
Explanation: Total time= (10+6 2/3) = 16 2/3 years
C
Question: On dividing a number by 56, we get 28 as remainder. On dividing the same number by 8, what will be the remainder ?
A.2
B.3
C.4
D.5
Answer: C.4
Explanation: Number=56x+28 (∵ since the number gives 28 as remainder on dividing by 56)
=(7×8×x)+(3×8)+4
Hence, if the number is divided by 8, we will get 4 as remainder.
ANSWER:C
Question: A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
A.65 sec
B.89 sec
C.100 sec
D.150 sec
Answer: B.89 sec
Explanation: Explanation:
Speed =240/24 m/sec = 10 m/sec
Required time =(240+650 /10)sec=89sec
ANSWER IS B
Question: A car travels from point A to point B. The average speed of the car is 60 km/hr and it travels the first half of the trip at a speed of 50 km/hr. What is the speed of the car in the second half of the trip?
A.55
B.60
C.75
D.80
Answer: C.75
Explanation: Let D be the distance and let V be the speed in the second half.
The total time = T1 + T2
D/60 = D/100 + (D/2) / V
D/150 = D/2V and so V = 75 km/hr
The answer is C.
Question: Suppose that the numbers 1,2,4,8,16,32,64,128,256
are placed into the nine squares in such a way that
the product of the numbers appearing in any row,
column or diagonal is the same. What is the value
of this common product?
A.512
B.4096
C.8192
D.16384
Answer: B.4096
Explanation: The product of the numbers in all three rows is simply the product of the numbers
1,2,4,8,..,256 or, equivalently, of the numbers 20in zero,21in first,22in round,23in third ,..,28in eighth. The product is
2->0+1+2+...+8 = 236in thirty sixth
so correct answer B
Question: The number of boys in a class is (3/2) times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ?
A.A)48
B.B)44
C.C)42
D.D)40
Answer: D.D)40
Explanation: Explanation:
Let number of girls = x and number of boys = 1.5x.
Then, 1.5x + x = 2.5x = total number of students.
Thus, to find exact value of x, the total number of students must be divisible by 2.5.
Answer:D
Question: The amount of time that three people worked on a special project was in the ratio of 2 to 4 to 6. If the project took 144 hours, how many more hours did the hardest working person work than the person who worked the least?
A.47 hours
B.45 hours
C.48 hours
D.49 hours
Answer: C.48 hours
Explanation: Let the persons be A, B, C.
Hours worked:
A = 2*144/12 = 24 hours
B = 4*144/12 = 48 hours
C = 6*144/12 = 72 hours
C is the hardest worker and A worked for the least number of hours. So the difference is 72-24 = 48 hours.
Answer : C
Question: If a fair coin is flipped six times in a row, what is the probability that there will be at least one head and one tail?
A.3/4
B.11/12
C.15/16
D.31/32
Answer: D.31/32
Explanation: The number of possible outcomes is 2^6 = 64
There is one way to get no heads and one way to get no tails.
Thus there are 62 outcomes with at least one head and one tail.
P(at least one head and one tail) = 62/64 = 31/32
The answer is D.
Question: If 49x = 343^y, which of the following expresses x in terms of y?
A.(343/49)^y
B.y^(343/49)
C.y^(343-49)
D.7^(3y-2)
Answer: D.7^(3y-2)
Explanation: By exponential simplification. 49 = 7^2 and 343=7^3 therefore (7^2)x=(7^3)^y gives x=(7^3y)/(7^2) further simplified to x=(7^3y)(7^-2) which gives x=7^(3y-2) (because exponential is additive in multiplication. i.e. a^b*a^c=a^(b+c). Answer: D
Question: Find the smallest number which when divided by 13 and 15 leaves respective remainders of 2 and 4
A.187
B.197
C.184
D.219
Answer: C.184
Explanation: Let 'N' is the smallest number which divided by 13 and 15 leaves respective remainders of 2 and 4.
Required number = (LCM of 13 and 15) - (common difference of divisors and remainders) = (195) - (11) = 184.
ANSWER:C
Question: A train running at the speed of 54 km/hr crosses a pole in 7 seconds. Find the length of the train.
A.150 meter
B.105 meter
C.140 meter
D.135 meter
Answer: B.105 meter
Explanation: Explanation:
Speed = 54*(5/18) m/sec = 15 m/sec
Length of Train(Distance) = Speed * Time
=15*7=105 meter
Option B
Question: At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
A.12
B.11
C.10
D.9
Answer: A.12
Explanation: A
12
In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.
Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.
This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.
Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.
Question: There were two candidates in an election. Winner candidate received 70% of votes and won the election by 280 votes. Find the number of votes casted to the winning candidate?
A.228
B.744
C.490
D.199
Answer: C.490
Explanation: W = 70% L = 30%
70% - 30% = 40%
40% -------- 280
70% -------- ? => 280/40*70 = 490
Answer: C
Question: If the area of a circle decreases by 42%, then the radius of a circle decreases by
A.20%
B.18%
C.24%
D.64%
Answer: C.24%
Explanation: If area of a circle decreased by x % then the radius of a circle decreases by
(100−10√100−x)%=(100−10√100−42)%
= (100−10√58)%
= 100 - 76 = 24%
Answer C
Question: Two pipes X and Y can separately fill a cistern in 18 and 24 hours respectively. If they are turned on alternately for one hour each, how long will it take to fill the cistern?
A.20 1/2 hours
B.20 1/7 hours
C.22 1/2 hours
D.20 1/3 hours
Answer: A.20 1/2 hours
Explanation: 1/18 + 1/24 = 7/72
72/7 = 10 2/7
7/72 * 10 = 35/36 ----- 20 hours
WR = 1 – 35/36 = 1/36
1 h ----- 1/18
? ----- 1/36 = 1/2 hours
=> 20 1/2 hours
Answer: A
Question: How many arrangements of the letters of the word ‘BENGALI’ can be made if the vowels are to occupy only odd places.
A.334
B.576
C.776
D.297
Answer: B.576
Explanation: Explanation:
There are 7 letters in the word Bengali of these 3 are vowels and 4 consonants.
There are 4 odd places and 3 even places. 3 vowels can occupy 4 odd places in \inline {\color{Black}4P_3{}} ways and 4 constants can be arranged in \inline {\color{Black}4P_4{}} ways.
Number of words = \inline {\color{Black}4P_3{}} x \inline {\color{Black}4P_4{}}= 24 x 24 = 576
Answer: B
Question: The 15 homes in a new development are each to be sold for one of three different prices so that the developer receives an average (arithmetic mean) of $200,000 per home. If 4 of the homes are to be sold for $170,000 each and 5 are to be sold for $200,000 each, what will be the selling price of each of the remaining 10 homes?
A.$200,000
B.$212,000
C.$215,000
D.$220,000
Answer: B.$212,000
Explanation: IMO the answer has to be D.
5 houses are being sold for 200,000. 4 houses are being sold for $30,000 less, resulting in a loss of $120,000. To make the average selling price intact i.e. $200,000, the remaining 10 houses must be sold at such a profit that it compensates for the loss of 120,000. Hence 10x=120,000.
x=12,000.
The 10 houses are sold at $12,000 profit or at $212,000. (ANSWER B)
Question: Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?
A.23
B.23.5
C.24
D.24.5
Answer: D.24.5
Explanation: Let the present ages of sachin and rahul be 7x and 9x
sachin is younger than rahul in 7 years
So 9x-7x=7
2x=7
x=3.5
Sachin;s age= 7x= 7*3.5=24.5
answer :D