RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A, B and C, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $ 1170, what will be B's share of the earnings?
A.$390
B.$520
C.$1080
D.$1170
Answer: A.$390
Explanation: Explanatory Answer
A, B and C will share the amount of $1170 in the ratio of the amounts of work done by them.
As A takes 6 days to complete the job, if A works alone, A will be able to complete 1/6 th of the work in a day.
Similarly, B will complete 1/8th and C will complete 1/12th of the work.
So, the ratio of the work done by A : B : C when they work together will be equal to 1/6 : 1/8 : 1/12
Multiplying the numerator of all 3 fractions by 24, the LCM of 6, 8 and 12 will not change the relative values of the three values.
We get 24/6 : 24/8 : 24/12 = 4 : 3 : 2.
i.e., the ratio in which A : B : C will share $1170 will be 4 : 3 : 2.
Hence, B's share will be 3*1170/9 = 390.
correct choice is (A)
Question: What is the number of different committees of 4 women that can be selected from a group of 7 women?
A.a) 20
B.b) 35
C.c) 80
D.d) 120
Answer: B.b) 35
Explanation: 7c4 = 35
Answer is B.
Question: If there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if the total number of wheels is 54?
A.11
B.12
C.13
D.14
Answer: C.13
Explanation: four wheeler=13*4=52(max)
2 wheel=1
so no of 4 wheeler=13
ANSWER:C
Question: If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in?
A.20
B.21
C.30
D.9
Answer: D.9
Explanation: C = 1/4 - 1/12 â€“ 1/18 = 1/9 => 9 days
ANSWER D
Question: Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 2-cent stamps she could have bought ?
A. 5
B. 10
C. 7.5
D. 20
Answer: C. 7.5
Explanation: 2.65 = 0.05x + 0.25x + 2 * 0.10x + 0.02y
=> 2.65 = 0.30x + 0.20x + 0.02y
=> 265 = 50x + 2y
So Max value of 50x < 265 = 250
Hence y = 7.5
Answer - C
Question: A 340-liter solution of Kola is made from 88% water, 5% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 10 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar?
A.6%
B.7.5%.
C.9.2%
D.10.5%.
Answer: B.7.5%.
Explanation: Denominator:
340+10+3.2+6.8=360
Numerator:
340(1-.88-.05)+3.2
340(0.07)+3.2
23.8+3.2
27
Ratio:
27/360=3/40
Answer: B
Question: A train of length 150 metres takes 40.5 seconds to cross a tunnel of length 300 metres. What is the speed of the train in km/hr ?
A.13 33
B.26.67
C.40
D.66.67
Answer: C.40
Explanation: Solution
speed	=(150 + 300 / 40.5)m/sec
=(450/40.5x18/ 5) km/hr
= 40 km/hr
Answer C
Question: 48% of respondents to a survey consisted of those who used both M and N and those who used neither M nor N. 38% of respondents did not use M. 32% used N. What percent of respondents used only N?
A.19.5%
B.11%
C.20%
D.18.5%
Answer: B.11%
Explanation: From the question, we can summarize the information as follows:
N Not N
M X
Not M Ans y 38
32 100
Then we can set a system of 3 equations 3 unknowns described below:
X + Y = 48
X + Ans = 32
Y + Ans = 38
Sum up all three equations to get 2X + 2Y + 2Ans = 118
Divide both sides by 2 to get X + Y + Ans = 59
Replace X + Y with 48 to get 48 + Ans = 59
Substract 48 from both sides to get Ans = 59 - 48 = 11
The answer must be B.
Question: A farmer needs to plant seeds on a plot of land. She will plant 300 seeds in a rectangle in the field. The rectangle will have E seeds in a row and F seeds in a column. If the number of seeds in a row is no less than 10 and no more than 30, how many different combinations of rectangular shapes are possible?
A.5
B.6
C.7
D.8
Answer: B.6
Explanation: firstly factors of 300 = 1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300
the question says each row will have seeds no less than 10 and no more than 30,
therefore, we should be interested in the factors between 10 and 30 (inclusive)
10(in each row) * 30(number of columns) =300, similarly
12 * 25
15 * 20
20 * 15
25 * 12
30 * 10
total possibilities = 6
option B
Question: How many multiples of 7 are there between 14 and 252 ?
A.33
B.46
C.59
D.66
Answer: A.33
Explanation: It should be mentioned whether 14 and 252 are inclusive.
If 14 and 252 are inclusive, then the answer is (252-14)/7+1=35.
If 14 and 252 are NOT inclusive, then the answer is (245-21)/7+1=33.
Since OA is A, then we have NOT inclusive case.
Question: If a train, travelling at a speed of 90 kmph, crosses a pole in 5 sec, then the length of train is?
A.167 m
B.125 m
C.761 m
D.143 m
Answer: B.125 m
Explanation: D = 90 * 5/18 * 5
= 125 m
Answer:B
Question: If n=4p where p is a prime number greater than 2, how many different positive even divisors does n have, WITHOUT N VALUE?
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: We're told that N = 4P and that P is a prime number greater than 2. Let's TEST P = 3; so N = 12
The question now asks how many DIFFERENT positive EVEN divisors does 12 have, including 12?
12:
1,12
2,6
3,4
How many of these divisors are EVEN? 2, 4, 6, …..3 even divisors.
ANSWER:C
Question: Ritesh and Co. generated revenue of Rs. 1,600 in 2006. This was 12.5% of its gross revenue. In 2007, the gross revenue grew by Rs. 2,500. What is the percentage increase in the revenue in 2007?
A.12.5%
B.19.53%
C.25%
D.50%
Answer: B.19.53%
Explanation: Explanation :
Given, Ritesh and Co. generated revenue of Rs. 1,600 in 2006 and that this was 12.5% of the gross revenue.
Hence, if 1600 is 12.5% of the revenue, then 100% (gross revenue) is:
=>(100/12.5)×1600.
=>12,800.
Hence, the total revenue by end of 2007 is Rs. 12,800. In 2006, revenue grew by Rs. 2500. This is a growth of:
=>(2500/12800)×100.
=>19.53%.
Answer : B
Question: (112 x 54) = ?
A.70000
B.71000
C.72000
D.73000
Answer: A.70000
Explanation: (112 x 54) = 112 x 10 4	=	112 x 104	=	1120000	= 70000
2	24	16
A)
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
A.1.8
B.1.6
C.1.3
D.1.5
Answer: D.1.5
Explanation: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer: D
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 2/7. What is the probability that they agree in stating the same fact?
A.16/35
B.16/37
C.16/39
D.16/33
Answer: A.16/35
Explanation: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 2/7 + 2/5 * 5/7
= 16/35
Answer:A
Question: p:q = 7:6 , q:r = 4 : 7 , p:q:r = ?
A.28 : 24 : 42
B.28 : 24 : 40
C.28 : 24 : 52
D.28 : 24 : 41
Answer: A.28 : 24 : 42
Explanation: p:q = 7:6 ,
q:r = 4 : 7
p:q:r =28 : 24 : 42
Answer : A
Question: Two partners (Moses and Norris) invested Rs 5000 and Rs.12000 in a business. Moses runs the business while Norris is a sleeping partner in the business. Moses receives 4% of the profit for managing the business the rest is divided in proportion of their capitals. Out of a total profit of Rs.5500, how much did Moses receive?
A.1772.95
B.1537.6
C.1877.6
D.1937.6
Answer: A.1772.95
Explanation: ratio of their investments Rs.5000:12000=5:12
4% of the profit for managing the business =4/100*5500=220
remaining profit=5500-220=5280
share profit in ratio of investment 5280/17 =310.59
Moses's ratio share=5*310.59=1552.95
total money Moses collects=1552.95+220=1772.95
Answer: A
Question: A person buys an article at $500. At what price should he sell the article so as to make a profit of 20%?
A.560
B.449
C.600
D.740
Answer: C.600
Explanation: C
600
Cost price = $500
profit = 20% of 500 = $100
Selling price = Cost price + Profit
= 500 + 100 = 600
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. What is the present age of the husband?
A.30
B.40 years
C.20
D.50
Answer: B.40 years
Explanation: Let the present age of the husband = h
Present age of the wife = w
Present age of the child = c
3 years ago, average age of husband, wife and their child = 27
=> Sum of age of husband, wife and their child before 3 years = 3 × 27 = 81
=> (h-3) + (w-3) + (c-3) = 81
=> h + w + c = 81 + 9 = 90 --- equation(1)
5 years ago, average age of wife and child = 20
=> Sum of age of wife and child before 5 years = 2 × 20 = 40
=> (w-5) + (c-5) = 40
=> w + c = 40 + 10 = 50 --- equation(2)
Substituting equation(2) in equation(1)
=> h + 50 = 90
=> h = 90 - 50 = 40
i.e., Present age of the husband = 40
Answer is B.
Question: A man divides $6800 Among 4 Sons, 4 Daughters and 2 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive?
A.A)$200
B.B)$1000
C.C)$800
D.D)$1200
Answer: C.C)$800
Explanation: Let the share of each nephews be $X.
Then, share of each daughter=$4X, share of each son= $5X.
So, 4*4X+4*4X+2*X=6800
16X+16X+2X=8600
34X=6800, X=200.
Daughter receives four times of nephew so 4 * 200 = 800.
So Each Daughter receives $800. answer is option C) $800.
Question: A , B , and C started a partnership business by investing $45,000 , $63,000 , and $72,000 respectively. At the end of the year, the profit was distributed among them. If C's share of profit is $16,000, what is the total profit?
A.$28,000
B.$32,000
C.$36,000
D.$40,000
Answer: D.$40,000
Explanation: A:B:C = 45000:63000:72000 which is a ratio of 5:7:8.
Let the total profit be x.
x * 8/20 = 16000
x = 16000*20/8 = 40,000.
The answer is D.
Question: A and B finish the job in 15 days.while A,B and C can finish it in 11 days . C alone will finish the job in
A.41.25 days
B.30.25 days
C.60.25 days
D.71.25 days
Answer: A.41.25 days
Explanation: Explanation:
11= (15 * x)/(15 + x)
165+11x=15x
4x=165
X=41.25
Answer: Option A
Question: Kim purchased n items from a catalog for $8 each. Postage and handling charges consisted of $2 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?
A.8n + 2
B.9n + 1
C.9n + 2
D.9n + 3
Answer: B.9n + 1
Explanation: its C
n items for $8 each
total price $8n
postage and handling of $3 for 1st item and $1 for the rest
total postage and handling = $ [2+ (n-1)]
= $ n+1
total cost
8n+n+1 = 9n+1
B
Question: Which of the following is satisfied with |x-4|+|x-3|<7?
A.0<x<7
B.2<x<5
C.2.5<x<4.5
D.2.5<x<4
Answer: A.0<x<7
Explanation: --> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<7 -> |x-4+x-3|<7 -> |2x-7|<7, -7<2x-7<7, 0<2x<14, 0<x<7
Therefore, the answer is A.
Question: A certain restaurant offers 5 different salads, 4 different main courses, and 7 different desserts. If customers choose one salad, one main course, and two different desserts for their meal, how many different meals are possible?
A.300
B.340
C.380
D.420
Answer: D.420
Explanation: The number of possible choices for desserts is 7C2 = 21
The number of possible meals is 5*4*21 = 420
The answer is D.
Question: find last digits of (1023^3923)+(3081^3921)
A.8
B.9
C.10
D.11
Answer: A.8
Explanation: we have (1023^3923)+(3081^3921)
(3923/4)=4n+3 (3921/4)=4n+1 where n can be any integer
now through cyclicity we can obtain or you can learn the chart from arun sharma
number ending in 4n+1 4n+2 4n+3 4n
1 1 1 1 1
2 2 4 8 6
3 3 9 7 1
in this way 7+1=8 is the unit's place digit
ANSWER:A
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
A.3 1/5 Kilometre
B.2 1/5 Km
C.3 Km
D.4 Km
Answer: A.3 1/5 Kilometre
Explanation: Formula = S1*S2/ S2-S1 * T1+T2/60
= 4*6/2 * 16/6
= 24/2 * 16/60
= 8 * 2/5
= 16/5 = 3 1/5 Km
A)
Question: A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 6 inches wide on each side, the total area would have been (M + 200) square inches. What is the perimeter of the photograph, in inches?
A.8
B.12
C.16
D.20
Answer: B.12
Explanation: Let x and y be the width and length of the photograph.
(x+2)(y+2)=M and so (1) xy + 2x + 2y + 4 = M
(x+12)(y+12)=M and so (2) xy + 12x + 12y + 144 = M+200
Let's subtract equation (1) from equation (2).
10x + 10y + 140 = 200
2x + 2y = 12, which is the perimeter of the photograph.
The answer is B.
Question: Find the one which does not belong to that group ?
A.16
B.28
C.36
D.64
Answer: C.36
Explanation: Explanation:
16, 36, 64 and 4 are perfect squares but not 28.
ANSWER IS C
Question: The average of 25 results is 18. The average of first 12 of those is 14 and the average of last 12 is 17. What is the 13th result?
A.74
B.75
C.69
D.78
Answer: D.78
Explanation: Solution: Sum of 1st 12 results = 12*14
Sum of last 12 results = 12*17
13th result = x (let)
Now,
12*14+12*17+x = 25*18
Or, x = 78.
Answer: Option D
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is -.
A.0.4869
B.0.5904
C.0.6234
D.0.5834
Answer: B.0.5904
Explanation: Explanation:
P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
ANSWER IS B
Question: Wendy begins sanding a kitchen floor by herself and works for 8 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself?
A.544/49 hours
B.3/20 hours
C.20/3 hours
D.80/9 hours
Answer: A.544/49 hours
Explanation: Let Wendy finishes sanding the floor alone in W hours while B be the hours for Bruce.
Thus in 1 hour Wendy finishes 1/w of the work while Bruce finishes 1/B of the work.
If wendy works for 8 hours and is then joined by Bruce to finish the work in 2 more hours,
8/W + 2/W+2/B = 1 (1 denotes the total amount of work)
10/W + 2/B =1 and given B =20 hours.
Thus W = 544/49 hours , A is the correct answer.
Question: In what time a sum of money double itself at 6% per annum simple interest?
A.33 1/8%
B.16 2/3%
C.33 7/3%
D.32 1/3%
Answer: B.16 2/3%
Explanation: P = (P*6*R)/100
R = 16 2/3%
Answer: B
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 172 votes. Find the total number of valid votes?
A.430
B.437
C.435
D.431
Answer: A.430
Explanation: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 172 => 4x/10 = 172
=> 4x = 1720 => x = 430.
Answer: A
Question: Two MBA admissions committees are to be formed randomly from 6 second year MBAs with 3 members each. What is the probability that Jane will be on the same committee as Albert?
A.12%
B.20%
C.33%
D.40%
Answer: D.40%
Explanation: Total number of ways to choose 3 member committee - 6C3=(6!/3!3!)=20
No. of ways Albert n Jane are in same committee:- (4C1 * 2)= 8
Probability= (8/20) *100 =40%.
ANS::D
Question: 6 men and 2 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ratio
A.1:1
B.1:3
C.2:1
D.2:3
Answer: A.1:1
Explanation: Explanation:
Let 1 man 1 day work = x
1 boy 1 day work = y
then 6x + 2y = 4(x+y)
=> 2x = 2y
=> x/y = 1/1
=> x:y = 1:1
Option A
Question: What is the least integer greater than –3+0.5?
A.–2
B.–1
C.0
D.1
Answer: A.–2
Explanation: This question is just about doing careful Arithmetic and remembering what makes a numberbiggerorsmallercompared to another number.
First, let's take care of the Arithmetic:
(-3) + (0.5) = -2.5
On a number line, since we're ADDING +.5 to a number, the total moves to the RIGHT (so we're moving from -3 to -2.5).
Next, the question asks for the LEAST integer that is GREATER than -2.5
Again, we can use a number line. Numbers become greater as you move to the RIGHT. The first INTEGER to the right of -2.5 is -2.
Final Answer:
A
Question: A certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts, by weight. What is the number of pounds of almonds in 280 pounds of the mixture ?
A. 200
B. 84
C. 40
D. 28
Answer: A. 200
Explanation: Almonds : Walnuts = 5 : 2
Total mixture has 7 parts
In a 280 pound mixture, Almonds are 5/7 (total mixture)
= 5/7 * 280 = 200 pounds
Answer (A)
Question: If A speaks the truth 65% of the times, B speaks the truth 60% of the times. What is the probability that they tell the truth at the same time
A.0.39
B.0.48
C.0.41
D.0.482
Answer: A.0.39
Explanation: Explanation:
Probability that A speaks truth is 65/100 = 0.65
Probability that B speaks truth is 60/100 = 0.6
Since both A and B are independent of each other
So probability of A intersection B is P(A) × P(B) =0.65 × 0.6 = 0.39
Answer: A
Question: A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 25%, what should be the sale price of the mixed tea?
A.23.75
B.22
C.20
D.19.2
Answer: C.20
Explanation: C.P. of mixture = 80×15+20×20 /80+20=16
∴ S.P. = (100+25)/100×16=20
Answer C
Question: During a certain two-week period, 58 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 5 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period?
A.10A
B.9A
C.8 2/3A
D.11A
Answer: C.8 2/3A
Explanation: Total movies = 100.
Comedies = 58.
Action + Drama = 42. Since there were 5 times as many dramas as action movies, then Action + 5*Action = 42 --> Action = A = 7.
Comedies = = 8 2/3A
Answer: C.
Question: If a 3-member subcommittee is to be formed from a certain 8-member committee, how many different such subcommittee are possible?
A.6
B.18
C.40
D.108
Answer: C.40
Explanation: Another way:
1st member can be selected in 8 ways
2nd can be selected in 6 ways
3rd can be selected in 5 ways
So total ways : 240
But to avoid the similar scenarios 240/3!=40
C
Question: For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+4 and 7*+7, inclusive ?
A.1
B.0
C.2
D.3
Answer: B.0
Explanation: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 7* + 4 = 7! + 4 and 7* + 7 = 7! + 7.
Now, notice that , we can factor out 4 our of 7! + 4 so it cannot be a prime number, ... The same way for all numbers between 7! + 4 and 7! +7, inclusive. Which means that there are no primes in this range.
Answer: B
Question: There are 5 burglars and once went to a bakery to rob it obviously. The first guy ate 1/2 of the total bread and 1/2 of the bread. The second guy ate 1/2 of the remaining and 1/2 of the bread. The third guy ,fourth guy and fifth guy did the same. After fifth guy there is no bread left out. How many bread are there?
A.30
B.31
C.32
D.33
Answer: B.31
Explanation: (1/2 + 1/2) = 1
2(1 + 1/2) = 3
2(3 + 1/2) = 7
2(7 + 1/2) = 15
2(15 + 1/2) = 31
ANSWER:B
Question: If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?
A.4/5 km
B.4/8 km
C.2/5 km
D.4/6 km
Answer: A.4/5 km
Explanation: x/3 – x/4 = 4/60
x = 4/5 km
Answer: A
Question: A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.21,000 earned at the end of 2years from the startingof the business?
A.s. 5,000
B.s. 5,500
C.s. 5,700
D.s. 6,300
Answer: D.s. 6,300
Explanation: A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.
B's share = Rs. 21000 x	3/10	= Rs. 6,300.
D
Question: In a group of dogs and people, the number of legs was 28 more than twice the number of
heads. How many dogs were there? [Assume none of the people or dogs is missing a leg.]
A.4
B.7
C.12
D.14
Answer: D.14
Explanation: If there were only people, there would be exactly twice the number of legs as
heads. Each dog contributes two extra legs over and above this number. So 28 extra legs
means 14 dogs.
correct answer D
Question: what smallest no. should subtracted from 5000,so that remainder completely divisible from 19?
A.3
B.4
C.5
D.6
Answer: A.3
Explanation: if 5000 is divided by 19 then remainder is 3.
no. should subtracted is 3.
answer A
Question: A and B start from Opladen and Cologne respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between Opladen and Cologne, A and B proceed to their destinations of Cologne and Opladen respectively. A reaches Cologne 40 minutes after the two meet and B reaches Opladen 60 minutes after their meeting. How long did A take to cover the distance between Opladen and Cologne?
A.1 hour
B.1 hour 20 minutes
C.2 hours 30 minutes
D.1 hour 40 minutes
Answer: B.1 hour 20 minutes
Explanation: v1 and V2 are speeds.
v1.t /60 = v2
v2.t/40 = v1
v1/v2 = 3/2
which train A would 60. 2/3 mins to cover the same distance
40 + 40 = 80 mins (ANS B)
Question: If a mixture is 1⁄7 alcohol by volume and 2⁄7 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture?
A.4/2
B.3/2
C.1/2
D.5/2
Answer: C.1/2
Explanation: Should be a sub-600 level Q..
volume= {1/7}/{2/7}=1/2
C
Question: If 1 + x^4 + x^3 + x^2 + x = 80, then the average (arithmetic mean)R of x, x^2, x^3, x^4 and x^5 is equal to which of the following?
A.12x
B.13x
C.14x
D.16x
Answer: D.16x
Explanation: 1 + x^4 + x^3 + x^2 + x = 81
i.e. 1 +x+ x^2+ x^3+ x^4 = 81
x+ x^2+ x^3+ x^4 = 80
x(1 +x+ x^2+ x^3) = 80
x(81-x^4) = 80
81x - x^5 = 80
x^5 = 81x -80
Now x+ x^2+ x^3+ x^4+ x^5 = 80 + 81x -80 = 81x
Average of R{x, x^2, x^3, x^4, x^5} = 81x/5 ~ 16x
AnswerD
Question: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
A.53
B.57
C.63
D.65
Answer: C.63
Explanation: Explanation:
We need to select 5 men from 7 men and 2 women from 3 women.
Number of ways to do this
= 7C5 × 3C2
= 7C2 × 3C1 [∵ nCr = nC(n-r)]
=
7
×
6
2
×
1
×
3
=
21
×
3
=63
C)
Question: John invests $x at the semi-annual constant compounded rate of 2 percent and also does $5,000 at the quarterly constant compounded rate of 4 percent. If the interests are the same after 1 year, what is the value of x??
A.10000
B.10100.5
C.20000
D.15000
Answer: B.10100.5
Explanation: A = P(1+r/n)^nt
A= total amount accrued
P = principal deposited
r = rate of interest in decimal form
n = number of times per year, interest compounded
t = time in number of years.
.
x(1+0.02/2)^2 - x = 5,000(1+0.04/4)^4 - 5,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal)
=> x[(1.01)^2 - 1] = 5,000[(1.01)^4 - 1]
=> x[(1.01)^2 - 1] = 5,000[(1.01)^2+1][(1.01)^2-1] --> Using a^2-b^2 = a+b X a-b formula and cancel common expression on both sides
=> x = 5,000(1.0201+1) =10,100.5
Hence answer is B.
Question: An design manager has 10patterns of chairs & 8patterns of tables. In how many ways can he make a pair of table & chair?
A.20
B.40
C.80
D.90
Answer: C.80
Explanation: He has has ten patterns of chairs and eight patterns of tables
Hence, A chair can be arranged in 10 ways and
A table can be arranged in 8 ways
Hence one chair and one table can be arranged in 10 x 8 ways = 80 ways
C
Question: The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?
A.40
B.60
C.20
D.10
Answer: B.60
Explanation: Let A = 2k, B = 3k and C = 5k.
A's new salary = 115/100 of 2k = (115/100) 2k = 23k/10
B's new salary = 110/100 of 3k = (110/100) 3k = 33k/10
C's new salary = 120/100 of 5k = (120/100) 5k = 6k
Therefore, New ratio	(23k/10) : (33k/10): 6k)
= 23 : 33 : 60
Answer is B.