RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A car moves at 80 km/hr. What is the speed of the car in meters per second ?
A.20 2/9m sec
B.22 2/9m sec
C.24 2/9m sec
D.26 2/9m sec
Answer: B.22 2/9m sec
Explanation: Explanation:
Speed=(80∗5/18)m/sec
=200/9m/sec
=22 2/9msec
Option B
Question: If n is the smallest integer such that 432 times n is the square of an integer, what is the value of n?
A.2
B.3
C.6
D.12
Answer: B.3
Explanation: The prime factorization of a square has to have even powers of all its prime factors. If the original number has a factor, say of 7, then when it’s squared, the square will have a factor of 7^2. Another way to say that is: any positive integer all of whose prime factors have even powers must be a perfect square of some other integer. Look at the prime factorization of 432
432 = (2^4)*(3^3)
The factor of 2 already has an even power —- that’s all set. The factor of 3 currently has an odd power. If n = 3, then 432*n would have an even power of 2 and an even power of 3; therefore, it would be a perfect square. Thus, n = 3 is a choice that makes 432*n a perfect square.
Answer: B.
Question: If 15% of A is the same as 20% of B, then A : B is :
A.3 : 4
B.4 : 3
C.17 : 16
D.16 : 17
Answer: B.4 : 3
Explanation: 15% of A I= 20 % of B
15A/100 = 20B/100
=4/3 = 4:3
ANSWER:B
Question: A man saves Rs 300 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years.
A.Rs 962
B.Rs 962.01
C.Rs 662.02
D.Rs 993.03
Answer: D.Rs 993.03
Explanation: Explanation:
=[300(21/20Ã—21/20Ã—21/20)+300(21/20Ã—21/20)+300(21/20)]=993.03
Option D
Question: In May Mrs Lee's earnings were 70 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?
A.64%
B.68%
C.72%
D.74%
Answer: D.74%
Explanation: Let in May Lee family's total income =100
in May Mrs Lee's income =70
in May rest of the family's income = 30
In june Mrs Lees income = 70*120/100 = 84
In june Total income = 84+ 30 = 114
% of Mrs Lee's income =84/114 =73.68
(D)
Question: The average of 45 results is 8. The average of first 22 of them is 15 and that of last 22 is 20. Find the 23 result?
A.600
B.470
C.750
D.650
Answer: B.470
Explanation: 23th result = sum of 45results - sum of 44 results
8*45-15*22+20*22 = 360-330+440 = 470
Answer is B
Question: If the area of circle is 616 sq cm then its circumference?
A.78 m
B.88 m
C.75 m
D.70 m
Answer: B.88 m
Explanation: Area of Circle = ∏r2
= 22/7(r2) = 616
= r2 = (616)(7/22)
= r = 14
Circumference = 2∏r = (2)(22/7)(14)
= 88 m
Answer: B
Question: A certain computer manufacturing firm last year produced 82 percent of its computers using parts made by its subsidiary company. If the remaining 10,890 computers were produced using parts purchased from another parts manufacturer, how many computers were produced by the computer manufacturing firm altogether?
A.60000
B.60100
C.60500
D.72000
Answer: C.60500
Explanation: 82% parts used of subsidary company, so 18% parts used of other companies.
Now, 18% parts = 10,890 computers
So, 1% parts = 10,890/18
Or, 100% parts = 60,500 computers.
Hence answer is (C)
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 10% 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.20%
B.21%
C.21.33%
D.22.109%
Answer: B.21%
Explanation: Lets say the indicated weight is x for $10
but the trader actually get 1.1x for $10
now he tells to the customer that its 1.1(1.1x) = 1.21x and charges the price accordingly i.e. 1.21x * 10/ x = 12.1
so profit % = (12.1-10)/ 10 = 0.21 = 21%
ANSWER:B
Question: In N is a positive integer less than 200, and 18N/60 is an integer, then N has how many different positive prime factors?
A.2
B.3
C.5
D.6
Answer: A.2
Explanation: (A).
18n/60 must be an integer. => 3n/10 must be an integer. Hence n must be a multiple of 2*5.
=> n has 2 different prime integers .
Question: A Bus travels first half distance between two places with a speed of 40 kmph and the rest half distance with a speed of 60 kmph. The average speed of the Bus is ?
A.48 kmph
B.78 kmph
C.28 kmph
D.18 kmph
Answer: A.48 kmph
Explanation: Explanation:
we know that speed = distance traveled/time taken
let the total distance traveled by the car is 2x km.
then time taken by it to cover first half is hour.
and for second half is hour.
Then average speed= total distance travelled / total time taken.
i.e.
=>
= 48 kmph.
Answer: A
Question: Mary works in a restaurant a maximum of 40 hours. For the first 20 hours, she is paid $8 per hour. For each overtime hour, she is paid at a rate which is 25% higher than her regular rate. How much Mary can earn in a week?
A.300
B.420
C.360
D.320
Answer: C.360
Explanation: Mary receives $8(20)=$160 for the first 20 hours.
For the 20 overtime hours, she receives $8(0.25) +$8 = $10 per hour, that is $10(20)=$200.
The total amount is $160+$200 = $360
Answer C 360.
Question: Of the four numbers, whose average is 75, the first is one-fourth of the sum of the last three. The first number is ?
A.60
B.29
C.11
D.48
Answer: A.60
Explanation: Explanation:
Let the first number be x,
Then, sum of the four numbers = x + 4x = 5x.
so, 5x/4 = 75 or x = (75 * 4) / 5 = 60
Answer: A
Question: A sum of money becomes triple itself in 5 years at simple interest. How many years will it become six times at the same rate?
A.12 ½ years
B.62 ½ years
C.18 ½ years
D.72 ½ years
Answer: A.12 ½ years
Explanation: 100 ---- 200 ---- 5
200 ---- 5
100 ---- 2 1/2
------------------
600 ---- 12 ½ years
Answer:A
Question: If |a+b|=|a-b|, then a*b must be equal to:
A.1
B.-1
C.0
D.2
Answer: C.0
Explanation: so, let b≠0b≠0
Distance of aa from bb, equals the distance of aa from -bb
Draw this on a number line, aa must equal zero
same logic holds for a≠0a≠0
So either aa or bb = 0, ab=0ab=0
or just solve using our normal absolute value method, two cases:
(a+b)=(a−b)(a+b)=(a−b)
b=0
−(a+b)=(a−b)−(a+b)=(a−b)
−a−b=a−b−a−b=a−b
a=0
so ab=0
ANSWER:C
Question: A type Q machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type Q machines and 3 type B machines working together and independently to complete the job?
A.1/5
B.29/35
C.5/6
D.35/29
Answer: D.35/29
Explanation: now D should be the answer.
Q need 5 hours to complete
and B needs 7 hours to compete
so 2Q + 3B will complete 2/5 + 3/7 or 29/35 portion of the job in 1 hour
so the whole job will take 35/29 hours....=D
Question: Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 00,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance.
What is the distance traveled by each tyre?
A.70,000
B.60,000
C.80,000
D.90,000
Answer: C.80,000
Explanation: C
80,000.
The distance traveled by each tyre:
4/5 * 1, 00, 000km = 80,000 km.
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
A.25200.
B.26200
C.28000
D.29000
Answer: A.25200.
Explanation: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
=7 x 6 x 5/3 x 2 x 1 x	4 x 3	/2 x 1
= 210.
Number of groups, each having 3 consonants and 2 vowels = 210.
Each group contains 5 letters.
Number of ways of arranging
5 letters among themselves	= 5!
= 5 x 4 x 3 x 2 x 1
= 120.
Required number of ways = (210 x 120) = 25200.
Answer: A
Question: Alex deposited x dollars into a new account that earned 10 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?
A.w/(1+1.08)
B.w/(1.08+1.16)
C.w/(1.16+1.24)
D.w/(1.10+1.10^2)
Answer: D.w/(1.10+1.10^2)
Explanation: Account at the end of the first year would be 1.10x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.10x+x) dollars. Account at the end of the second year would be (1.10x+x)*1.10=w --> x(1.10^2+1.10)=w --> x=w/(1.10+1.10^2).
Answer: D.
Question: If UVW= 1 , WXY = 0 , and UWX = 0, which of the following must be zero?
A.U
B.V
C.W
D.X
Answer: D.X
Explanation: UVW= 1 which means neither U / V/ W is 0
W x XY = 0 , we know W is not 0 from above hence either X or Y must be 0.
X x U x W = 0, we know from first expression that U and W are not 0 hence X =0.
OPTION D
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
A.50
B.120
C.100
D.60
Answer: C.100
Explanation: Explanation:
Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Answer:C
Question: 1398 x 1398 = ?
A.1624404
B.1851404
C.1951404
D.1954404
Answer: D.1954404
Explanation: Explanation :
1398 x 1398
= (1398)2
= (1400 - 2)2
= 14002 - (2 × 1400 × 2) + 22
= 1960000 - 5600 + 4
= 1954404. Answer : Option D
Question: Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $100, what was the final price of the sweater?
A.$25.75
B.$52.5
C.$15.75
D.$ 45.75
Answer: B.$52.5
Explanation: The price with 30% off
100 - 30% of 100 = 100 - (30 / 100) *100 = 70
The price with another 25% off
70 - 25% of 70 = 70 - (25/100)* 70 = $52.5
correct answer B
Question: If the average marks of three batches of 55, 60 and 45 students respectively is 45, 55, 60, then the average marks of all the students is:
A.53.33
B.54.68
C.52.97
D.56
Answer: C.52.97
Explanation: Explanation:
Required average = (55 × 45 + 60 × 55 + 45 × 60/55 + 60 + 45)
= (2475 + 3300 + 2700/160)
= 8475/160
= 52.97
Answer: C
Question: The annual income of Puja, Hema and Jaya taken together is Rs. 46,000. Puja spends 70 % of income, Hema spends 80 % of her income and Jaya spends 92 % of her income. If their annual savings are 15 : 11 : 10, find the annual saving of Puja?
A.10, 000 /-
B.12, 000 /-
C.17, 500 / -
D.25, 000 /-
Answer: A.10, 000 /-
Explanation: EXPLANATION:
Suppose income of Puja, Hema and Jaya are Rs A, Rs B and Rs C.
Annual income given is Rs 46, 000
If 70 % income is spent by Puja, then that means she saves 30 % (0.3). Similarly, Hema saves 20 % (0.2) and Jaya saves 8 % (0.08)
Given ratio of their annual savings are 15 : 11 : 10
(0.3A)/15	=	(0.2B)/11	=	(0.08C)/10	=	A/50	=	B/55	=	C/125
=	A/10	=	B/11	=	C/25	=	(A + B + C)/(10+11+25)	=	46000/46----(Since, A+B+C=46000)
=1000
From this equation, we can
A = 1000 x 10 = 10,000
B = 1000 x 11 = 11,000
C = 1000 x 25 = 25000
ANSWER IS A
Question: Three numbers are in the ratio 4 : 5 : 6 and their average is 30 . The largest number is:
A.28
B.32
C.36
D.42
Answer: C.36
Explanation: Explanation:
Let the numbers be 4x, 5x and 6x. Therefore,
(4x+5x+6x)/3 = 30
15x = 90
x = 6
Largest number = 6x = 36.
ANSWER C
Question: A local restaurant recently renovated its dining space, purchasing new tables and chairs to use in addition to the original tables and chairs. The new tables each seat six customers, while the original tables each seat four customers. Altogether, the restaurant now has 40 tables and is capable of seating 208 customers. How many more new tables than original tables does the restaurant have?
A.8
B.12
C.16
D.20
Answer: A.8
Explanation: If all the tables seated 4, the number of customers could be 4*40 = 160.
208-160 = 48, so 48/2 = 24 tables must be new tables seating 6 people.
The number of tables seating 4 people is 40-24 = 16.
The number of new tables is 24-16 = 8 more than the number of old tables.
The answer is A.
Question: What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?
A.814
B.820
C.840
D.844
Answer: A.814
Explanation: Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) cm2.
Required number of tiles =1517 x 902/(41^2)= 814.
ANSWER:A
Question: In a consumer survey, 90% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
A.5
B.10
C.15
D.20
Answer: A.5
Explanation: pick 100 and x= all set with exactly two items
90=30+50+20 -(X)-10
X=0
so the answer is 0+5/100= 5%
Answer A
Question: Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 30, the number of points equidistant from all the 3 lines is
A.1
B.3
C.4
D.0
Answer: C.4
Explanation: 4 points are possible in which 1 point is the incentre of the circle and other 3 are excentres
ANSWER:C
Question: If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 2 years would be
A.(1.5)^4
B.4(1.5)
C.(1.05)^2
D.1 + (0.05)^4
Answer: C.(1.05)^2
Explanation: f John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 2 years would be
1(1.05)^2
1.05^2
C. (1.05)^2
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
A.6 kmph
B.9 kmph
C.3 kmph
D.8 kmph
Answer: D.8 kmph
Explanation: Speed downstream = d/t = 85/(2 1/2)
= 34 kmph
Speed upstream = d/t = 45/(2 1/2)
= 18 kmph
The speed of the stream = (34 - 18)/2
= 8 kmph
Answer:D
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 138 m length?
A.82.1 sec.
B.12.4 sec
C.19.1 sec.
D.17.1 sec.
Answer: B.12.4 sec
Explanation: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 138 = 248 m.
Required time = 248/20 = 12.4 sec.
Answer: B
Question: There are 44 students in a hostel, due to the administration, 15 new students has joined. The expense of the mess increase by Rs. 33 per day. While the average expenditure per head diminished by Rs. 3, what was the original expenditure of the mess ?
A.Rs. 618
B.Rs. 612
C.Rs. 622
D.Rs. 616
Answer: D.Rs. 616
Explanation: Explanation:
Let the average expenditure per head be Rs. p
Now, the expenditure of the mess for old students is Rs. 44p
After joining of 15 more students, the average expenditure per head is decreased by Rs. 3 => p-3
Here, given the expenditure of the mess for (44+15 = 59) students is increased by Rs. 33
Therefore, 59(p-3) = 44p + 33
59p - 177 = 44p + 33
15p = 210
=> p = 14
Thus, the expenditure of the mess for old students is Rs. 44p = 44 x 14 = Rs. 616.
Answer: D
Question: Look at this series: 97, 97, 97, 81, 81, 81, 65, 65, 65 ... What number should come next?
A.45
B.33
C.43
D.38
Answer: B.33
Explanation: Explanation:
In this series, each number is repeated, then 16 is subtracted to arrive at the next number.
Answer: Option B
Question: 1/5 , ½ , 1/3 , 2/5 ,1, 2/3, 3/5, 1 ½ ,1, 4/5,?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: 1/5 , 1/2 , 1/3
1/5*2 , 1/2*2 ,1/3*2
1/5*3 , 1/2*3 ,1/3*3
1/5*4 , 1/2*4 ,1/3*4
so
1/5 , ½ , 1/3 , 2/5 ,1, 2/3, 3/5, 1 ½ ,1, 4/5,2
ANSWER:B
Question: In a clothing store, there are six different colored neckties ( orange, yellow, green, blue, and indigo) and five different colored shirts ( orange, yellow, green, blue, and indigo) that must be packed into boxes for gifts. If each box can only fit one necktie and one shirt, what is the probability that all of the boxes will contain a necktie and a shirt of the same color?
A.719/720
B.1/120
C.2/233
D.3/543
Answer: B.1/120
Explanation: 5 ties and 5 shirts...
red tie can take any of 5 shirts..
orange can take any of the remaining 4 shirts
yellow any of remaining 3..
and so on till last indigo chooses the 1 remaining..
Total ways= 5*4*3*2*1= 120
out of this 120, ONLY 1 way will have same colour tie and shirt..
prob = 1/120
B
Question: A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio?
A.16:18
B.16:13
C.16:15
D.16:12
Answer: C.16:15
Explanation: For an income of Re. 1 in 9% stock at 96, investment
= Rs. 96/9 = Rs.32/3
For an income Re. 1 in 12% stock at 120, investment
= Rs. 120/12 = Rs. 10.
Ratio of investments =(32/3) : 10
= 32 : 30 = 16 : 15
Answer: C
Question: The length of the bridge, which a train 140 m long and traveling at 45 km/hr can cross in 30 sec is?
A.377
B.367
C.235
D.245
Answer: C.235
Explanation: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (140 + x)/30 = 25/2
x = 235 m.
Answer: C
Question: Find the one which does not belong to that group ?
A.372
B.630
C.287
D.192
Answer: B.630
Explanation: Explanation:
30 = 33 + 3, 630 = 54 + 5, 10 = 23 + 2, 520 = 83 + 8 and 130 = 53 + 5.
30, 10, 130 and 520 can be expressed as n3 + n but not 630.
Answer:B
Question: There are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 50% play football, how many play both?
A.120
B.150
C.200
D.180
Answer: B.150
Explanation: n(A) = 75*600/100 = 450
n(B) = 50*600/100 = 300
n(AUB) = 600
n(AnB) = 450+300-600 = 150
Answer is B
Question: One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number?
A.8
B.7
C.1
D.9
Answer: D.9
Explanation: Explanation:
x/2 â€“ x/3 = 6 => x =6
3 + 6 = 9
Answer: D
Question: A and B are working on an assignment. A takes 6 hours to type 32 pages on a computer, while B takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
A.2 hours
B.5 hours
C.6 hours
D.8 hours
Answer: D.8 hours
Explanation: Number of pages typed by A in one hour=32/6=16/3
Number of pages typed by B in one hour=40/5=8
Number of pages typed by both in one hour=((16/3)+8)=40/3
Time taken by both to type 110 pages=110*3/40=8 hours.
Answer : D.
Question: In an election between two candidates, 75 % of the voters cast their votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes
A.16800
B.15800
C.16700
D.15700
Answer: A.16800
Explanation: Explanation:
Let the total number of votes enrolled are x.
Number of votes cast = 75% of x
Valid votes = 98% of 75% of x
Now, as 9261 is the 75% of valid casted votes so,
75% of 98% of 75% of x = 9261 [imporant]
=>75×98×75×x / 100×100×100=9261=>x=16800
Option A
Question: Of the 13 employees in a certain department, 1 has an annual salary of 38,000, 2 have an annual salary of 45,500 each, 2 have an annual salary of 42,500 each, 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each. What is the median annual salary for the 13 employees?
A.38,000
B.40,000
C.42,500
D.45,500
Answer: D.45,500
Explanation: Median is just the value in the middle when you arrange all values in the ascending order
In this question, the 7th value would be the median (Since there are 13 employees)
38, 40, 40, 40, 42.5, 42.5,45.5
So, 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.A)25
B.B)30
C.C)20
D.D)21
Answer: B.B)30
Explanation: M = 15
S = 15
DS = 15 + 15 = 30
Answer:B
Question: A box contains 4 black, 3 red and 6 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?
A.24/78
B.24/709
C.24/76
D.24/71
Answer: A.24/78
Explanation: Explanation:
Total marbles in a box = 4 black + 3 red + 6 green marbles = 13 marbles
2 marbles are drawn from 13 marbles at random. Therefore,
n(S) = 13C2 = 78 ways
Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is
n(A) = 4C2 + 3C2 + 6C2 = 6 +3 + 15 = 24
Therefore, by definition of probability of event A,
P(A) = n(A)/n(S) = 24/78
ANSWER:A
Question: If C is a whole number, C+1 is a whole number after that. If A is a whole number, what is a whole number before that?
A.7
B.1
C.2
D.3
Answer: B.1
Explanation: We know that the number ‘0’ together with the natural numbers gives us the numbers 0, 1, 2, 3, 4, 5, …………… which are called whole numbers.
If A is a whole number and it is greater than 0 then the whole number before that is A – 1, which will always be a whole number.
Again, when A is a whole number and it is equal to 0 then the whole number before that is A – 1 which means 0 – 1 = -1, which is not a whole number.
Therefore, if A is a whole number then the number before that will not always be a whole number.
Answer:B
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
A.6
B.5
C.8
D.9
Answer: C.8
Explanation: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer: C
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
A.5
B.6
C.7
D.1
Answer: B.6
Explanation: Let rate = R% and time = R years.
Then, (1200 * R * R) / 100 = 432
12R2 = 432
R2 = 36 => R = 6.
Answer:B
Question: If 6 Men or 8 Women take 6 days to complete some work, how many days will 8 Men and 4 Women working together take to complete the work?
Can anyone explain please? The OA is 9/4
A.1. 36/11 days
B.2. 2 Days
C.3. 9/4 days
D.4.5/2 days
Answer: A.1. 36/11 days
Explanation: 6 men or 8 women takes 6 days to complete the work
So 6M = 8W
W = 3/4M
1 man in 1 day does 1 unit of work
so 6 M in 6 M = 36 units of work
now 8 M and 4 W = 8M + 4(3/4)M
= 8M + 3M
= 11M
Since both set do the same work
11M in n Days = 36 units of work
n = 36 /11 days.
A
Question: Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 77, the three numbers in order are?
A.33, 66, and 132
B.33, 132, and 66
C.66, 33, and 132
D.66, 132, and 33
Answer: C.66, 33, and 132
Explanation: Let the numbers be 2x, x and 4x
(2x + x + 4x)/3 = 77
7x/3 = 77
x = 33
The numbers in order are 66, 33, and 132
The answer is C.
Question: If 6/w + 6/x = 6/y and wx = y, then the average (arithmetic mean) of w and x is
A.1/2
B.1
C.2
D.4
Answer: A.1/2
Explanation: Given: 6/w + 6/x = 6/ywx=y
Find: (w+x)/2 = ?
6(1/w + 1/x) = 6(1/y) - divide both sides by 6
(1/w + 1/x) = 1/y
(x+w)/wx = 1/wx - sub'd in y=wx
x+w - 1 = 0
x+w = 1
Therefore (w+x)/2 = 1/2
Ans: A
Question: Peter invests $100,000 in an account that pays 10% annual interest: the interest is paid once, at the end of the year. Martha invests $100,000 in an account that pays 10% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Peter's account, approximately how much more does Martha’s account have?
A.$471.31
B.$4713.10
C.$47.13
D.$4.71
Answer: A.$471.31
Explanation: Peters interest= $100,000*0.10 = $10,000 or $833.33 each month.
Martha’s interest, 10%/12 = 0.833% each month:
For the 1st month = $100,000*0.00833 = $833.33;
For the 2nd month = $833.33 + 0.833% of 833.33 = ~$840, so we would have interest earned on interest (very small amount);
For the 3rd month = $840 + 0.833% of 840 = ~$847;
For the 4th month = $847 + 0.833% of 847 = ~$854;
...
For the 12th month = $905 + 0.833% of 905 = ~$912.
The difference between Peters interest and Martha’s interest = ~(7 + 14 + ... + 77) = $462.
Answer: A.