RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If W is the set of all the integers between 49 and 114, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
A.34
B.44
C.45
D.55
Answer: B.44
Explanation: Official Solution:
Number of multiples of 3
Step 1. Subtract the extreme multiples of 3 within the range (The greatest is 114, the smallest is 51): 114 - 51 = 63
Step 2. Divide by 3: 63 / 3 = 21
Step 3. Add 1: 21 + 1 = 22.
So there are 22 multiples of 3 within the range: examples are 51, 54, 57, 60, etc.
Number of multiples of 2
Step 1. Subtract the extreme multiples of 2 within the range (The greatest is 114, the smallest is 50): 114 - 50 = 64
Step 2. Divide by 2: 64 / 2 = 32
Step 3. Add 1: 32 + 1 = 33.
So there are 33 multiples of 2 within the range: examples are 50, 52, 54, 56, 58, 60 etc.
Add the 22 multiples of 3 and the 33 multiples of 2: 22+33=55.However, by adding the multiples of 2 and the multiples of 3, we are effectively counting several numbers twice: for example, 54 and 60 are parts of both the lists above. So we can't just take 22+33=55. Find the Number of multiples of 6 (which are the double counted, as 6 is divisible by both 2 and 3), and subtract it from 55:
Step 1. Subtract the extreme multiples of 6 within the range (The greatest is 72, the smallest is 54): 114 - 54 = 60
Step 2. Divide by 6: 60 / 6 = 10
Step 3. Add 1: 10 + 1 = 11.
So there are 11 multiples of 6 within the range: we counted 11 numbers twice.
Subtract the 11 multiples of 6 from the sum of the multiples of 2 and 3:
= 22+33 - 11
= 55 - 11
= 44
Therefore, the final number of multiples of 2, 3 or 6 is 44.
Hence, this is the correct answer. (B)
Question: A can do a piece of work in 6days of 9 hours each and B alone can do it in 12 days of 9 hours each.how long will they take it to do working together
4 1/2 hours a day?
A.8 days
B.9 days
C.7 days
D.6 days
Answer: A.8 days
Explanation: A's work per hour=1/54
B's work per hour=1/108
A & B's work per hour together=(1/54)+(1/108)=3/108=1/36
so A & B together complete the work in 36 hours...
if they work 4 1/2=9/2 hours a day,
it will take (36)/(9/2) days=8 days...
ANSWER: A
Question: In order to obtain an income of Rs. 1000 from 50% stock at Rs. 500, one must make an investment of
A.Rs.17000
B.Rs.16050
C.Rs.15400
D.Rs.10000
Answer: D.Rs.10000
Explanation: Explanation :
Market Value = Rs.500.
Required Income = Rs. 1000.
Here face value is not given. Take face value as Rs.100 if it is not given in the question
To obtain Rs.50 (ie,50% of the face value 100), investment = Rs.500
To obtain Rs.1000, investment = 500/50Ã—1000=10000
Answer : Option D
Question: If 6th March, 2017 is Sunday, what was the day of the week on 6th March, 2016?
A.Sunday
B.Saturday
C.Tuesday
D.Wednesday
Answer: B.Saturday
Explanation: Solution
The year 2016 is a leap year. So, it has 2 odd days.
But, Feb 2016 not included because we are calculating from March 2016 to March 2017. So it has 1 odd day only.
The day on 6th March, 2017 will be 1 day beyond the day on 6th March, 2016. Given that, 6th March, 2017 is Sunday.
6th March, 2016 is Saturday (1 day before to 6th March, 2017)
Answer B
Question: A sum of Rs.48000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
A.28880
B.31200
C.28770
D.29990
Answer: B.31200
Explanation: Let A be the amount received at the end of the three years.
A = 48000[1 + 10/100][1 + 20/100][1 + 25/100]
A = (48000 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.79200
So the interest = 79200 - 48000 = Rs.31200
Answer: B
Question: Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $150, what were her original savings?
A.$500
B.$600
C.$700
D.$800
Answer: B.$600
Explanation: If Linda spent 3/4 of her savings on furniture, the rest
4 / 4 - 3 / 4 = 1 / 4 on a TV
But the TV cost her $150. So 1 / 4 of her savings is $150. So her original savings are 4 times $150 = $600
correct answer B
Question: Two spherical balls lie on the ground touching. If one of the balls has a radius of 7 cm, and the point of contact is 10 cm above the ground, what is the radius of the other ball (in centimeters)?
A.30/7
B.50/3
C.70/4
D.80/5
Answer: C.70/4
Explanation: A straight line will join the two centers and the point of contact, thus making similar triangles.
3/7 = (r-10)/r
3r = 7r - 70
r = 70/4
The answer is C.
Question: In a basketball game, Dhoni scored 15 points more than Dravid, but only half as many points as Shewag. If the three players scored a combined total of 77 points, how many points did Dhoni score?
A.23
B.33
C.25
D.28
Answer: A.23
Explanation: Let Dravid scored point = x
Then Dhoni Scored = x+15
Shewag Scored = 2*(x+15) = 2x+30
As given, x+x+15+2x+30 = 77 points
4x+45 = 77
x = 77-45/4 = 8
So Dhoni Scored = x +15 i.e) 8+15 = 23
Answer : A
Question: A park square in shape has a 3 metre wide road inside it running along its sides. The area occupied by the road is 1764 square metres. What is the perimeter along the outer edge of the road?
A.576 metres
B.589 metres
C.600 metres
D.700 metres
Answer: C.600 metres
Explanation: Solution
Let the length of the outer edges be x metres.
Then, length of the inner edge = ( x - 6)m.
∴ x2 - (x-6)2 = 1764
‹=› x2-(x2-12x+36)= 1764
‹=›12x = 1800
‹=›x = 150.
∴ Required perimeter = (4x)m
‹=› (4 x 150)m = 600m.
Answer C
Question: A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
A.228
B.277
C.299
D.860
Answer: D.860
Explanation: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Answer:D
Question: If x > y and y > z, which of the following represents the greatest number R?
A. x − z
B. x − y
C. y − x
D. z − y
Answer: A. x − z
Explanation: Because x>y>z
thus R=x- z wil lbe greatest
Ans: A
Question: Twenty times a positive integer is less than its square by 96. What is the integer?
A.24
B.20
C.30
D.Cannot be determined
Answer: A.24
Explanation: Let the positive integer be x.
Now, x2 – 20x = 96
or, x2 – 20x – 96 = 0
or, x2 – 24x + 4x – 96 = 0
or, x(x – 24) + 4(x – 24) = 0
or, (x – 24)(x + 4) = 0
or, x = 24, – 4
x ≠ –4 because x is a positive integer
Answer A
Question: A merchant who marked his goods up by 50% subsequently offered a discount of 20% on the marked price. What is the percentage profit that the merchant made after offering the discount?
A.30%
B.125%
C.25%
D.20%
Answer: D.20%
Explanation: Explanatory Answer
The easiest way to solve these kinds of problems is to assume a value for the merchant's cost price.
To make calculations easy, it is best to assume the cost price to be $100.
The merchant marks his goods up by 50%.
Therefore, his marked price (quoted price) = cost price + mark up.
Marked price = $100 + 50% of $100 = 100 + 50 = $150.
The merchant offers a discount of 20% on his marked price.
Discount offered = 20% of 150 = $30.
Therefore, he finally sold his goods for $150 - $30 = $ 120.
We assumed his cost to be $100 and he sold it finally for $120.
Therefore, his profit = $20 on his cost of $ 100.
Hence, his % profit = profit/cost price * 100 = 20/100 * 100 = 20%.
Choice D
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is:
A.2:5
B.2:3
C.2:4
D.2:1
Answer: B.2:3
Explanation: Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.4 = (k + 1) * 15.8
= (16.4 - 15.8)k = (15.8 - 15.4)
= k = 0.4/0.6 = 2/3
Required ratio = 2/3 : 1 = 2:3.
Answer:B
Question: Suppose you have three identical prisms with congruent equilateral triangles as the end-polygons. Suppose you attach them by the rectangular faces so they are perfectly aligned. There will be some large faces created by two or more co-planar faces of the individual prisms: count each such large face as one. Given that, how many faces does the resultant solid have?
A.4
B.6
C.9
D.10
Answer: B.6
Explanation: The top and the bottom are each single faces formed by three equilateral triangles joining, as in the diagram on the left, to make an isosceles trapezoid. Top = 1 face, and bottom = 1 face. This is a four-sided figure, so there are four rectangles extending from the bottom of this prism to the congruent figure at the top. Notice, in particular, the larger vertical face in the “back” of the diagram to the right is formed by two faces of the original triangular prisms lying next to each other and smoothly joining. Total = 1 top + 1 bottom + 4 sides = 6 faces. Answer = B.
Question: 1, 9, 25, 49, 81, ?
A.100
B.121
C.144
D.169
Answer: B.121
Explanation: The series consists of squares of consecutive prime numbers.
Answer : B.
Question: The price of a T.V. set worth Rs. 20000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
A.19002
B.19028
C.27788
D.19000
Answer: D.19000
Explanation: Money paid in cash = Rs. 1000
Balance payment = (20000 - 1000) = Rs. 19000
Answer: D
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
A.1/455
B.1/417
C.1/418
D.1/420
Answer: A.1/455
Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue
= ³C₃/¹⁵C₃
= (1 * 3 * 2 * 1)/(15 * 14 * 13)
= 1/455
Answer: A
Question: A rectangular lawn of dimensions 80 m * 50 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
A.A)3820
B.B)930
C.C)9309
D.D)3600
Answer: D.D)3600
Explanation: Explanation:
Area = (l + b – d) d
(80 + 50 – 10)10 => 1200 m2
1200 * 3 = Rs.3600
Answer: Option D
Question: Concentrated lime juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated lime juice, at the most, can fit into 3 wooden boxes?
A.24.
B.28.
C.36.
D.42.
Answer: A.24.
Explanation: Concentrated lime juice comes inside a cylinder tube since height of a tube is 15 inches , the tubes can fit only in one way .
now, diameter of each tube = 5 inches
therefore, 4*2 can be put in each wooden box
in 3 boxes 3*4*2 can be accommodated
= 24=A
Question: The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?
A.246
B.248
C.492
D.15,128
Answer: C.492
Explanation: OK let's take a crack at this one.
So basically we have 144^2 - 142^2
So then (144+142)(144-142)
(246)(2) = 492
ANSWER:C
Question: A Bell Curve (Normal Distribution) has a mean of − 1 and a standard deviation of 1/8 . How many integer values O are within three standard deviations of the mean?
A.0
B.1
C.3
D.6
Answer: B.1
Explanation: Got the question correctly -- the second item -- [highlight] bthe list of elements in the set is required.[/highlight] is not required.
With the new information, there is only one integer value (-1) that is between (-1.375, -0.625) i.e., falls within the three 3 SD range.B
Question: In a recent election, Ms. Robinson received 8000 voters cast by independent voters, that is, voters not registered with a specific political party. She also received 50 percent of the votes cast by those voters registered with a political party. IF N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Mrs. Robbins received?
A. 0.06N+3200
B. 0.3N+8000
C. 0.4N+7200
D. 0.1N+8000
Answer: B. 0.3N+8000
Explanation: 40% of N are independent voters, hence 60% of N are not independent voters. From this group she received 50% votes so, 0.5*0.6*N plus 8,000 votes from independents: total=0.5*0.6*N+8,000=0.3*N+8,000.
Answer: B.
Question: There are 25 stations between Delhi and Chennai. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
A.802
B.850
C.852
D.702
Answer: D.702
Explanation: The total number of stations = 27
From 27 stations we have to choose any two stations and the direction of travel (i.e., Delhi to Chennai is different from Chennai to Delhi) in 27P2 ways.
27P2= 27 * 26 = 702
ANSWER: D
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.7
B.9
C.8
D.65
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: If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate?
A.Rs. (xd/y)
B.Rs. xd
C.Rs. (yd/x)
D.Rs. yd
Answer: C.Rs. (yd/x)
Explanation: Explanation:
cost of x metres of wire = Rs.d
cost of 1 metre of wire = Rs.(d/x)
cost of y metre of wire = Rs.(y × d/x) = Rs. (yd/x)
Answer: Option C
Question: The area of a square garden is A square feet and the perimeter is p feet. If a=2p+15, what is the perimeter of the garden, in feet?
A.28
B.36
C.40
D.56
Answer: C.40
Explanation: Perimeter of square = P
Side of square = P/4
Area of Square = (P^2)/16 =A
Given that A = 2P + 15
(P^2)/16 = 2P + 15
P^2 = 32P +240
P^2 -32P -240 = 0
P^2 -40P + 6P -240 = 0
P(P-40)+6(P+40) = 0
(P-40)(P+6) = 0
P = 40 or- 6
Discarding negative value , P = 40
Answer is C
Question: When the positive integer A is divided by 9 and 7, the remainder is 3 and 4, respectively. When the positive integer B is divided by 9 and 7, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B?
A.35
B.48
C.54
D.63
Answer: D.63
Explanation: A = 9k+3 = 7j+4
B = 9m+3 = 7n+4
A-B = 9(k-m) = 7(j-n)
Thus A-B is a multiple of 9 and 7, so it is multiple of 63.
The answer is D.
Question: Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 40 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?
A.20
B.34
C.38
D.40
Answer: C.38
Explanation: Nice question +1
We have that X/24 - (60-X)/2R = 40
Also X/R - (60-X)/2R = 120
So we get that 2x - 60 = 80R
3x - 60 = 240R
Get rid of R
120 = 3x
x = 38
Hence answer is C
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
A.Rs.600
B.Rs.480
C.Rs.500
D.Rs.450
Answer: B.Rs.480
Explanation: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.160
SP = CP - Loss = 640 - 160 = Rs.480
ANSWER:B
Question: Calculate the cost of u bags of fruits given that the cost of h bags of said fruit is r rupees?
A.Rs.(ur/h)
B.Rs.(r*h)
C.Rs.(ur*h)
D.Rs.(u/h)
Answer: A.Rs.(ur/h)
Explanation: Cost of h bags = Rs. r.
Cost of 1 bag = Rs.	r/h
Cost of u bags = Rs.(r/h)* u= Rs.(ur/h)
Answer is A.
Question: In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is
A.20 m
B.22 m
C.24 m
D.26 m
Answer: C.24 m
Explanation: Explanation:
Each row contains 12 plants.
There are 11 gapes between the two corner trees (11 x 2) metres and 1 metre on each side is left.
Therefore Length = (22 + 2) m = 24 m.
Answer: C
Question: The ratio of white balls to black balls is 1:2.If 9 grey balls are added then the ratio of white:black:grey is 2:4:3.Find the number of black balls.
A.11
B.12
C.13
D.15
Answer: B.12
Explanation: If 9 grey balls added means, ratio of grey = 3 in all (i.e., 9/3 = 3)
Therefore, black balls = 3 *4 = 12
and the White balls = 3 *2 = 6
i.e., White = 6 ; Black = 12 ; Grey = 9
ANSWER:B
Question: A store is having a store-wide sale of 10% off all merchandise. If a discontinued item is an additional 25% off, what is the sale price of an item whose original non-sale price was $50?
A. $33.50
B. $33.75
C. $34.00
D. $34.25
Answer: B. $33.75
Explanation: sale price = (original price - 10% decrease) - 25% decrease
price = [50 * (90/100)] * (75/100) = 50 * (.90) * (.750) = 45 * .75 = 33.75
The answer is B.
Question: A person crosses a 600 metre long street in 5 minutes. What is his speed in km per hour?
A.8.2
B.4.2
C.6.1
D.7.2
Answer: D.7.2
Explanation: Distance = 600 m = 0.6 km
time = 5 min = 1/12 hr
speed = dist/time = 06./(1/12) = 7.2 km/hr
ANSWER D
Question: Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $36400, how many months will it take Joan to pay back her mortgage?
A.6
B.8
C.10
D.11
Answer: A.6
Explanation: Joan starts off with 100 $ .. which is to be tripled every month
Her monthly payments look like this :
100 , 300 , 900 , 2700 ......... Upto 36400
This can be re written as :
100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 ...... 100 x 364
So we have 1 , 3 , 9 , 27 ..... 36400 in GP
We know that a =1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula Tn = a3^n-1 ...)
Therefore to find the Sum of n terms of a GP we use this formula :
Sn = a (1-r^n) / 1 -r
Using this and plugging in the information we get ...
364 = 1 - 3^n / 1-3 ; 1-3^n / -2
Cross multiplying we get
364 x -2 = 1- 3^n
- 728 = 1 - 3^n
- 729 = - 3 ^n
729 = 3 ^n (negatives cancel out)
729 can also be re written as 3 ^ 6
Therefore ; 3 ^6 = 3 ^n
Thus n = 6 (A)
Question: How many ways could three boxes can be arranged in a shelf with five boxes space in which two places in the shelf will remain empty?
A.118
B.60
C.8
D.12
Answer: B.60
Explanation: ways in which 3 places out 5 can be selected = 5C3
ways in which 3 boxes can be arranged in 3 places = 3!
Total ways of arrangement = 5C3*3!
=5*4/2*6
=10*6
=60
Ans = B
Question: What is the greatest possible (straight line) distance, between any two points on a hemisphere of radius 2?
A.0.4
B.1
C.π/4
D.4
Answer: D.4
Explanation: Maximum distance straight line is diameter
d = 2r = 4..
ANS option D.
Question: Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
A.7.19
B.7.18
C.7.16
D.7.15
Answer: D.7.15
Explanation: T = (121 + 165)/ (80 + 65) * 18/5
T = 7.15
Answer: D
Question: A train passes a man standing on the platform. If the train is 125 meters long and its speed is 90 kmph, how much time it took in doing so?
A.6 sec
B.2 sec
C.9 sec
D.5 sec
Answer: D.5 sec
Explanation: D = 125
S = 90 * 5/18 = 25 mps
T = 125/25 = 5 sec
Answer:D
Question: Addison High School’s senior class has 300 boys and 240 girls. If 60% of the boys attended the college then 60% of the total class attended college, what percentage of the girls class attended college?
A.60
B.50
C.46
D.55.56
Answer: A.60
Explanation: Number of boys attending the party : 0.60*300 = 180
Total students = 300+240 = 540
number of students attending the party: 0.60*540 = 324
number of girls attending = 324-180 = 144
% of girls attending = 144/240 = 60%. A is the correct answer
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
A.2.5 sec
B.2.9 sec
C.2.7 sec
D.8.7 sec
Answer: A.2.5 sec
Explanation: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40 = 2.5 sec.
Answer: A
Question: In a certain country, 60 percent of the population likes basketball, and 32 percent of the population likes both basketball and golf. What percentage of the people who like basketball also like golf?
A.20%
B.33%
C.40%
D.53%
Answer: D.53%
Explanation: Correct Answer: (D).
Since this is a percent problem without concrete numbers, we can assign our own. If we assume that there are 100 people in the country, then 60 people like basketball, and 32 people like basketball and golf. We’re looking for people who like both divided by people who like basketball, so 32/60 = 53%, or choice D.
Question: The C.P of 15 books is equal to the S.P of 19 books. Find his gain% or loss%?
A.16 2/3%
B.16 2/8%
C.16 2/5%
D.21 1/19%
Answer: D.21 1/19%
Explanation: 15 CP = 19 SP
19 --- 4 CP loss
100 --- ? => 21 1/19% loss.Answer: D
Question: In the rectangular coordinate system, if the line x = 5y + 5 passes through points (m,n) and (m + 2,n + p), what is the value of p?
A.1/2
B.2/3
C.1/4
D.2/5
Answer: D.2/5
Explanation: x = 5y+5, and thus y = x/5 - 1
The slope is 1/5.
The slope of a line through points (m,n) and (m + 2,n + p) is (n+p-n)/(m+2-m) = p/2
p/2 = 1/5 and thus p = 2/5
The answer is D.
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
A.31/32
B.31/37
C.31/29
D.31/28
Answer: A.31/32
Explanation: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T)
= 1 - 1/32
= 31/32
Answer: A
Question: Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?
A.9:37
B.9:31
C.9:27
D.9:19
Answer: B.9:31
Explanation: 1/4 : 3/4 = (1:3)5 = 5:15
1/5 : 4/5 = (1:4)4 = 4:16
------
9:31
Answer: B
Question: A man persuaded Weary Willie, with some difficulty, to try to work on a job for thirty days at eight dollars a day, on the condition that he would forfeit ten dollars a day for every day that he idled. At the end of the month neither owed the other anything, which entirely convinced Willie of the folly of labor. Can you tell just how many days' work he put in and on how many days he idled?
A.1673 &13 1/3 days
B.1633 &13 1/2 days
C.1433 &13 1/6 days
D.2173 &13 1/5 days
Answer: A.1673 &13 1/3 days
Explanation: A
1673 &13 1/3 days
Weary Willie must have worked 1673 days and idled 13 1/3 days. Thus the former time, at $8.00 a day, amounts to exactly the same as the latter at $10.00 a day
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?
A.11
B.18
C.99
D.77
Answer: B.18
Explanation: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
6/25 * 75 = 18
Answer: B
Question: If f(b)=b^2, what is the value of (f(a+b)−f(a))/b ?
A.a
B.b
C.2a + b
D.2a +-b
Answer: C.2a + b
Explanation: start with f(a+b) before start calculations: f(a+b)=(a+b)^2= a^2+2ab+b^2
a^2+2ab+b^2 - a^2/b = (simplify a^2)
2ab+b^2/b = (cancel b's)
= 2a+b
Ans : C
Question: Three years ago the average age of a family of six members was 19 years. A boy have been born, the average age of the family is the same today. What is the age of the boy?
A.1
B.4
C.3
D.8
Answer: A.1
Explanation: 6 * 22 = 132
7 * 19 = 133
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1
Answer: A