RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area?
A.67.5%
B.37.5%
C.77.5%
D.47.5%
Answer: B.37.5%
Explanation: 100 * 100 = 10000
110 * 125 = 13750
-----------
3750
10000 ------ 3750
100 ------- ? => 37.5%
Answer:B
Question: A certain ornaments was marked down 10% the first week and another 30% the next week. What percent of the regular price was the final cost of the ornaments after the two markdowns?
A.30%
B.36%
C.40%
D.63%
Answer: D.63%
Explanation: If the price of the ornament is 100, and it is marked down by 10% then by 70% or charged 90% of the price first and 70% of the price of reduced price, the final price is :-
100*70*90/10000= 63
63% is the final price of old price.
D is the answer
Question: A number x is 4 times another number y. The percentage that y is less than x is
A.12.5%
B.75%
C.80%
D.11%
Answer: B.75%
Explanation: Say y=1 and x=4.
Then y=1 is less than x=4 by (4-1)/4*100=3/4*100=75%.
Answer: B.
Question: Two trains A and B are 100 m and 150 m long and are moving at one another at 54 Km/hr and 36 Km/hr respectively. Arun is sitting on coach B1 of train A. Calculate the time taken by Arun to completely cross Train B.
A.10 s
B.6 s
C.4 s
D.8 s
Answer: B.6 s
Explanation: DETAILED SOLUTION
Speed of A = 54∗1000/60∗60 = 15 m/s
Speed of B = 36∗1000/60∗60 = 10 m/s
Relative speed = S1 + S2 = 15 + 10 m/s = 25 m/s
The length that needs to be crossed = length of train B = 150 m. Therefore time taken = 150/25 = 6s.
What is the time taken for trains to completely cross each other? The length that needs to be crossed = 100 + 150 = 250 m. Time taken = 250/25 = 10 s.
CORRECT ANSWER B.
Question: What is x if 2x - y = 14 and y = 2?
A.6
B.8
C.10
D.12
Answer: B.8
Explanation: Substitute y by 2 in 2x - y = 14
2x - 2 = 14
2x = 16
If we substitute x by 8 , we have 2(8) = 16. Hence
x = 8 correct answer B
Question: The number of positive integers valued pairs (x, y) satisfying 4x -17y = 1 and x <= 1000 (x is less than or equal to 1000) is
A.fifty nine
B.57
C.55
D.58
Answer: A.fifty nine
Explanation: 4x-17y=1
y=(4x-1)/17
x has to be a positive integer such that 1 <=x<=1000(4x-1) is a factor of 17 so that y is also a positive integer
So we need to know how many numbers in the set {3,7,11,15,....,3999} are divisible by 17
Lets try to observe the pattern
1. 3 mod 17 = 3
2. 7 mod 17 = 7
3. 11 mod 17 = 11
4. 15 mod 17 = 15
5. 19 mod 17 = 2
6. 23 mod 17 = 6
7. 27 mod 17 = 10
8. 31 mod 17 = 14
9. 35 mod 17 = 1
10. 39 mod 17 = 5
11. 43 mod 17 = 9
12. 47 mod 17 = 13
13.51 mod 17 = 0
14. 55 mod 17 = 4
15. 59 mod 17 = 8
16. 63 mod 17 = 12
17. 67 mod 17 = 16
... and after this the remainders will repeat (this is no co-incidence that the cyclicity is also 17)
So the right choices are x=13,13+17,13+17+17,.....
The number of such numbers is 59 (highest one being 999) A
Question: A trader marks his books 40% more than the cost price. If he allows 40% discount, then find his gain or loss percent?
A.2% profit
B.16% loss
C.4% loss
D.No profit No loss
Answer: B.16% loss
Explanation: Let CP of an book = 100
MP of an book = 140
Discount 40 % on 140 = 56
SP of the book = 140 - 56 = 84
loss = 16%
Answer : B
Question: In the x- y plane, there are 4 points (0,0), (0,4), (8,4), and (8,0). If these 4 points makes a rectangle, what is the probability that x+y<4?
A.1/2
B.1/3
C.2/3
D.1/4
Answer: D.1/4
Explanation: The line y=-x+4 intersects the rectangle and these three points of intersection (0,0), (0,4) and (4,0) form a triangle.
The points below the line y=-x+4 satisfy x+y<4.
The area of this triangle is (1/2)(4)(4)=8
The area of the rectangle is 32.
P(x+y<4) = 8/32 = 1/4
The answer is D.
Question: A man can row his boat with the stream at 10 km/h and against the stream in 6 km/h. The man's rate is?
A.2 kmph
B.7 kmph
C.98 kmph
D.6 kmph
Answer: A.2 kmph
Explanation: DS = 10
US = 6
S = ?
S = (10 - 6)/2 = 2 kmph
Answer: A
Question: The number of boys in a class is three times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ?
A.48
B.44
C.42
D.40
Answer: C.42
Explanation: Explanation:
Let number of girls = x and number of boys = 3x.
Then, 3x + x = 4x = total number of students.
Thus, to find exact value of x, the total number of students must be divisible by 4.
Answer: C
Question: Find the area of a parallelogram with base 24 cm and height 16 cm?
A.298 cm2
B.384 cm2
C.278 cm2
D.286 cm2
Answer: B.384 cm2
Explanation: Area of a parallelogram = base * height = 24 * 16
= 384 cm2
Answer:B
Question: 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:
A.20 cm
B.23 cm
C.25 cm
D.30 cm
Answer: C.25 cm
Explanation: L*b*h=Total water displaced=200(given)
To find height i.e rise in the water level
h=200/L*B
H=25cm
answer :C
Question: Nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw. If the total weight of one screw and one nail is half that of 6 screws and one nail, then the total weight of 3 screws, and 3 nails is how many times that of 1 screws and 5 nails?
A.a. 4
B.b. 5/2
C.c. 2
D.d. 3/2
Answer: B.b. 5/2
Explanation: let the weight of nail be n and that of screw be s..
so s+w=1/2 * (6s+1n)...
or 1n = 4s..
lets see the weight of 3 s and 3n= 3s+3*4s=15s..
and weight of 1s and 5n= 1s+5*1s=6s..
ratio= 15s/6s=15/6=5/2
B
Question: A grocery shop has a sale of Rs. 6535, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
A.4857
B.4184
C.4012
D.4891
Answer: D.4891
Explanation: Let the sale in the sixth month =x
Then
(6535+6927+6855+7230+6562+x)/6 =6500
=>6535+6927+6855+7230+6562+x =6×6500
=> 34109+x=39000
=> x=39000−34109
=4891
ANSWER:D
Question: A merchant sells an item at a 20% discount, but still makes a gross profit of 20 percent of the cost. What percent P of the cost would the gross profit on the item have been if it had been sold without the discount?
A.20%
B.40%
C.50%
D.60%
Answer: C.50%
Explanation: Let the Market Price of the product is MP.
Let the Original Cost Price of the product is CP.
Selling Price (Discounted Price) = 100%of MP - 20%MP
= 80% of MP. ---------------- (1)
Profit made by selling at discounted price = 20% of CP -------------- (2)
Apply the formula:
Profit = Selling Price - Original Cost Price
=> 20% of CP = 80% of MP - 100% CP
=> MP = 120CP/80 = 3/2 (CP)
Now if Product is sold without any discount, then,
Profit = Selling Price (without discount) - Original Cost Price
= Market Price - Original Cost Price
= MP - CP
= 3/2 CP - CP
= 1/2 CP
P==50%of CP
Thus, Answer should beC.
Question: A florist has 3 azaleas, 4 buttercups, and 5 petunias. The florist puts two flowers together at random in a bouquet. However, the customer calls and says that she does not want two of the same flower. What is the probability that the florist does not have to change the bouquet?
A.19/66
B.31/66
C.47/66
D.87/132
Answer: C.47/66
Explanation: The probability that two of the same flowers were chosen:
P(AA) = 3/12 * 2/11 = 6/132
P(BB) = 4/12 * 3/11 = 12/132
P(PP) = 5/12 * 4/11 = 20/132
The sum of these probabilities is 19/66
P(two flowers are different) = 1 - 19/66 = 47/66
The answer is C.
Question: A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 350 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?
A.90
B.110
C.120
D.130
Answer: A.90
Explanation: Orchestra Seats - a
Balcony Seats - b
a+b = 350
and 12a + 8b = 3320
Solving equations simultaneously (Multiply Equation 1 with 8 and subtract from second equation)
4a = 3320 - 8*350 = 3320 - 2800 = 520
i.e. a = 130
and b = 350-130 = 220
More seats in balcony than orchestra = b-a = 220 - 130 = 90
Answer: option A
Question: How many odd numbers between 10 and 1500 are the squares of integers?
A.11
B.14
C.17
D.20
Answer: C.17
Explanation: The numbers are the squares of 5, 7, 9,...,37 which includes 17 numbers.
The answer is C.
Question: X men can do a work in 120 days. If there were 20 men less, the work would have taken 60 days more. What is the value of X?
A.30
B.70
C.80
D.60
Answer: D.60
Explanation: D
60
We have M1 D1 = M2 D2
120X = (X - 20)180
=> 2X = (X - 20) 3 => 2X = 3X - 60
=> X = 60
Question: In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 50% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?
A.80
B.95
C.105
D.120
Answer: A.80
Explanation: 20% of the workerswithoutretirement plan are women, this means 80% of the workerswithoutretirement plan are men right? Makes 100% = no retirement plan.
Then 40% of those wo have a retirement plan are men, which means 60% of those who have a retirement plan are women. These percentages are always refering to the subgroupsRetirement plan = YesandNo Retirement Plan.
Make the total workers equal x and work from there and it should be fine > x/3 have no retirement plan at all. I struggled with the question a lot, it was hard for me although usually I have no problems with sets questions like this. I believe it must be a 700+ question.
Yes, you are right. I read the question incorrectly! I glazed overnotfor some reason.
If20% of the workers who do not have a retirement plan are women,80% who do not have retirement plan are men. Also 40% who do have retirement plan are men. Since 1/3 do not have retirement plan and 2/3 do have, it becomes a simple weighted average question.
Cavg = (80*1 + 50*2)/3 = 60% are men
Total = 120*100/60 = 200
No. of women = 200 - 120 = 80
A
Question: 1=5,2=25,3=253,4=150,5=225 then 150=?
A.1
B.255
C.4
D.445
Answer: C.4
Explanation: 1=5,2=25,3=253,4=150,5=225 then 150=?
150=4
check the fourth eqn.
ANSWER:C
Question: If f(x) = 2x^2 + y, and f(2) = 50, what is the value of f(5)?
A.104
B.60
C.92
D.50
Answer: C.92
Explanation: f(x) = 2x^2 + y
f(2) = 50
=> 2*(2)^2 + y = 50
=> 8 + y = 50
=> y = 42
f(5)= 2*(5)^2 + 42
= 92
Answer C
Question: when a no. divided by 406 it gives 115 as a remainder. when it divided by 29 what is the remainder.???
A.7
B.28
C.29
D.2
Answer: B.28
Explanation: let x is divided by 406 & gives quotient y & remainder 115 then
x = 406 * y + 115
now, x / 29 = (406 * y + 115)/29 = 406 * y/29 + 115/29
=> rem = 115/29 = 28
ANSWER:B
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
A.16 2/8%
B.16 8/3%
C.19 2/3%
D.16 2/3%
Answer: D.16 2/3%
Explanation: 600 ---- 100
100 ---- ? => 16 2/3%
Answer: D
Question: A volunteer organization is recruiting new members. In the fall they manage to increase their number by 5%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring?
A.16.16%
B.15.15%
C.14.95%
D.13.33%
Answer: C.14.95%
Explanation: (100%+5%)*(100%-19%) = 1.05*.81 = 0.8505.
1-0.8505 = 14.95% lost = -14.95%
The Answer is C
The organization has lost 14.95% of its total volunteers from fall to spring.
Question: If the average (arithmetic mean) of x and y is 40, and z – x = 60, what is the average of y and z?
A.20
B.50
C.65
D.70
Answer: D.70
Explanation: x+y/2 = 40
=> x+y = 80
x = z - 60...sub this value
z-60+y = 80
=>z+y = 140
=>z+y/2 = 70.
ANSWER:D
Question: Bob invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest (compounded annually) for the same 2 years at the same rate of interest and received $600 as interest. What was the annual rate of interest?
A. 5%
B. 10%
C. 18%
D. 15%
Answer: C. 18%
Explanation: First divide $550/2years to get 275$/yr non-compounding interest.
Next, subtract from the total compound after 2 years to see the interest gained in the second year. This can be done because the same amount has been invested in both accounts and the interest gained for the first year will be the same. So, $600-$275= $325.
To find the difference in interest gained, $325-$275= $50 increase in interest after the first year through compounding.
From this information we can set up the equation $275 * X% = $50.=18% giving us answer choice C.
Question: How many seconds will a 600 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
A.23 sec
B.36 sec
C.27 sec
D.28 sec
Answer: B.36 sec
Explanation: Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18
= 50/3 m/sec.
Time taken to pass the man = 600 * 3/50
= 36 sec.
Answer:B
Question: The average expenditure of a labourer for 6 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i
A.70
B.72
C.75
D.78
Answer: D.78
Explanation: Income of 6 months = (6 × 85) – debt
= 510 – debt
Income of the man for next 4 months
= 4 × 60 + debt + 30
= 270 + debt
∴ Income of 10 months = 780
Average monthly income = 780 ÷ 10 = 78
Answer D
Question: Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 4 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
A.28 km
B.20 km
C.65 km
D.18 km
Answer: A.28 km
Explanation: Distance = Relative Speed * Time
= (4 + 3) * 4 = 28 km
[ They are travelling in the opposite direction, relative speed
= sum of the speeds].
Answer: A
Question: The sum of ages of 5 children born 1 year different each is 50 yrs. What is the age of the Elder child?
A.8
B.9
C.16
D.17
Answer: B.9
Explanation: Let the ages of children be x, (x + 1), (x + 2), (x + 3) and (x + 4) years.
Then, x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 50
5x = 40
x = 8
x+4= 8+1= 9
Answer : B
Question: Of the books standing in a row on a shelf, an atlas is the 30th book from the left and the 33rd book from the right. If 4 books to the left of the atlas and 4 books to the right of the atlas are removed from the shelf, how many books will be left on the shelf?
A.54
B.57
C.58
D.61
Answer: A.54
Explanation: 100%. There are total of 30+33-1=62 books and 4+4=8 books are removed, thus 62-8=54 books are left.
Answer: A.
Question: The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?
A.156
B.432
C.288
D.355
Answer: B.432
Explanation: Explanation:
2(3x + x) = 96
l = 36 b = 12
lb = 36 * 12 = 432
Answer: B
Question: The area of the rectangle ABCD is 30. The points E and F are on the diagonal AC as shown,
and 2(AE + FC) = 3 EF. What is the area of △BEF ?
A.5
B.6
C.9
D.10
Answer: B.6
Explanation: We have EF =
2/5AC. Thus, the ratio of the areas of 4BEF and 4BAC is
2/5
correct answer B
Question: In a shop 30% of the articles are sold at a profit of 40% and the remaining at a loss of 20%.what is the overall profit/loss?
A.2% loss
B.5% loss
C.15% profit
D.3% profit
Answer: A.2% loss
Explanation: 30*1.4+70*0.8/100=0.98
ANSWER:A
Question: How many different pairs of positive integers (a, b) satisfy the equation 1/a+1/b=30/51 ?
A.6
B.3
C.2
D.1
Answer: D.1
Explanation: There is no certain way to solve 2 unknown with 1 equation. The best way is to look at the question and retrospect the most efficient way. In this question, a and b are only positive integers. So that is a big relief. Now, we can start with putting a=1,2,.. and so on till the time we are confident about one of the options.
So, we start with
a=1, we get b as -ve. out
a=2, we get b as 6. Yes (Now (a,b) = (2,6). We can directly see that (a,b)=(6,2) will also satisfy. So we have 2 possible solutions)
a=3, we get b as 3. Yes (Now we have 3 possible solutions)
a=4, we get b as fraction. Out
a=5, we get b again as some fraction. Out
a=6 already taken.
We have A,B options left. C,D,E are out.
A is 6. To have 6 as the answer, we will need one more pair like2,6and one more solution where a=b.
When a=b, we have only 1 solution = 1. So, one more solution, where a=b is not possible.
So, answer will be D.
Question: When positive integer x is divided by 10, the quotient is y and the remainder is 3. When 2x is divided by 7, the quotient is 3y and the remainder is 1. What is the value of 11y – x?
A.2
B.-2
C.3
D.-3
Answer: A.2
Explanation: (1) x = 10y+3
(2) 2x = 21y+1
(2)-(1): x=11y-2
11y-x=2
The answer is A.
Question: A train of length 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
A.3
B.7
C.6
D.8
Answer: C.6
Explanation: Explanation:
Distance = 110 m
Relative speed = 60 + 6 = 66 kmph (Since both the train and the man are in moving in opposite direction)
= m/sec = m/sec
Time taken to pass the man = = 6 s
Answer: C) 6
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 624 is required to paint the floor at the rate of Rs. 4 per sq m, then what would be the length of the floor?
A.22.8m.
B.21.6m.
C.21.1m.
D.20.6m.
Answer: B.21.6m.
Explanation: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 624/4= 156 sq m
l b = 156 i.e., l * l/3 = 156
l2 = 468 => l = 21.6m.
ANSWER:B
Question: In a circuit board factory, all circuit boards that pass a verification process are certified. Every board that fails the verification process is indeed faulty, but 1/8 of those that pass are also faulty.
Approximately how many faulty circuit boards exist in a group of 800 circuit boards where 32 fail inspection?
A.72
B.192
C.200
D.128
Answer: D.128
Explanation: Total of 800 boards. All that fail verification are indeed faulty. So the 32 are indeed faulty. 1/8 those that pass are also faulty.
From the 800 we know 32 fail. So 768 must pass. Of these 1/8 are faulty. 768 divided by 8 gives you 96.
What one must do now is to add to the 96 which were not detected the actually detected faulty ones, namely the 32.
Total faulty: 128.
Answer: D
Question: A set S = {x, -8, -7, -6, 6, 8, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of |x|-|y|?
A.1
B.0
C.2
D.-1
Answer: C.2
Explanation: Median of the set = (-6+6)/2 = 0
As per statement, Mean of the set = 0
Mean of the set
|y|- |x| +23-21 = 0 (where x is negative n y is positive)
|y|- |x| = -2
So the absolute difference between two numbers is 2
Answer C
Question: A part of certain sum of money is invested at 6% per annum and the rest at 15% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
A.4:6
B.4:9
C.4:3
D.5:2
Answer: D.5:2
Explanation: 15:6
= 5:2
Answer: D
Question: Look at this series: 1.2, 1.9, 2.6, 3.3, ... What number should come next?
A.3.8
B.4
C.4.7
D.5
Answer: B.4
Explanation: B
4
In this simple addition series, each number increases by 0.7.
Question: Six friends go to pizza corner there are 2 types of pizzas. And six different flavors are there they have to select 2 flavors from 6 flavors. In how many ways we can select?
A.10
B.15
C.20
D.30
Answer: D.30
Explanation: 6C2 = 6*5 = 30
Answer D
Question: Gill drives 120 miles from Los Angeles to San Diego to fetch a package. On her way there she drives at 40 miles per hour. On her way back she drives 50% faster. What is Gill's average velocity R for the round trip?
A.24 miles per hour
B.48 miles per hour
C.50 miles per hour
D.53 1/3 miles per hour
Answer: B.48 miles per hour
Explanation: Here's an Average Speed question in which the prompt gives you almost all of the immediate numbers needed to work with.
Driving from LA to SD, we have a distance of 120 miles and a speed of 40 miles/hour.
D = (R)(T)
120 = (40)(T)
120/40 = 3 = T
3 hours to drive to SD
On the way back, she drives 50% FASTER. Gill's return speed is (1.5)(40) = 60 miles/hour.
D = (R)(T)
120 = (60)(T)
120/60 = 2 = T
2 hours to drive to SD
Total Distance = 240 miles
Total Time = 3+2 = 5 hours
Average Speed = 240/5 = 48 miles/hour
Final Answer:
B
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
A.33 1/7%
B.33 8/3%
C.33 1/3%
D.36 1/3%
Answer: C.33 1/3%
Explanation: 1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Answer:C
Question: 5 OUT OF 2250 PARTS OF EARTH IS SULPHUR. WHAT IS THE PERCENTAGE OF SULPHUR IN EARTH
A.11/50
B.2/9
C.1/45
D.2/45
Answer: B.2/9
Explanation: REQUIRED PERCENTAGE=(5/2250*100)%=2/9%
CORRECT OPTIONS: B
Question: What is the area of a triangle with the following vertices L(1, 3), M(4, 1), and N(3, 5) ?
A.3
B.4
C.5
D.6
Answer: C.5
Explanation: There is a direct formula to calculate the are of a triangle based on coordinates of its vertices and one could use it to solve this problem.
Though if you make a diagram minimum simple calculations will be needed:
Answer: C.
Question: Calculate the share of profit made by 2 business partners, who invested $1500 and $3500 respectively in a business if the profit made is $2500.
A.$750,$1750
B.$710,$1400
C.$750,$1200
D.$753,$1400
Answer: A.$750,$1750
Explanation: A:B = 1500:3500
A:B = 3 : 7
A's share = 2500*3/10 = $750
B's share = 2500*7/10 = $1750
Answer is A
Question: A towel, when bleached, lost 30% of its length and 20% of its breadth. What is the percentage decrease in area?
A.24%
B.30 %
C.44%
D.54%
Answer: C.44%
Explanation: percentage change in area
=(−30−20+(30×20)/100)%=−44%
i.e., area is decreased by 44%
ANSWER:C
Question: Some of 50%-intensity red paint is replaced with 20% solution of red paint such that the new paint intensity is 30%. What fraction of the original paint was replaced?
A.1/30
B.1/5
C.2/3
D.3/4
Answer: C.2/3
Explanation: 30% is 10%-points above 20% and 20%-points below 50%.
Thus the ratio of 25%-solution to 50%-solution is 2:1.
2/3 of the original paint was replaced.
The answer is C.
Question: A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
A.9
B.8
C.7
D.5
Answer: A.9
Explanation: 3/12+(3+x)/16 = 1
x = 9 days
ANSWER A
Question: 8 kilograms of oranges contained 98% of water. If the next day the concentration of water decreased by 2%, what was the new weight of the oranges, in kilograms?
A. 4.9
B. 4.8
C. 4.5
D. 4
Answer: D. 4
Explanation: Eight kilograms of oranges contained 98% of water. If the next day the concentration of water decreased by 2%, what was the new weight of the oranges, in kilograms?
(A) 4.9
(B) 4.8
(C) 4.5
(D) 4
(E) 0.2
If D is the answer, then the question means that the concentration of water the newt day became 96%.
Out of 8 kilograms 98%, or 7.84 kilograms was water and 0.16 kilograms was non-water.
The next day, after some water evaporated, oranges became 96% water and 4% of non-water, so the next day 0.16 kilograms of non-water composed 4% of oranges, which means that the new weight of the oranges was x*0.04=0.16 --> x=4 kilograms.
Answer: D.
Question: It takes 7 high school students, working at identical constant individual rates, 10 hours to paint a certain house. At what time will the house be fully painted if 7 students start painting at 9:00 am and one student, working at the same rate, is added per hour starting at 5:00 pm?
A.5:40 pm
B.6:00 pm
C.6:20 pm
D.6:40 pm
Answer: D.6:40 pm
Explanation: Each student paints at a rate of 1/70 of the house per hour.
In 8 hours, the 7 students can paint 56/70 of the house.
From 5 pm to 6 pm, 8 students paint another 8/70 for a total of 64/70.
9 students can paint the remaining 6/70 of the house in 6/9 of an hour = 40 minutes.
The house is completed at 6:40 pm.
The answer is D.