RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A man can do a piece of work in 5 days, but with the help of his son he can do it in 4 days. In what time can the son do it alone ?
A.2 days
B.6 days
C.12 days
D.20 days
Answer: D.20 days
Explanation: Explanation:
In this type of question, where we have one person work and together work done. Then we can easily
get the other person work just by subtracting them. As
Son's one day work =
(1/4−1/5)=(5−4)/20=1/20
So son will do whole work in 20 days
Answer: D
Question: A farmer has 3,000 seeds which is enough for him to plant seeds every day for 50 days. After 10 days he loses some of the seeds and the remaining seeds is now enough for him to plant for the same period of 50 days as before. How many seeds did he lose?
A.200
B.600
C.1,000
D.900
Answer: B.600
Explanation: 3,000 ---- 50
3,000 ---- 40
x = 50
x*50 = 3,000*40
x = 2,400
3,000
-------
600
Answer = B
Question: What will come in place of the x in the following Number series? 3, 6, 12, x , 33
A.33
B.37
C.39
D.21
Answer: D.21
Explanation: (D)
The pattern is + 3, + 6, + 9, +12 â€¦â€¦â€¦..
So the missing term is = 12 + 9= 21
Question: If 50% of x is 30 less than 25% of 1500, then x is?
A.690
B.860
C.560
D.875
Answer: A.690
Explanation: 50% of x = x/2 ; 25% of 1500 = 25/100 * 1500 = 375
Given that, x/2 = 375 - 30 => x/2 = 345 => x = 690.
Answer: A
Question: A sum of 14,800 amounts to 19,800 in 3 years at the rate of simple interest. What is the rate of interest?
A.12%
B.11%
C.16%
D.15%
Answer: B.11%
Explanation: B
11%
S.I. = (19800 - 14800) = 5000.
Rate = (100 x 5000)/(14800x3)% = 11%
Question: A basket contains 8 apples, of which 1 is spoiled and the rest are good. If we select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple?
A.1/2
B.1/3
C.1/4
D.1/5
Answer: C.1/4
Explanation: The total number of ways to choose 2 apples is 8C2 = 28
The number of ways that include the spoiled apple is 7C1 = 7
P(the spoiled apple is included) = 7/28 = 1/4
The answer is C.
Question: A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 5 days before the project is completed, in how many days will the project be completed?
A.18 days
B.27 days
C.26.67 days
D.15 days
Answer: D.15 days
Explanation: Let X = the number of days taken to complete the project.
The amount of work done by A is (x-10) * (1/20).
The amount of work done by B is (x) * (1/30).
(1/20)*(x-5) + (1/30)*(x) = 1
(x/20) + (x/30) - (5/20) = 1
5x/60 = 5/4
x = 60/4
x = 15
Therefore, the answer is D: 15.
Question: There are 12 cans in the refrigerator. 7 of them are red and 5 of them are blue. In how many ways we can remove 11 cans so that at least one red and at least one blue cans to remain the refrigerator.
A.4
B.490
C.493
D.455
Answer: A.4
Explanation: Ways to pick 1 cans so that at least one red and at least one blue cans to remain the refrigerator =
total ways to pick 1 can out of 12 - ways to pick 1 red out of 7 red - ways to pick 1 blue out of 5 blue
12C1âˆ’7C1âˆ’5C1=12âˆ’7âˆ’1=4
ANSWER:A
Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 54 kmph?
A.22 sec
B.77 sec
C.16.7 sec
D.18 sec
Answer: C.16.7 sec
Explanation: D = 100 + 150 = 250
S = 54 * 5/18 = 15 mps
T = 250/15 = 16.7 sec
Answer:C
Question: If d + xy = d and x is not equal to 0, which of the following must be true?
A.x=0
B.x+y=0
C.x<y
D.y=0
Answer: D.y=0
Explanation: d + xy = d --> xy=0. Since x is not equal to 0, thus y = 0.
Answer: D.
Question: (1-1/n)+( 1-2/n)+(1-3/n)+…… up to n terms=?
A.1/2n
B.1/2(n-1)
C.1/2n(n-1)
D.none of these
Answer: B.1/2(n-1)
Explanation: Solution: Given sum=(1+1+1+…. to n terms)-(1/n+2/n+3/n+…. to n terms)
= n-(n(n+1)/2)/n
= n-(n+1)/2=1/2(n-1).
Answer B
Question: In a fraction, if numerator is added by 2 and denominator by 1 it results 1, and if numerator added again by 4 and denominator by 2 it results 1/2. Find the fraction?
A.3/4
B.5/4
C.7/4
D.9/4
Answer: B.5/4
Explanation: x+2/y+1 =1 i.e, x-y+1=0;--------(1)
x+4/y+2 =1/2 i.e., 2x-y+6=0;---------(2)
solving 1 and 2...we get x= -5 and y= -4
answer is 5/4...
ANSWER:B
Question: LCM of two numbers is 7700 and HCF is 11. If one number is 308 then other number is
A.269
B.285
C.300
D.275
Answer: D.275
Explanation: Option D
Question: There are two numbers whose sum is 72. One number is twice the other. What are the
numbers?
A.32-55
B.24-48
C.35-42
D.20-40
Answer: B.24-48
Explanation: Read the problem. It is about numbers.
The question at the end asks, “What are the numbers?”
Create a let statement.
Let x smaller number
2x= larger number
Reread the problem. It states that the sum of the two numbers is 72.
Translate the problem into an equation and solve.
x+2x=72
3x=72
x=24
2x=48
The answers are: The smaller number is 24 and the larger number is 48.
Is this sensible? Yes, because the sum of 24 and 48 is 72.
correct answer B
Question: In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 5 rows in all and a total of 100 bricks in the wall, how many bricks does the bottom row contain ?
A.18
B.16
C.17
D.15
Answer: A.18
Explanation: The bottom row has x bricks
x+x-1+x-2+x-3+x-4 = 100
5x-10=100
5x=90
x= 18
Answer:A
Question: In track last week, the boys ran 15 laps. The girls ran 5 more
laps. Each lap is a one-fifth of a mile. How many miles did the girls run?
A.2 miles
B.3 miles
C.4 miles
D.5 miles
Answer: C.4 miles
Explanation: The girls ran 15 + 5 = 20 laps. 20 x 1/5 = 20/5, which reduces to 4.
The girls ran 4 miles
correct answer C
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age five years back was?
A.16 years
B.14 years
C.18 years
D.19 years
Answer: B.14 years
Explanation: Let the son's present age be x years.
Then, (38 - x) = x
2x = 38 => x = 19
Son's age 5 years back = (19 - 5)
= 14 years.
Answer: B
Question: P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
A.4/5
B.2/7
C.8/15
D.7/5
Answer: C.8/15
Explanation: Explanation :
Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15
ANSWER:C
Question: A man can row upstream at 25 kmph and downstream at 37 kmph, and then find the speed of the man in still water?
A.86
B.67
C.31
D.15
Answer: C.31
Explanation: US = 25
DS = 37
M = (37 + 25)/2
= 31
Answer: C
Question: A number exceeds 20% of itself by 40. The number is
A.50
B.60
C.80
D.320
Answer: A.50
Explanation: Explanation:
Let the answer be 'a'
Then a−20/100a=40⇒5a−a=200
⇒a=50⇒a=50
Correct Option: A
Question: Calculate the time it will take for a train that is 120 meter long to pass a bridge of 160 meter length, if the speed of the train is 40 km/hour ?
A.21.2 seconds
B.25.2 seconds
C.29.2 seconds
D.35.2 seconds
Answer: B.25.2 seconds
Explanation: Speed = 40 Km/hr = 40*(5/18) m/sec = 11.1111 m/sec
Total distance = 120+160 = 280 meter
Time = Distance/speed
= 280 * (1/11.1111) = 25.2 seconds
Answer: B
Question: The least value of expression 2log10 x - logx (1/100) for x>1 is:
A.2
B.3
C.4
D.5
Answer: C.4
Explanation: 2log10 x = logx1/100 x = log10 10^-2/log10 x
=2log10 x + 2/log10 x
=2[log10 x - 1/log10 x]
since x>1=>log10 x >0
log10 x+ 1/log10^x>=2=> for x = 10, 2[log10 x + 1/log 10 x] > 4
Hence least value is 4
ANSWER C
Question: A person covered one-fourth of the total distance at 22 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
A.21 (1/8)
B.21 (1/15)
C.23 (7/15)
D.29 (1/15)
Answer: C.23 (7/15)
Explanation: Let the total distance be x km
total time taken = (x/4)/22 + (3x/4)/24 = 15x/352
Average speed = x/(15x/352) = 23 (7/15)kmph.
Answer: C
Question: 24 oz of juice P and 25 oz of juice E are mixed to make smothies X and Y . The ratio of p to E in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X?
A.5
B.10
C.15
D.20
Answer: D.20
Explanation: Easy way to solve this question is start from the answer and then conform the information provided in the question.
we can start from option D i.e 20 ... as a quantity of juice P in X because it is the only one option that gets divided by 4 is 20 ... since in the X the juice P to E ratio is 4:1
this gives us that quantity of juice P in X = 20 therefore quantity of Juice E will be 5 ... hence ratio = 4:1
This will lead to quantity of juice P in X = 4 and quantity of Juice E = 20 ... hence ratio 1:5
if we calculate total Juice P = 24 and total of juice V = 25
it fits because totals are same as what mentioned in the question ...
thus ans is D
Question: Rich has 3 green, 2 red and 3 blue balls in a bag. He randomly picks 5 from the bag without replacement. What is the probability T that of the 5 drawn balls, Rich has picked 1 red, 2 green, and 2 blue balls?
A.T=8/28
B.T=9/28
C.T=10/28
D.T=10/18
Answer: B.T=9/28
Explanation: (3c2*2c1*3c2)/8c5
=(3*2*3)/ (8*7*6/3*2)
=18/56
=9/28
B
Question: How many different subsets of the set {10, 14, 13, 24} are there that contain an odd number of elements?
A. 3
B. 6
C. 8
D. 10
Answer: C. 8
Explanation: Answer = C = 8
{10}
{14}
{13}
{24}
{10, 14, 13}
{14, 13, 24}
{10, 13, 24}
{10, 14, 24}
Question: Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 12 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?
A.4
B.4.5
C.6
D.8
Answer: C.6
Explanation: Work done by AB in a day = xy respectively.
When A starts:
No. of days when A works = 6No. of days when B works = 6 → 6x + 6y = 1
When B starts:
No. of days when A works = 6.5No. of days when B works =5.5 → 6.5x +5.5y = 1
Solving the above two equations for xy
x = 1/12 y = 1/12
→ Total work done by AB in a day = 1/12 + 1/12 = 2/12 =1/6
→ No. of days to complete the work when both work together = 6
Answer: C
Question: How many possible positive integer values are there for k if -24 < 9k – 6 ≤ 3?
A.Zero
B.One
C.Two
D.Three
Answer: B.One
Explanation: -24 < 9k – 6 ≤ 3
Add 6: -18 < 9k ≤ 9
Divide by 9: -2< k ≤ 1.
k can take only one positive integer value: 1.
Answer: B.
Question: hree number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:
A.40
B.50
C.60
D.70
Answer: A.40
Explanation: Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400 or x = 40.
The numbers are (3 x 40), (4 x 40) and (5 x 40).
Hence, required H.C.F. = 40.
ANSWER :A
Question: John started a business, investing Rs.18000. After 3 months and 4 months respectively, Rose and Tom joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.4125. What is the difference between Rose ’s and Tom ’s share in the profit?
A.s.340
B.s.362
C.s.375
D.s.382
Answer: C.s.375
Explanation: John : Rose : Tom
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rose’s and Tom’s share = 1 share
:.i.e. = Rs. 4125 × 1/11 = Rs.375.
C)
Question: By travelling at 80 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
A.25 kmph
B.40 kmph
C.35 kmph
D.46 kmph
Answer: B.40 kmph
Explanation: Let the time taken to reach the destination be 3x hours. Total distance = 80 * 3x = 240x km
He covered 2/3 * 240x = 160x km in 1/3 * 3x = x hours So, the remaining 80x km, he has to cover in 2x hours. Required speed = 80x/2x
=40 kmph.
Answer: B
Question: On a particular mathematics exam, the student has 5 answers to choose from. If the student guesses at the answers, the probability of the student getting a correct answer on each question is 1/5. What is the least number of times that the student should guess in order to take the probability of getting a correct answer at least once to more than 50%.
A.4
B.1
C.2
D.5
Answer: A.4
Explanation: Rule of Subtraction: P(A) = 1 - P(A')
Rule of Multiplication: P(A ∩ B) = P(A) P(B)
The probability that the student gets a correct answer at least once in 2 guesses is 1- (4/5)^2 = 1 - 16/25 = 9/25 < 50%.
The probability that the student gets a correct answer at least once in 3 guesses is 1- (4/5)^3 = 1 - 64/125 = 61/125 < 50%.
The probability that the student gets a correct answer at least once in 4 guesses is 1- (4/5)^4 = 1 - 256/625 = 369/625 > 50%.
Answer: A
Question: Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 8 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?
A.R-4
B.R/(R+4)
C.R/(R-16)
D.8/(R-8)
Answer: C.R/(R-16)
Explanation: Let T be the time thatAlexwill have been walking when Brenda has covered twice as much distance as Alex.
In T hours Alex will cover 4T miles;
Since Brenda begins her journey 1 hour later than Alex then total time for her will be T-1 hours, and the distance covered in that time will be R(T-1);
We want the distance covered by Brenda to be twice as much as that of Alex: 2*8T=R(T-1) --> 16T=RT-R --> T=R/(R-16).
Answer: C.
Question: The ratio between the presents of the A and B is 2:3. If B is 5 years older than A, what will be the ratio of the ages of A and B after 5 years?
A.3:4
B.1:2
C.2:3
D.5:6
Answer: A.3:4
Explanation: Let A and B ages will be 2x and 3x
3x - 2x = 5
x = 5
Required ratio = 2x+5 : 3x+5 = 15:20 = 3:4
Answer is A
Question: If a randomly selected non-negative single digit integer is added to {2, 3, 6, 8}. What is the probability that the median of the set will increase but the range still remains the same?
A.0.2
B.0.3
C.0.4
D.0.5
Answer: C.0.4
Explanation: We are selecting from non-negative single digit integers, so from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. These 10 digits represent the total number of outcomes.
Hence, the total number of outcomes is 10.
We need to find the probability that the median of the set will increase but the range still remains the same.
The median of the set is (3 + 6)/2 = 4.5, thus the number selected must be 5 or greater.
For the range to remain the same, the number must be between 2 and 8 inclusive.
To satisfy both conditions, the number selected must be 5, 6, 7, or 8.
The probability is 4/10 = 0.4
The answer is C.
Question: A cubic object 3'' x 3'' x 3'' is painted blue on all the outside surfaces, including the top and bottom. If the cube is cut into 27 cubes of 1'' x 1'' x 1'' , how many 1" cubes do have any painted surfaces?
A.15
B.22
C.26
D.33
Answer: C.26
Explanation: C
26
Only the box in the very centre of the stack will not suffer the strokes of the paint brush, whereas all the other 26 boxes will have at least one side painted.
Question: Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?
A.22.5 years
B.24.5 years
C.12.5 years
D.28.5 years
Answer: B.24.5 years
Explanation: Let Rahul's age be X years.
Then, Sachin's age = (X - 7) years.
Therefore (X - 7) / X	=	7/9
9X - 63 = 7X
2X = 63
X = 31.5
Hence, Sachin's age =(X - 7) = 24.5 years.
ANSWER:B
Question: If x is a sum of all even integers on the interval 13...55 and y is their number, what is the GCD (x, y)?
A. 1
B. 21
C. 26
D. 52
Answer: B. 21
Explanation: x = 14 + 16 + ... + 54 = (largest + smallest)/2 *(# of terms) = (14 + 54)/2*21= 34*21.
GCD of 21 and 34*21 is 21
Answer: B.
Question: If one-third of one-fourth of a number is 15, then three-tenth of that number is:
A.45
B.65
C.54
D.34
Answer: C.54
Explanation: Let the number be x.
Then,1/3 of 1/4 of x = 15 <=> x = 15 x 12 = 180.
So, required number =3/10 x 180= 54.
ANSWER:C
Question: A bullet train leaves Kyoto for Tokyo traveling 240 miles per hour at 12 noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160 miles per hour. If Tokyo and Kyoto are 380 miles apart, at what time will the trains pass each other?
A.12:40pm
B.12:49pm
C.12:55pm
D.1:01pm
Answer: D.1:01pm
Explanation: Train A: going from K to T
Train B: going from T to K
First I calculated how far Train A will have travelled by the time Train B starts at 12:10:
10 minutes at 240 mph
1/6*240=40miles
They have 380-40=340 miles to travel to meet each other.
I found the combined rate of the two trains
Rate(A) + Rate(B) = 400mph
Divide Distance/Rate to find total time each will travel:
340/400>>> 51 Minutes to meet
12:10+51 minutes = 1:01 or Answer D
Question: On taking delivery of a consignment of eggs the market stall owner was furious to find that several were cracked. In fact, on counting them up in order to assess the damage he found that 72 were cracked, which was 12 percent of the total consignment. How many eggs in total were in the consignment?
A.500
B.600
C.800
D.200
Answer: B.600
Explanation: B
600
72 ÷ 12 × 100 = 600.
Question: A man walks at certain place and rides back in 10 hours. He could ride both ways in 8 hours. The time taken by him to walk both ways?
A.10
B.12
C.14
D.16
Answer: B.12
Explanation: W + R = 10and 2R = 8, R = 4so, W = 6 so, walking both sides, he will take = 12 hours Answer: B
Question: In Arun's opinion, his weight is greater than 66 kg but leas than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 69 kg. If all of them are correct in their estimation, what is the average of diferent probable weights of Arun ?
A.86.5 kg
B.67.5 kg
C.46.5 kg
D.26.5 kg
Answer: B.67.5 kg
Explanation: Let Arun's weight be X kg.
According to Arun, 66 < X < 72.
According to Arun's brother, 60 < X < 70.
According to Arun's mother, X < 69.
The values satisfying all the above conditions are 67 and 68.
Required average = (67 + 68) / 2 = 67.5 kg
Answer: B
Question: A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train?
A.356
B.250
C.127
D.279
Answer: B.250
Explanation: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 15 = 250 m
Answer: B
Question: For integers x, y, and z, if (3^x) (4^y) (5^z) = 838,860,800,000 and x + y + z = 19, what is the value of xy/z?
A.0
B.2
C.4
D.6
Answer: A.0
Explanation: The number 838,860,800,000 is not divisible by 3. (We can verify this by adding the digits of the number to see that the sum is not a multiple of 3.)
Thus x = 0 and xy/z = 0.
The answer is A.
Question: The average (arithmetic mean) of 16 students first quiz scores in a difficult English class is 60.5. When one student dropped the class, the average of the remaining scores increased to 64.0. What is the quiz score of the student who dropped the class?
A.a) 8
B.b) 25
C.c) 40
D.d) 55
Answer: A.a) 8
Explanation: Total Score of 16 students is 16*60.50 = 968
Total Score of 15 students is 15*64 = 960
So, the score of the person who left is 8 ( 968 - 960 )
Answer will be (A
Question: 8 points are marked on a straight line and another 9 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?
A.91
B.105
C.196
D.20
Answer: D.20
Explanation: assuming that the top line can have either 2 points or 1 point...
8! / 1!7! - 8! / 2! 6! yields 20.
D
Question: When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 15-inch boxes. If the university pays $0.50 for every box, and if the university needs 3.06 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes?
A.$255
B.$275
C.$510
D.$1,250
Answer: A.$255
Explanation: Total no. Of boxes = 3060000/(20×20×15) = 510
Total cost = 510×$0.5=$255
Answer A
Question: The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 14 cm each. The radius of the sphere is
A.3 cm
B.4 cm
C.6 cm
D.7 cm
Answer: D.7 cm
Explanation: Solution
4Î R2	= 2Î 7x14
â‡’ R2 = (7x14/2)
â‡’ 49
â‡’ R = 7 cm.
Answer D
Question: A train 110 m long is running with a speed of 36 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
A.5
B.6
C.7
D.9
Answer: D.9
Explanation: Speed of train relative to man = 36 + 6 = 42 km/hr.
= 42 * 5/18 = 35/3 m/sec.
Time taken to pass the men = 110 * 3/35 = 9 sec.Answer: D
Question: A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 106. What was the number he chose?
A.123
B.267
C.277
D.122
Answer: D.122
Explanation: Let xx be the number he chose, then
2â‹…xâˆ’138=106
x=122
Answer:D
Question: In a camp, there is a meal for 160 men or 220 children. If 160 children have taken the meal, how many men will be catered to with remaining meal?
A.41
B.16
C.15
D.14
Answer: B.16
Explanation: B
16
There is a meal for 200 children.
180 children have taken the meal.
Remaining meal is to be catered to 20 children.
Now, 200 children 160 men.
20 children = (160/200)x 20= 16 men.
Question: 2 friends A n B running up hill and then to get down length of road 440 yads A on his return journey met B going up at 20 yards from top if A has finished race 5 minute earlier than B then how much time A had taken to complete the race ?
A.100 minute
B.110 minute
C.120 minute
D.130 minute
Answer: B.110 minute
Explanation: total journey= 440*2=880
A meet B 20 yards from top in getting down it means he has covered 440+20=460 yards while B is 420 yards.so he is 40 yards ahead of B which is equals to 5 minute.
so 40 yards in 5 min
880 yards will be in 5*880/(40)=110 minute
ANSWER:B
Question: Wilson can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows?
A.40 minutes.
B.1 hour and 30 minutes.
C.1 hour.
D.1 hour and 40 minutes.
Answer: C.1 hour.
Explanation: Rate =Output/Time
Wilson Rate=25/20=5/4
Dylan Rate=25/60=5/12
Combined rate = 5/4+5/12= 20/12
CombinedRate*CombinedTime= CombinedOutput
20/12*t=150
t=90 mins => 1 hr 30 min
Question: Lucy deposited $62500 in an investment fund that provided 20 percent annual return compounded quarterly. If she made no other transactions with the fund, in how much time, in months, did her investment earn a total interest of $5100?
A.0.5
B.2.4
C.3
D.6
Answer: B.2.4
Explanation: A = P + I = 62500 + 5100 = 67600
67600 = 62500(1 + 20/4*100)^(4t)
(676/625) = (105/100)^(4t)
t = 1/5 yrs = 2.4 months
Answer: B
Question: The amount of electrical current that flows through a wire is inversely proportional to the resistance in that wire. A wire originally carries 4 amperes of electrical current. Then the resistance is reduced to one-fourth of its original value. How many amperes of electrical current will flow through the wire?
A.2
B.4
C.8
D.16
Answer: D.16
Explanation: Given that, I∝1/R, I*R is a constant value.
I1*R1 = I2*R2
I1*R1 = I2*R1/4
I2 = 4*I1 = 16 amperes
The answer is D.
Question: The average marks obtained by 120 cndidates in a certainexaminationis 35.if the average marks of passed candidate is 39 and that of the failedcandidates is 15,what is the number of candidates who passed the examination
A.14 years
B.14 years 5 month
C.14 years 8 month
D.15 years
Answer: C.14 years 8 month
Explanation: (d) Let No. of passed candidates are x
So, x * 39 + (120 – x) 15= 120 * 35
x = 100
2.(a) Total increase = 8 * 2 = 16 years
So, total age of two women = 35 + 45 +16= 96
Average age of two women=96/2=48 years
3(d) Total decrease = 20 * 2 = 40 month
= 3 years 4 month
So, age of new boy = 18 years – 3 years 4 month
= 14 years 8 month
C