mathewhe/aqua_rat huggingface dataset:
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is -.
(A) 1/26
(B) 3/52
(C) 15/26
(D) 11/26
(E) 1/13
Rationale: Explanation:
Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26
ANSWER IS A
Answer: (A) 1/26
Question: (7/10^2)*(8/10^2)*(6/10^2)=?
(A) 0.000336
(B) 0.336
(C) 0.0336
(D) 0.00337
(E) 0.00336
Rationale: 7/10^2=0.07
8/10^2=0.08
6/10^2=0.06
=0.07*0.08*0.06 multiply the whole number (i.e) 7*8*6=336
Move the place depend upon the decimal places (i.e) 0.000336
Option A is answer
Answer: (A) 0.000336
Question: How many multiples of 10 are there between 100 and 10000 (both are inclusive)?
(A) 456
(B) 789
(C) 991
(D) 1020
(E) 1100
Rationale: the answer is (10000-100)/10+1=991
Answer is C
Answer: (C) 991
Question: A man can row upstream at 7 kmph and downstream at 10kmph.find man’s rate in still water and the rate of current.
(A) 1.5 km/hr
(B) 1 km/hr
(C) 1.5 km/min
(D) 0.5 km/hr
(E) 1.75 km/hr
Rationale: Rate in still water=1/2(10+7)km/hr=8.5 km/hr.
Rate of current=1/2(10-7)km/hr=1.5 km/hr.
Answer is A.
Answer: (A) 1.5 km/hr
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 15 seconds. The speed of the train is?
(A) 35
(B) 50
(C) 88
(D) 22
(E) 12
Rationale: Speed of the train relative to man = (125/15) m/sec = (25/3) m/sec. [(25/3) * (18/5)] km/hr = 30 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 30 ==> x
= 35 km/hr.Answer:A
Answer: (A) 35
Question: 11 persons are sittingin a row. how many ways can 11 persons be arranged in a row such that 3 persons should always be together?
(A) 7!×2!
(B) 10!×1!
(C) 9!×3!
(D) 8!×2!
(E) 6!×3!
Rationale: Given that three particular persons should always be together. Hence, just group these three persons together and consider as a single person.
Therefore we can take total number of persons as 9. These 9 persons can be arranged in 9! ways.
We had grouped three persons together. These three persons can be arranged among themselves in 3! ways.
Hence, required number of ways
=9!×3!
C
Answer: (C) 9!×3!
Question: The no. of gift pack bought by Dexter is 1 more than the price, in rupees, of each gift pack. The amount of Rs.380 which Dexter had, fell short of the required amount. What is theamount by which he might have fallen short.
(A) 30
(B) 40
(C) 50
(D) 70
(E) 80
Rationale: Let the price of gift pack be 'aa'
Then number of packs bought =a+1=a+1
Hence total cost is a(a+1)a(a+1)
It is given that 380<a(a+1)380<a(a+1)
If a=19a=19, the total cost =19×20=380=19×20=380
Dexter would not have fallen short, If:
a=20a=20, a(a+1)=420a(a+1)=420
So he would have fallen short by Rs 40.
This is the minimum amount by which he may have fallen short.
B)
Answer: (B) 40
Question: The average age of 30 students in a class is 15 years. If the age of teacher is also included, the average becomes 16 years, find the age of the teacher.
(A) 46
(B) 55
(C) 43
(D) 39
(E) 54
Rationale: Explanation:
If teacher's age is 15 years, there is no change in the average. But teacher has contributed 1 year to all the students along with maintaining his age at 16.
Age of teacher = Average age of all + Total increase in age
= 16 + (1 x 30 ) = 46 years
Answer:A
Answer: (A) 46
Question: In a certain office 1/3 of the workers are women ½ of the women are married and 1/3 of the married women have children if ¾ of the men are married and 2/3 of the married men have children what part of workers are without children?
(A) 11/18
(B) 12/18
(C) 13/18
(D) 10/18
(E) None of them
Rationale: Let the total no of workers be x
No of women =x/3
No of men =x-(x/3)=2x/3
No of women having children =1/3 of ½ ofx/3=x/18
No of men having children=2/3 of ¾ of2x/3=x/3
No of workers having children = x/8 +x/3=7x/18
Workers having no children=x-7x/18=11x/18=11/18 of all wprkers
Answer is A.
Answer: (A) 11/18
Question: A group of hikers is planning a trip that will take them up a mountain using one route and back down using another route. They plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up, but the time each route will take is the same. If they will go up the mountain at a rate of 5 miles per day and it will take them two days, how many miles long is the route down the mountain?
(A) 4
(B) 6
(C) 8
(D) 12
(E) 15
Rationale: On the way down, the rate is 1.5*5 = 7.5 miles per day.
The distance of the route down the mountain is 2*7.5 = 15 miles.
The answer is E.
Answer: (E) 15
Question: Working alone, printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 16, 12, and 8 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates?
(A) 5/2
(B) 7/4
(C) 8/5
(D) 10/3
(E) 12/5
Rationale: The time it takes printer X is 16 hours.
The combined rate of Y and Z is 1/12 + 1/8 = 5/24
The time it takes Y and Z is 24/5
The ratio of times is 16 / (24/5) = 5*16/24 = 10/3
The answer is D.
Answer: (D) 10/3
Question: A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in days?
(A) 22 1/6
(B) 22 1/2
(C) 22 1/0
(D) 22 1/9
(E) 22 1/1
Rationale: 1/18 + 1/30 = 8/90 = 4/45
45/4 = 11 1/4 *2 = 22 1/2 days
Answer: B
Answer: (B) 22 1/2
Question: The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $800 per sq. metre.
(A) $12500
(B) $13500
(C) $16500
(D) $14500
(E) $18500
Rationale: C
$16500
Area =5.5×3.75 sq. metre.
Cost for 1 sq. metre. = $800
Hence, total cost
=5.5×3.75×800=5.5×3000= $16500
Answer: (C) $16500
Question: On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 15 more transactions than Cal. How much transactions did Jade handled?
(A) 80
(B) 81
(C) 82
(D) 83
(E) 84
Rationale: Solution:
Mabel handled 90 transactions
Anthony handled 10% more transactions than Mabel
Anthony = 90 + 90 × 10%
= 90 + 90 × 0.10
= 90 + 9
= 99
Cal handled 2/3rds of the transactions than Anthony handled
Cal = 2/3 × 99
= 66
Jade handled 15 more transactions than Cal.
Jade = 66 + 15
= 81
Jade handled = 81 transactions.
Answer: B
Answer: (B) 81
Question: If the numbers 1 to 100 are written on 100 pieces of paper, (one on each) and one piece is picked at random, then What is the probability that the number drawn is neither prime nor composite?
(A) 1/50
(B) 1/25
(C) 1/100
(D) 1
(E) 2
Rationale: There are 25 primes, 74 composite numbers from 1 to 100. The number
which is neither prime nor composite is 1.
Therefore, required probability = 1/100.
ANSWER:C
Answer: (C) 1/100
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 300 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
(A) 31 km/hr.
(B) 32 km/hr.
(C) 60 km/hr.
(D) 35 km/hr.
(E) 90 km/hr.
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (300 + 300)/12
2x = 50
x = 25.
Speed of each train = 25 m/sec = 25 x 18/5 km/hr = 90 km/hr.
answer :E
Answer: (E) 90 km/hr.
Question: Uncle Bruce is baking chocolate chip cookies. He has 50 ounces of dough (with no chocolate) and 40 ounces of chocolate. How much chocolate is left over if he uses all the dough but only wants the cookies to consist of 30% chocolate?
(A) 22.86
(B) 23.86
(C) 25
(D) 26
(E) 27
Rationale: First, you must find the total weight of the mixture given that 80% of it will be dough.
70%*Total = 40 => (7/10)Total=40 => Total=400/7 => Total=57.14 oz,
From there, you must find 30% of the total 57.14 oz of the mixture.
30%*Total => (3/10)(57.14)= 17.14 oz choclate used,
Not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate. 40-17.14 = 22.86 oz chocolate left over.
Answer : A
Answer: (A) 22.86
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 27, what is the total amount?
(A) 109
(B) 105
(C) 129
(D) 119
(E) 113
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 27
35 --- ? => 105
Answer:B
Answer: (B) 105
Question: In how many ways can a cricket 15 be chosen out of a batch of 20 players?
(A) 12500
(B) 18250
(C) 13250
(D) 15504
(E) 14520
Rationale: Required number of ways = 20C15 = 20C (20-15) = 20C5
20C5 = (20*19*18*17*16)/(5*4*3*2*1) = 15504
Answer is D
Answer: (D) 15504
Question: The price of commodity X increases by 30 cents every year, while the price of commodity Y increases by 20 cents every year. If in 2001, the price of commodity X was $4.20 and the price of commodity Y was $4.40, in which year will commodity X cost 90 cents more than the commodity Y?
(A) 2010
(B) 2011
(C) 2012
(D) 2013
(E) 2014
Rationale: The cost of commodity X increases by 10 cents per year relative to commodity Y.
The price of X must gain 20 + 90 = $1.10 cents on commodity Y, which will take 11 years.
The answer is C.
Answer: (C) 2012
Question: A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 70% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?
(A) 1000
(B) 1250
(C) 1300
(D) 1600
(E) 1857.14
Rationale: 300 gallons of water increases capacity by 30% that means
30% is 300 gallons, so 100% would be = 300*100/30= 1000 gallons
Now 1000 +300 gallons is 70% capacity of tank.
so 100% capacity would be= 1300 *100/70= 1857.14
E is the answer
Answer: (E) 1857.14
Question: What is the present worth of Rs. 187 due in 2 years at 5% simple interest per annum?
(A) 288
(B) 266
(C) 120
(D) 277
(E) 170
Rationale: Let the present worth be Rs. x. Then,
S.I. = (187 - x)
(x * 5 * 2) / 100 = (187 - x)
10x = 18700 - 100x
110x = 18700 => x = 170.
Answer: E
Answer: (E) 170
Question: If a real number x is chosen at random in the interval [0,5] and a real number y is chosen at random in the interval [0,6], what is the probability that x < y?
(A) 2/3
(B) 3/5
(C) 5/12
(D) 7/12
(E) 11/15
Rationale: Since x is in [0,5] and y is in [0,6] we can draw a rectangle in the coordinate plane with vertices (0, 0), (5, 0), (0, 6), and (5, 6).
The points above the line y=x satisfy x < y.
The part of the rectangle below y=x has an area of 12.5
The whole rectangle has an area of 30.
P(x < y) = (30-12.5)/30 = 17.5/30 = 35/60 = 7/12
The answer is D.
Answer: (D) 7/12
Question: In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 49 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?
(A) 70
(B) 245
(C) 150
(D) 35
(E) 350
Rationale: Since 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7 = 0.14, or 14% of the boys in the camp are from school A and do not study science.
We are told that this number equals to 49, so 0.14*{total} = 49 --> {total} = 350.
Answer: E.
Answer: (E) 350
Question: A merchant purchased a jacket for $54 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 40 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?
(A)  $0
(B)  $3
(C)  $4
(D)  $12
(E)  $18
Rationale: Actual Cost = $54
SP = Actual Cost + Mark up
= Actual Cost + 40% SP
= 54*100/60
on sale SP = 80/100(54*100/60) = 72
Gross profit = $18
Answer is E
Answer: (E)  $18
Question: On the xy co-ordinate plane, point C is (3,-2) and point D is (-1,2.5). The point on line segment CD that is twice as far from C as from D is:
(A) (1,-1)
(B) (1,1)
(C) (2,0.25)
(D) (3,0.5)
(E) (3,1)
Rationale: We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.
*It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:
Taking the x-coordinate first, the distance between C and D is |(x-coordinate of C) - (x-coordinate of D)|= |5 - (-1)| = 6
The x-coordinate that is twice as far from C as it is from D (and in between C and D) will be 4 units from C and 2 units from D. So the x coordinate of the point we're looking for is 5-4 = 1, or (-1)+2 = 1.
Now looking at the y-coordinate, we do the same thing. The distance between C and D is |(-2) - 2.5| = 4.5
The y-coordinate that is twice as far from C as it is from D (and in between C and D) will be 3 units from C and 1.5 units from D. So the y coordinate of the point we're looking for is (-2)+3 = 1, or 2.5-1.5 = 1.
So now we have our coordinates of the point on the line that is twice as far from C as it is from D: (3,0.5)
Answer: D
Answer: (D) (3,0.5)
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his avg by 3. Find his average after 17th inning.
(A) 24
(B) 52
(C) 39
(D) 36
(E) 85
Rationale: Sol. Let the average after 17th inning = x.
Then, average after 16th inning = (x - 3).
16 (x - 3) + 87 = 17x or x = (87 - 48) = 39.
Ans: C
Answer: (C) 39
Question: There are 7 books on a shelf, of which 2 are paperbacks and 5 are hardbacks. How many possible selections of 4 books from this shelf include at least one paperback?
(A) a) 30
(B) b) 45
(C) c) 50
(D) d) 55
(E) e) 60
Rationale: approach 1
at-least 1 paper back = total - no paper back
7c4-5c4 = 30
approach 2
at-least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back
= 2c1*5c3+2c2*5c2 = 30
Answer is A
Answer: (A) a) 30
Question: If 4 men can color 48 m long cloth in 2 days, then 6 men can color 36 m long cloth in
(A) 2 days
(B) 1 day
(C) 3 days
(D) 4 days
(E) 5 days
Rationale: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day.
B
Answer: (B) 1 day
Question: Given a set of numbers {5,6,7,8,9,10}, what is the probability that is two numbers are selected randomly that their sum will be greater than 12?
(A) 13/15
(B) 9/12
(C) 13/12
(D) 13/11
(E) 13/16
Rationale: First problem is 6C2 = 12 .. Not 20..
Point 2, your sum should be greater than 12, so these are the following possibilities you have
({5,8},{5,9},{5,10},{6,7},{6,8},{6,9},{6,10},{7,8},{7,9},{7,10},{8,9},{8,10},{9,10}) which leads to 13 pairs
So the probability is 13 on 12 or 13/12..
ANSWER:C
Answer: (C) 13/12
Question: If x/y = 7/3, then (x + y)/(x - y) = ?
(A) 5
(B) 5/2
(C) -1/6
(D) -1/5
(E) -5
Rationale: Any x and y satisfying x/y = 7/3 should give the same value for (x + y)/(x - y).
Say x=7 and y=3, then (x + y)/(x - y) = (7 + 3)/(7-3) = 5/2.
Answer: B.
Answer: (B) 5/2
Question: If the sum of three consecutive even numbers is 50 more than the average of these numbers, then the largest of these numbers is?
(A) 20
(B) 24
(C) 22
(D) 26
(E) 27
Rationale: Explanation:
Let the smallest of these number be x. The other two numbers are (x + 2) and (x + 4).
x + (x + 2) + (x + 4) = (X + (X+2) + (x+4)) / 3 + 50
3x + 3*(x + 2) + 3*(x + 4) = x + (x + 2) + (x + 4) + 150
9x + 18 = 3x + 156
6x = 138
x = 23
Therefore, the largest number is 27.
ANSWER E
Answer: (E) 27
Question: In one hour, a boat goes 7 km along the steram and 5 km against the stream. The speed of the boat in still waer (in km/hr) is:
(A) 2
(B) 4
(C) 6
(D) 12
(E) 15
Rationale: Sol.
Speed in still water = 1/2 (7+5) kmph = 6 kmph.
Answer C
Answer: (C) 6
Question: A contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/10 that a person who randomly guesses the answer to each question will be a winner?
(A) 5
(B) 10
(C) 50
(D) 100
(E) 1000
Rationale: A contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be a winner?
A.5
B.10
C.50
D.100
E.1000
Soln: ans is B
Probability that one question is answered right is 1/2.
Now for minimum number of questions needed to take probability less than 1/1000 is
=> (1/2)^n < 1/1000
n = 10 satisfies this.
D
Answer: (D) 100
Question: In a colony of 70 resident s, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony?
(A) 1:9
(B) 1:6
(C) 1:3
(D) 1:1
(E) 1ratio 3
Rationale: Number of men in the colony = 4/7 (70) = 40
Number of women in the colony = 3/7 (70) = 30
Number of educated women in the colony = 1/5 (30) = 6
Number of uneducated women in the colony = 4/5 (30) = 24
Number of educated persons in the colony = 8/35 (70) = 16
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 40 - 10 = 30
Number of educated men and uneducated men are in the ratio 10:30 => 1:3
Answer: E
Answer: (E) 1ratio 3
Question: A card is drawn from a pack of 52 cards. The probability of not getting a face card?
(A) 9/13
(B) 5/12
(C) 3/13
(D) 6/17
(E) 1/13
Rationale: Clearly in the 52 cards other than face cards = 52-16 = 36
probability of not getting a face card = 36/52 = 9/13
correct option is A
Answer: (A) 9/13
Question: How many 3-digit positive integers are there, where each digit is positive, and no 3 adjacent digits are same?
(A) 1236
(B) 504
(C) 4096
(D) 4608
(E) 6561
Rationale: First digit.. 9 posibilities
Second digit, 8 possibilities
third digit, 7 possibilities
9*8*7 = 504.
B
Answer: (B) 504
Question: Starting from his house one day, a student walk at a speed of 2 kmph and reaches his school 10 minutes late. Next he increased his speed by 1 kmph and reaches the school 10 minutes early. How far is the school from his house?
(A) 1km
(B) 2km
(C) 3km
(D) 4km
(E) 5km
Rationale: Let the distance be x km
Difference in timings = 20 min = 20/60 = 1/3 hr
x/2-x/3 = 1/3
x = 2km
Answer is B
Answer: (B) 2km
Question: Calculate how many seconds it eill take for 4 bells to toll together again, given that they begin to toll together respectively at the intervals of 2, 5, 8 and 11 seconds. ?
(A) 440
(B) 420
(C) 410
(D) 442
(E) 422
Rationale: LCM of 2, 5, 8 and 11 is
440
LCM=440
ANSWER:A
Answer: (A) 440
Question: When two dice are tossed, what is the probability that the total score is a prime number?
(A) 1/6
(B) 3
(C) 5/12
(D) 7/12
(E) 9/12
Rationale: Total number of outcomes possible=36
probability of total score is a prime number=15
P(E) =15/36=5/12
ANSWER:C
Answer: (C) 5/12
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of6% p.a. was Rs.370.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.
(A) Rs.3360.80
(B) Rs.3370.80
(C) Rs.3320.70
(D) Rs.3230.80
(E) Rs.3130.80
Rationale: Let the sum be Rs.P
P{ [ 1 + 6/100]2 - 1 } = 370.80
P(6/100)(2 +6/100) = 370.80 [a2 - b2 = (a - b) ( a + b)] P = 246 / (0.05)(2.05) = 3000. Amount =Rs.3370.80. Answer :B
Answer: (B) Rs.3370.80
Question: A team has to design a flag. The team has six blue strips of cloth and seven red strips of cloth that they must use as is to make the flag. How many different flags can the team design with the materials at hand?
(A) 42
(B) 120
(C) 720
(D) 1,716
(E) 5,040
Rationale: The # of permutations of total 6+7=13 strips where 6 are identical blue and 7 are identical red is 13!/(6!*7!)=1716 (note that they must use all the materials at hand, also I guess that the strips must be either only vertical or only horizontal).
Answer: D.
Answer: (D) 1,716
Question: The area of a rhombus is equal to the area of a rectangle whose length is 20cm and the breadth is 10cm. If one of the diagonals is 32cm what is the length of other diagonal?
(A) 10
(B) 12.5
(C) 15
(D) 16
(E) 17.5
Rationale: Area of rectangle=20x10=200cmÂ²
Let 'l' the length of other diagonal = 0.5x32xl = 200
which gives x=12.5cm
Answer: B
Answer: (B) 12.5
Question: An investor bought a 1-year $6,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
(A) $480
(B) $489.60
(C) $634.64
(D) $800.32
(E) $240
Rationale: 1.04*1.04*6000 = $6489.60
The answer is B.
Answer: (B) $489.60
Question: A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B ?
(A) 160 km
(B) 180 km
(C) 200 km
(D) 220 km
(E) None
Rationale: Solution
Speed Downstream	= (14 + 4) km/hr
= 18 km/hr.
Speed upstream	=(14 - 4) km/hr
= 10 km/hr..
Let the distance b/w A and B
be xkm.Then	=(x/18+ x/2 / 10)
= 19
= 19x / 180 = 19
x= 180.
Answer B
Answer: (B) 180 km
Question: The distance between two towns is 380 km. At the same moment, a passenger car and a truck start moving towards each other from different towns. They meet 4 hours later. If the car drives 5 km/hr faster than the truck, what are their speeds?
(A) 50 and 45
(B) 45 and 50
(C) 30 and 35
(D) 35 and 30
(E) 40 and 50
Rationale: The main idea used in this kind of problems is that the distance equals speed multiplied by time S=V⋅t
V (km/hr) t (hr) S (km)
Car x + 5 4 4(x +5)
Truck X 4 4x
4(x+5)+4x=380
4x+4x=380−20
8x=360
x=3608
x=45
Therefore the truck's speed is 45 km/hr, and the car's speed is 50 km/hr.
So answer is B.
Answer: (B) 45 and 50
Question: Fred can fill K cans of water in 5 minutes. If there are T cans of water in one gallon, how many gallons can Fred fill in 35 minutes?
(A) 7K/T
(B) 7KT
(C) 7T/K
(D) 35KT
(E) 35T/K
Rationale: Fred can fill this number of cans in 35 minutes: (35/5)K = 7K.
One can is 1/T gallons.
Fred can fill 7K*(1/T) = 7K/T gallons of water in 35 minutes.
The answer is A.
Answer: (A) 7K/T