divelab/Sys2Bench huggingface dataset:
Question: Square X is inscribed in circle Y. If the perimeter of X is 100, what is the circumference of Y?
Options:
A)30√ 2π
B)2√ 2π
C)5√ 2π
D)4√ 2π
E)25√ 2π
Rationale: square forms two right angled triangles.
Any time we have a right angle triangle inside a circle, the hypotenuse is the diameter.
hypotenuse here = diagonal of the square = 25 sqrt(2) = diameter
=> radius = 12.5 sqrt(2)
Circumference of the circle = 2pi r = 25 pi sqrt(2)
Answer is E.
Answer: E
Question: A painting is painted on a cardboard 19 cm and 14 cm wide, such that there is a margin of 1.5 cm along each of its sides. Find the total area of the margin.
Options:
A)80
B)85
C)88
D)90
E)92
Rationale: Length of the cardboard = 19 cm
Breadth of the cardboard = 14 cm
Area of the cardboard = 19 × 14 cm² = 266 cm²
Length of the painting excluding the margin = [19 - (1.5 + 1.5)] cm = 16 cm
Breadth of the painting excluding the margin = 14 - (1.5 + 1.5) = 11 cm
Area of the painting excluding the margin = (16 × 11) cm² = 176 cm²
Therefore, area of the margin = (266 - 176) cm² = 90 cm²
ANSWER : OPTION D
Answer: D
Question: When processing flower-nectar into honey bees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 30% water?
Options:
A)1.2 kg
B)1.5 kg
C)1.4 kg
D)1.9 kg
E)None of these
Rationale: Explanation :
Flower-nectar contains 50% of non-water part.
In honey this non-water part constitutes 70% (100-30).
Therefore 0.5 X Amount of flower-nectar = 0.70 X Amount of honey = 0.70 X 1 kg
Therefore amount of flower-nectar needed =
(0.70/0.51)kg=1.4 kgs
Answer : C
Answer: C
Question: The variables a and b are non-zero integers W. If a = 2b^3/c, what happens to c when a is halved and b is doubled?
Options:
A)c is not changed.
B)c is halved.
C)c is doubled.
D)c is multiplied by 4.
E)c is multiplied by 16.
Rationale: a=2b^3/c
c=2b^3/a
when a is halved and b is doubled
c=2(2b)^3/(a/2)
c=16*2b^3/a
Ans. E c is multiplied by 16.
Answer: E
Question: A certain psychologist charges $40 more for the first hour of therapy than for each additional hour. If the total charge to a patient who receives 5 hours of therapy is $375, what is the total charge to a patient who receives only 2 hours of therapy ?
Options:
A) $120
B) $135
C) $150
D) $174
E) $192
Rationale: Let the charge for first hour = x+40
then charge for each additional hour = x
x+40 + 4x = 375
=> 5x = 335
=> x = 67
Total charge for patient for 3 hours of therapy = x+40 + x = 2x+40
= 174 $
Answer D
Answer: D
Question: 20% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair?
Options:
A)25
B)30
C)50
D)55
E)60
Rationale: 20% of employees are women with fair hair.
40% of fair-haired employees are women.
So,
20% * Employees = 40% * Fair Haired Employees (because both are equal to the number of fair haired women employees)
(1/2) * Employees = Fair Haired Employees
Answer (C)
Answer: C
Question: At 11:00 a.m., Tom begins traveling on a certain bike path from Riverdale at a constant rate of 10 mph. If, at 1:00 p.m., Jim begins traveling from Riverdale on the same path at a constant rate of 20 mph, at what time will he catch up to Peter?
Options:
A)3:00 p.m.
B)4:00 p.m.
C)5:00 p.m.
D)6:00 p.m.
E)7:00 p.m.
Rationale: By the time Jim starts, Tom has already covered = 2 hr * 10 mph = 20 miles
Relative speed = 20- 10 = 10mph
To catch up, Jim needs to cover 20 miles which can be covered in = 20/10= 2 hours
If Jim leaves at 1 pm, he will catch Tom at 3 pm
Answer: A
Answer: A
Question: Students are in cultural program as follows: music-10, Dance-15, and skits -6. No student is in all three cultural program , but 4 are in both music and Dance, 3 are in both music and skits, and 2 are in Dance and skits.
How many different students are in at least one of the three cultural program?
Options:
A)34
B)28
C)26
D)22
E)18
Rationale: Total students = M + D + S - (sum of 2-group overlaps) + (all three)
Total students = 10 + 15 + 6 - (3 + 4 + 2) + 0 = 22 students.
Answer is D
Answer: D
Question: You are distributing vegetable oil. there are 21 bottles in total out of which 7 are full, 7 half empty, 7 empty. the oil has to be distributed among three people. how will you distribute so that each person gets equal number of bottles and the same quantity of oil
Options:
A)1st person : 3 full, 1 half, 3 empty , 2nd person: 3 full, 1 half, 3 empty,, 3rd person : 1 full, 5 half, 1 empty
B)1st person : 1 full, 1 empty ,1half , 2nd person: 3 full, 1 half, 2 empty, 3rd person : 1 full, 2 half, 4 empty
C)1st person : 1 full, 2 half, 3 empty , 2nd person: 3 full, 1 empty , 3 empty, 3rd person : 3 full, 5 half, 2 empty
D)1st person : 1 full, 1 half, 2 empty , 2nd person: 2 full, 1 half, 1 empty, 3rd person : 1 full, 5 half, 2 empty
E)None
Rationale: Correct Answer : A
Answer: A
Question: Two cars start at the same time from opposite ends of a highway that is 45 miles long. One car is riding at 14 mph and the second car is riding at 16 mph. How long after they begin will they meet?
Options:
A)1
B)1.2
C)1.25
D)1.35
E)1.5
Rationale: As cars are moving in opposite directions their speeds will be added. So their relative speeds: 16+14 = 30 mph
Total distance to be covered = 45 miles.
Time taken would be: 45 miles/30 mph = 1.5 hours
E is the answer.
Answer: E
Question: If 3x=8y=z, what is x+y, in terms of z?
Options:
A)z/2
B)2z
C)11z/24
D)3z/5
E)z/9
Rationale: 3x=8y=z
x = z/3
and y = z/8
x+y = z/3 + z/8 = 11z/24
Answer is C
Answer: C
Question: A man walks from B to C, a distance of x miles, at 10 miles per hour and returns at 15 miles per hour. What is his average speed?
Options:
A)10 mph
B)12 mph
C)8.8 mph
D)8.4 mph
E)14 mph
Rationale: Total distance covered = 2x
Time taken12miles / hour = x/15 hrs
Time taken @ 8 miles / hour = x/10 hrs
Avg speed = 2x / (x/10 + x/15) = 12 mph
Ans is B
Answer: B
Question: When x is divided by y, the quotient is z with remainder t. Which of the following is equal to t?
Options:
A)yz – x
B)y/x−z
C)x – y – z
D)x – yz
E)zx – y
Rationale: (x/y)=z(+t)
(18/8)=2(+2)
x-yz
which is 18-(8*2)=2
Answer is D
Answer: D
Question: A list of numbers has six positive integers. Three of those integers are known: 4, 5 and 24 and three of those are unknown: x, y and z. The three unknowns are known to be distinct. It is also known that the mean of the list is 10 and the median lies between 7 and 8 (exclusive). Which of the following CANNOT be the value of any one of the unknowns?
Options:
A)13
B)12
C)11
D)10
E)5
Rationale: Mean = 10
Therefore sum of the 6 digits = 6*10 = 60 -------- (1)
The 3 digits are 4,5 & 24 -------------- (2)
Now, 7 < median < 8
-> 7 < (sum of 2 digits)/2 < 8
-> 14 < (sum of 2 digits) < 16
Therefore the sum of 2 digits = 15.
The 2 digits whose sum is 15 & whose median is b/w 7 & 8 can be :
1. 7, 8,
2. 6, 9,
3. 5, 10, or
But as soon as we take 4, 11 -> the series becomes 4,4,5,11,12,24 &
11 pairs up with 5 to give median as 8.
Hence the number can't be 11 !!
Answer : C
Answer: C
Question: Find the number of ways of arranging the boy and 12 guests at a circular table so that the boy always sits in a particular seat?
Options:
A)3!
B)8!
C)11!
D)12!
E)14!
Rationale: Ans.(D)
Sol. Total number of persons = 13 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 12 places => 12! Ways ... The number of required arrangements = 12! x 1= 12! = 12! ways
Answer: D
Question: A survey was conducted to find out how many people in a housing colony of 144 residents could swim, dance and drive a car. It was found that the number of people who could not swim was 85, the number of people who could not dance was 100 and that the number of people who could not drive a car was 91. If the number of people who could do at least two of these things, was found to be 37 and the number of people who could do all these things was found to be 6, how many people could not do any of these things?
Options:
A)28
B)31
C)33
D)35
E)37
Rationale: T=n(A)+n(B)+n(C)-n(Exactly two of the events)-2*n(All 3 Events)+n(None of the events)
T=144
n(A)=T-n(A')=144-85=59
n(B)=T-n(B')=144-100=44
n(C)=T-n(C')=144-91=53
n(Exactly two of the events)=n(At least 2 Events)-n(All 3 Events)=37-6=31
n(All 3 Events)=6
144=59+44+53-31-2*6+n(None of the events)
n(None of the events)=144-55-44-53+31+12=31
Ans:B
Answer: B
Question: Excluding stoppages, the speed of a train is 54 kmph and including stoppages it is 40 kmph. Of how many minutes does the train stop per hour?
Options:
A)A)13.55
B)B)14.55
C)C)15.55
D)D)16.55
E)E)17.55
Rationale: Explanation:
T = 14/54 * 60 = 15.55
Answer: Option C
Answer: C
Question: Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?
Options:
A)635.50
B)635.58
C)635.52
D)635.59
E)635.51
Rationale: 4000
200 ---- I
200
10 ---- II
---------------
4410
2210
--------
2000
110 ---- III
110
5.50 ---- IV
-----------
2425.50
2210
-----------
4635.50
4000
----------
635.50
Answer: A
Answer: A
Question: In a group of ducks and cows, the total number of legs are 28 more than twice the number of heads. Find the total number of cows.
Options:
A)14
B)12
C)16
D)8
E)6
Rationale: Explanation :
Let the number of ducks be d
and number of cows be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 28 more than twice the number of heads
=> 2(d + 2c) = 28 + 2(c + d)
=> d + 2c = 14 + c + d
=> 2c = 14 + c
=> c = 14
i.e., total number of cows = 14
Answer : A
Answer: A
Question: If i is a positive integer and i^2 is divisible by 12, then the largest positive integer that must divide i ^3 is
Options:
A) 2^3
B) 2^6
C) 3^3
D) 6^3
E) 12^2
Rationale: Since i is an integer so i cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making i^2 as a multiple of 12))
i^2 is divisible by 12 (12 = 2*2*3), So, i should have at least one 2 and one 3 so that i^2 has a 2^2 and two 3
So, i will have a 2 and a 3. Or i will be a multiple of 6
So, largest possible integer than should divide i^3 is 6^3
So, Answer will be D
Answer: D
Question: What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, & the last is three times the second?
Options:
A)1234
B)1567
C)1349
D)1456
E)1356
Rationale: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C
Answer: C
Question: A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers D are possible?
Options:
A)2
B)4
C)6
D)3
E)Not possible
Rationale: Firstly , we should note that 1 is NEITHER a prime nor a composite number.The first composite number is 4.Thus, when the problem states that there are 4 factors that are not composite, these nos are 1,2,3,5. Thus, the given number = 2^a*3^b*5^c. Also, (a+1)*(b+1)*(c+1) = 32. We can break down 32 into 3 integers as : 2*2*8 or 4*4*2
Also, the only possible combinations for a,b,c are : 3,3,1 OR 1,1,7. Thus, each combination has 3 possible orders and we have a total D of 6 possibilities.
C.
Answer: C
Question: Pat, kate and mark charged a total of 180 hours to a certain project . If pat charged twice as much time to the project as kate and 1/3 as much times as mark, how many more hours did mark charge to the project than kate.
Options:
A)18
B)36
C)72
D)90
E)100
Rationale: Let Kate charge for x hours,
then Pat charged for 2x and Mat - for 6x.
So, 2x+6x+x = 180 -total hours charged for,
x= 20.
Mat charged 6x-x or 5x for more hours than kate, or for 100 hours .
E is correct
Answer: E
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 600 m long?
Options:
A)266 Sec
B)180 Sec
C)776 Sec
D)166 Sec
E)997 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1800 m
T = D/S
T = 1800/10
T = 180 Sec
Answer: B
Answer: B
Question: A train 210 m in length crosses a telegraph post in 13 seconds. The speed of the train is?
Options:
A)77 kmph
B)55 kmph
C)54 kmph
D)58 kmph
E)76 kmph
Rationale: S = 210/13 * 18/5
= 58 kmph
Answer: D
Answer: D
Question: From January 1, 1991, to January 1, 1993, the number of people enrolled in health maintenance organizations increased by 30 percent. The enrollment on January 1, 1993, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 1991 ?
Options:
A) 35
B) 39
C) 40
D) 41
E) 42
Rationale: 1.30x=45 --> 13/10*x=45 --> x=45*10/13=450/13=~35.
Answer: A.
Answer: A
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
Options:
A)20/8 sec
B)20/4 sec
C)20/7 sec
D)22/7 sec
E)60/7 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 100/35 = 20/7 sec.Answer:C
Answer: C
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. 36, what is the total amount?
Options:
A)166
B)140
C)178
D)177
E)169
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 36
35 --- ? => 140
Answer: B
Answer: B
Question: If there are ten positive real numbers n1 < n2 < n3 … < n10, how many triplets of these numbers (n1, n2, n3), (n2, n3, n4) … can be generated such that in each triplet the first number is always less than the second number, and the second number is always less than the third number?
Options:
A)45
B)90
C)120
D)180
E)150
Rationale: Three numbers can be selected and arranged out of ten numbers in 10P3 ways=10!/7!=10*9*8. Now this arrangement is restricted to a given condition that first number is always less than the second number, and the second number is always less than the third number. Hence three numbers can be arranged among themselves in 3! ways.
Required number of arrangements=(10*9*8)/(3*2)=120
ANS:C
Answer: C
Question: A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
Options:
A)278
B)277
C)278
D)450
E)272
Rationale: 10 * 150 = 1500
3 * 100 + 5 * 150 = 1050
1500 – 1050 = 450
Answer:D
Answer: D
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 48km/h, what is the circumference of the tire?
Options:
A)7 meters
B)9 meters
C)8 meters
D)2 meters
E)3 meters
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 48,000 m : C is the circumference
C = 2 meters
correct answer D
Answer: D
Question: Anil and Suresh are working on a special assignment. Anil needs 6 hours to type 32 pages on a computer and Suresh needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 110 pages?
Options:
A)7 hour 15 minutes
B)7 hour 30 minutes
C)8 hour 15 minutes
D)8 hour 30 minutes
E)8 hour 45 minutes
Rationale: Explanation :
Pages typed by Anil in 1 hour = 32/6 = 16/3
Pages typed by Suresh in 1 hour = 40/5 = 8
Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3
Time taken to type 110 pages when Anil and Suresh work together = 110 × 3 /40 = 33/4
= 8 ¼ hours = 8 hour 15 minutes
Answer : Option C
Answer: C
Question: When positive integer X is divided by positive integer Y, the remainder is 5.76. If X/Y = 96.12, what is the value of Y?
Options:
A)96
B)75
C)48
D)25
E)12
Rationale: When positive integer x is divided by positive integer y, the remainder is 5.76 --> x=qy+5.76;
x/y=96.12 --> x=96y+0.12y (so q above equals to 96);
0.12y=5.76 --> y=48.
Answer: C.
Answer: C
Question: The sum of 33 consecutive integers is 3333. What is the greatest integer in the set?
Options:
A)113
B)115
C)117
D)119
E)121
Rationale: Let x be the first integer in the set, then x+32 is the largest integer.
The sum is: x+(x+1)+(x+2)+...+(x+32)
= 33x + 32*33/2
= 33(x+16)
Then x+16=101
x=85
The largest integer in the set is 85+32=117
The answer is C.
Answer: C
Question: Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 1.3 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
Options:
A)7/17
B)13/33
C)7/15
D)17/35
E)1/2
Rationale: The easiest way for me is to plug in numbers.
Let the number of basic stereos produced be 40, and number of delux stereos produced be 20. Total of 60 stereos.
If it takes an hour to produce a basic stereo then it will take 1.3 hours to produce a deluxe stereo.
40 basic stereos = 40 hours.
20 delux stereos = 26 hours.
Total hours = 66.
Then the fraction would be 26/66 = 13/33. Therefore answer B
B.
Answer: B
Question: A profit of Rs. 1000 is divided between X and Y in the ratio of 1/2:1/3 . What is the difference between their profit shares ?
Options:
A)s. 200
B)s. 100
C)s. 300
D)s. 50
E)s. 90
Rationale: A profit of Rs. 1000 is divided between X and Y in the ratio of 1/2 : 1/3 or 3:2.
so profits are 600 and 400.
difference in profit share = 600-400=200
ANSWER:A
Answer: A
Question: A store raised the price of an item by exactly 30 percent. Which of the following could NOT be the resulting price of the item?
Options:
A)19.5
B)195
C)325
D)168
E)18.2
Rationale: If it raised the value by 30% then the resulting price is 1.3 times the original price. So the final answer has to be a multiple of 1.3. Check the answers.
19.5 - Yes
195 - Yes
325 - Yes
168 - No
18.2 - Yes
Answer : D
Answer: D
Question: A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium.If the company declares 8% dividend at the end of the year,then how much does he get ?
Options:
A)Rs. 500
B)Rs. 600
C)Rs. 960
D)Rs. 720
E)None
Rationale: Solution
Number of shares = (14400/120) = 120.
Face value = Rs. (100x120 ) = Rs. 12000.
Annual income = Rs.(8/100x12000) = Rs. 960.
Answer C
Answer: C
Question: Of the following, which is the closest approximation of (50.2*0.49)/199.8 ?
Options:
A)0.121
B)0.125
C)0.122
D)0.123
E)0.124
Rationale: Ans: For approximation (50.2$ \times $0.49)/199.8 can be taken as
50$ \times $0.5/200 = 25/200 = 1/8 = 0.125
Answer:B
Answer: B
Question: At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number T of different possible seating arrangements for the group?
Options:
A)5
B)10
C)24
D)32
E)120
Rationale: Circular arrangements= (n-1)!
Hence (4!) = 24=T
Answer is C
Answer: C
Question: A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 35%, what should be the sale price of the mixed tea?
Options:
A)23.75
B)21.6
C)20
D)19.2
E)None of these
Rationale: C.P. of mixture = 80×15+20×20 /80+20=16
∴ S.P. = (100+35)/100×16=21.6
Answer B
Answer: B
Question: A train 125 m long passes a man, running at 8 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Options:
A)36
B)53
C)88
D)66
E)22
Rationale: Speed of the train relative to man
= (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 8) km/hr. x - 8
= 45 ==> x
= 53 km/hr.
Answer:B
Answer: B
Question: 2 pipes A and B can separately fill a cistern in 10 and 15 mins respectively. A person opens both the pipes together when the cistern should have beenwas full he finds the waste pipe open. He then closes the waste pipe and in another 4mins the cistern was full. In what time can the waste pipe empty the cistern when fill?
Options:
A)6
B)8
C)9
D)10
E)12
Rationale: 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
B
Answer: B
Question: An atom's atomic number is determined by the number of:
Options:
A)neutrons minus protons
B)protons
C)electrons
D)neutrons
E)WW2
Rationale: protons
Answer:B
Answer: B
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
A)6
B)7
C)5
D)8
E)9
Rationale: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2
= 8 kmph
Answer: D
Answer: D
Question: A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?
Options:
A)11
B)5
C)70
D)11
E)13
Rationale: x/24 + x/30 + x/40 = 1
x = 11 days
Answer:D
Answer: D
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
Options:
A)65 cm2
B)30 cm2
C)76 cm2
D)68 cm2
E)46 cm2
Rationale: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle
= 6 * 5
= 30 cm2
Answer: B
Answer: B
Question: If x > 0.6, which of the following could be the value of x?
Options:
A)√0.6
B)√0.007
C)√0.006
D)√0.008
E)√0.009
Rationale: Answer : A
Answer: A
Question: Joseph completes work worth $3.25 in hour and his cost to company per hour is $2.85. Ray completes worth worth of $2.80 in an hour and his cost to company is $2.65 per hour. If Joseph works for 55,000 hours, how many must Ray work so that company makes at least as much in total gross profit as in case of Joseph ?
Options:
A)7,858
B)8,301
C)14,667
D)63,840
E)146,667
Rationale: Joseph : Profit/hour = 3.25-2.85 = 0.4
: No of hours = 55,000
: Gross Profit = 55,000*0.4 = 22,000
Ray : Profit/hour = 0.15
: Gross Profit = 22,000
: No of hours = 22,000/0.15 = 220,000/1.5 (only closes is 146,667)
Answer E
Answer: E
Question: The simple form of the ratio 4/5:8/9 is?
Options:
A)5:8
B)4:9
C)5:9
D)5:3
E)9:10
Rationale: 4/5 : 8/9 = 9:10
Answer: E
Answer: E
Question: If 0.8 of a number is equal to 0.09 of another number, the ratio of the numbers i
Options:
A)2 : 3
B)3 : 4
C)9 : 80
D)20 : 3
E)None
Rationale: Sol.
0.8A = 0.09 B â‡” A / B = 0.09 / 0.8 = 9/80 = .
âˆ´ A : B = 9 : 80.
Answer C
Answer: C
Question: A, B, and C working alone can finish constructing a house in 6, 8, and 12 hours respectively. A starts alone and works for 1 hour. He is then joined by B and they work together for 1 hour. Finally C joins them and they all work together to finish the work. If they start working at 9 am, at what time will they finish?
Options:
A)11:36 am
B)11:48 am
C)12:05 pm
D)12:27 pm
E)12:43 pm
Rationale: A completes 1/6 of the job each hour.
B completes 1/8 of the work each hour.
C completes 1/12 of the work each hour.
A completes 1/6 of the work in the first hour.
Working together, A and B complete another 7/24 for a total of 11/24.
Working together, A, B, and C can complete 9/24 of the work each hour.
To complete 13/24, the time required is (13/24) / (9/24) = 13/9 hours.
The work will be completed at 12:00 plus 4*60/9 minutes which is about 12:27 pm.
The answer is D.
Answer: D
Question: Machine A working alone can complete a job in 10 hours. Machine A+B working alone can do the same job in 16 hours. How long will it take machine B working at their respective constant rates to complete the job?
Options:
A)20/3
B)80/3
C)50/4
D)90/11
E)23/7
Rationale: Machines ( A ) ( B ) (A+B)
---Time - 10 - ( - ) -(16)
---Rate 16--- 6 -- 10
--Work 160 --160 -160
A+B = (160/6) = 80/3
B
Answer: B