divelab/Sys2Bench huggingface dataset:
Question: The sum of two numbers is 56, and one of them is 12 more than the other. What are the two numbers?
Options:
A)36-48
B)22-34
C)60-24
D)42-42
E)21-63
Rationale: In this problem, we are asked to find two numbers. Therefore, we must let x be one of them. Let x, then, be the first number.
We are told that the other number is 12 more, x + 12.
The problem states that their sum is 56:
word problem = 56
The line over x + 12 is a grouping symbol called a vinculum. It saves us writing parentheses.
We have:
2x = 56 âˆ’ 12
= 44.
x = 44/2
= 22.
This is the first number. Therefore the other number is
x + 12 = 22 + 12 = 34.
The sum of 22 + 34 is 56.
B
Answer: B
Question: Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $200 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $245 as interest. What was the value of his total savings before investing in these two bonds?
Options:
A)4000
B)3500
C)2500
D)3000
E)2000
Rationale: So, we know that Shawn received 20% of the amount he invested in a year. We also know that in one year Shawn received $100, thus 0.2x = $100 --> x = $1,000.
Since, he invested equal sums in his 2 bonds, then his total savings before investing was 2*$1,000 = $2,000
Answer E
Answer: E
Question: A man complete a journey in 10 hrs. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km?
Options:
A)876 km
B)224 km
C)657 km
D)176 km
E)168 km
Rationale: Let the total distance be x km.
Then, [(1/2 x) / 21 + (1/2 x) / 24] = 10
15x = 168 * 20 => x = 224 km.
Answer: B
Answer: B
Question: Find the sum of first 20 natural numbers
Options:
A)470
B)210
C)465
D)463
E)485
Rationale: Explanation:
Sum of n natural numbers
=n(n+1)/2
=20(20+1)/2=20(21)/2=210
Answer: Option B
Answer: B
Question: In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-3, 1), (1, 1), (1, -2) and (-3, -2)?
Options:
A)12
B)24
C)20
D)30
E)36
Rationale: Length of side 1= 3+1=4
Length of side 2= 2+1= 3
Area of rectangle= 4*3= 12
A is the answer
Answer: A
Question: If 6^k = 4, then 6^(2k+3) =
Options:
A)2925
B)3456
C)4581
D)3683
E)1308
Rationale: 6^k=4
6^2k=4^2
6^2k=16
6^(2k+3)
=6^2k*6^3
=16*216
=3456
Answer: B
Answer: B
Question: Magnabulk Corp sells boxes holding y magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, in cents, if Magnabulk charges m dollars for each crate?
Options:
A)100by/m
B)m/(by)
C)by/(100m)
D)100m/(by)
E)by/m
Rationale: We're given some facts to work with:
1) Magnabulk Corp sells boxes holding Y magnets each.
2) The boxes are shipped in crates, each holding B boxes.
3) Magnabulk charges M DOLLARS for each crate
We're asked for the price charged per magnet, in CENTS....
IF....
Y = 2
B = 3
M = 12
(2 magnets per crate)(3 crates) = 6 magnets
$12 for 6 magnets = $2 per magnet = 200 cents per magnet
So we're looking for an answer that equals 200 when Y=2, B=3 and M=12. There's only one answer that matches...
Answer is D
Answer: D
Question: If x and y are integers and 2x–y= 11, then 4x+ y CANNOT be
Options:
A)–5
B)1
C)13
D)17
E)55
Rationale: 2x-y=11
2x=11+y
4x=22+2y
now we need to check the value of 4x+4 => 22+2y+y=22+3y
hence 22+3y=value(in the options)
so y=value-22/3
so checking the options only D is unfit
ANSWER:D
Answer: D
Question: In how many ways can seven different rings be worn on four fingers of one hand?
Options:
A)10
B)12
C)35
D)16
E)18
Rationale: Required number of ways = ways of selecting 4 objects out of 7 given objects
= 7C4 = 7*6*5*4/24= 35
Answer C
Answer: C
Question: The ages of two person differ by 12 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages(in years) are respectively
Options:
A)30, 10
B)25, 5
C)29, 9
D)50, 30
E)20, 8
Rationale: Let their ages be x and (x + 12) years.
Then, 5(x - 5) = (x + 12 - 5)
=> 4x = 32
=>x =8
Their present ages are 20 years and 8 year.
ANSWER:E
Answer: E
Question: In a neighborhood having 90 households, 11 did not have either a car or a bike. If 14 households had a both a car and a bike and 44 had a car, how many had bike only?
Options:
A)30
B)35
C)20
D)18
E)10
Rationale: {Total}={Car}+{Bike}-{Both}+{Neither} --> 90=44+{Bike}-14+11 --> {Bike}=49 --> # those who have bike only is {Bike}-{Both}=49-14=35.
Answer: B.
Answer: B
Question: The volume of a box with a square base is 128 cubic cm. The area of the base of the box is 8 inches more than the height. What is the length of the base of the box?
Options:
A)4 cm
B)8 cm
C)16 cm
D)24 cm
E)None of the above
Rationale: l x w x h = 64
l x w - 8 = h
l=w
Solving the 3 equations we get Area of Base = 16 square cm and height = 8 cm, which means length = 4 cm and width = 4 cm
Correct Answer: A
Answer: A
Question: A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
Options:
A)588 apples
B)742 apples
C)750 apples
D)600 apples
E)700 apples
Rationale: Suppose originally he had X apples.
Then, (100 - 40)% of X = 420.
60/100 x X = 420
x =(420 x 100)/60= 700.
answer E
Answer: E
Question: In a certain random experiment, exactly one of the outcomes A, B, and T will occur. In each random experiment, the probability that outcome A will occur is 1/3 , and the probability that outcome B will occur is 1/3. What is the probability that when the random experiment is conducted 6 independent times, each of outcomes A, B, and T will occur twice?
Options:
A)5/243
B)1/12
C)10/81
D)1/6
E)16/81
Rationale: Number of ways in which a group of 2A,2B,2T can be formed in any order = 6!/(2!*2!*2!) [ formula for total of 6 items with 2 each of similar kind)
Total number of ways in which the die can be thrown independently = _ _ _ _ _ _ ; there are 6 places .First can be filled in 3 different ways A/B/T; Second in 3 diff ways again and so on.
So total number of ways = 3X3X3X3X3X3 = 3^6
There fore probability = 6!/(2!x2!x2!) by 3^6 = 90/3^6 = 10/81 Answer C
Answer: C
Question: A squirrel has 13 nuts, then he finds 8 more nuts. Now how many nuts he have?
Options:
A)5
B)9
C)21
D)11
E)16
Rationale: 13+8=21. Answer is C
Answer: C
Question: If a, p, q, and r are positive integers and (p)×(q)×(r)=a^2, which of the following could be the values of p, q, and r?
Options:
A)3, 16, 25
B)9, 25, 24
C)2, 25, 32
D)2, 9, 16
E)8, 16, 36
Rationale: This is one of those questions where using the given options is fastest way to get the solution. We need to find a set where 3 numbers can be paired into 2 pairs of some numbers because we need a product which is a square number.
C fits the bill. 2*25*32 = 2*5*5*8*4 = 5*5*8*8
ans C
Answer: C
Question: Four angles of a quadrilateral are in G.P. Whose common ratio is an intiger. Two of the angles are acute while the other two are obtuse. The measure of the smallest angle of the quadrilateral is
Options:
A)12
B)24
C)36
D)46
E)52
Rationale: Let the angles be a, ar, ar 2, ar 3.
Sum of the angles = a ( r 4- 1 ) /r -1 = a ( r 2 + 1 ) ( r + 1 ) = 360
a< 90 , and ar< 90, Therefore, a ( 1 + r ) < 180, or ( r 2 + 1 ) > 2
Therefore, r is not equal to 1. Trying for r = 2 we get a = 24
Therefore, The angles are 24, 48, 96 and 192.
ANSWER:B
Answer: B
Question: Jack and Christina are standing 270 feet apart on a level surface. Their dog, Lindy, is standing next to Christina. At the same time, they all begin moving toward each other. Jack walks in a straight line toward Christina at a constant speed of 4 feet per second and Christina walks in a straight line toward Jack at a constant speed of 5 feet per second. Lindy runs at a constant speed of 8 feet per second from Christina to Jack, back to Christina, back to Jack, and so forth. What is the total distance, in feet, that Lindy has traveled when the three meet at one place?
Options:
A)150
B)180
C)210
D)240
E)270
Rationale: The relative speed of Jack and Christina is 4 + 5 = 9 feet per second.
The distance between them is 210 feet, hence they will meet in (time) = (distance)/(relative speed) = 270/7 = 30 seconds.
For all this time Lindy was running back and forth, so it covered (distance) = (speed)*(time) = 8*30 = 240 feet.
Answer: D.
Answer: D
Question: In a T.V. factory, an average of 60TVs are produced per day for the fist 25days of the months. A few workers fell ill for the next five daysreducing the daily avg for the month to 58 sets/day. The average production perday for day last 5days is ?
Options:
A)36
B)39
C)48
D)50
E)53
Rationale: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 58 - 25 x 60
= 240
∴ Average for last 5 days = 240 / 5
= 48
C
Answer: C
Question: 14, 23, 32, 41, 50, 59, …
In the sequence above, each term is 9 more than the previous term. What is the 41st term Q of the sequence?
Options:
A)360
B)365
C)369
D)374
E)383
Rationale: First term , a= 14
Common difference , d = 9
nth term , tn = a + (n-1)d
41st term Q, t41 = a+ 40*d = 14 + 40*9 = 374
Answer D
Answer: D
Question: At exactly what time past 5:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time?
Options:
A)20 13/21 minutes past 7:00
B)20 13/17 minutes past 7:00
C)21 9/11 minutes past 5:00
D)21 9/11 minutes past 7:00
E)22 4/9 minutes past 7:00
Rationale: 5.5 is the angle between minute n hour, this is what I was taught...so shouldn't it be solve by dividing 90 with 5.5?
That would have been the case if your initial difference between the hour and the minute hand was = 0 degrees or in other words, both minute and hour hands were at the same location. But as per the question, you are asked for time AFTER 5:00. At 5:00, the angle between the hour and the minute hand is 210 degrees. you need to take this into account as well.
So in order for the difference to decrease to 90 degrees, the minute hand must eat away this difference of 210-90 = 120 degree at the rate of 5.5 degrees per minute ---> 120/5.5 = 21 9/11 minutes.
Thus, C is the correct answer.
Answer: C
Question: find the number, If 50 is subtracted from two-third of number, the result is equal to sum of 40 and one-fourth of that number.
Options:
A)214
B)216
C)114
D)116
E)118
Rationale: Explanation:
Let the number is x,
=>2/3x−50=1/4x+40
<=>2/3x−1/4x=90
<=>5x/12=90
<=>x=216
Option B
Answer: B
Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 900 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
Options:
A)8/3
B)3/8
C)8/5
D)4/1
E)5/3
Rationale: Distance traveled by Eddy = 900 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 900/3 = 300 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 300/75 = 4/1
Answer D
Answer: D
Question: To furnish a room in a model home an interior decorator is to select 3 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 100 different combinations are possible, how many tables are there in the warehouse?
Options:
A)A)5
B)B)8
C)C)10
D)D)15
E)E)30
Rationale: Total number of ways to choose 3 chairs from 5= 5C3=10
Total number of combination=100
That means we need get 10 combinations from the selection of tables....
Screening through the answers.... 5C2=10..... 10*10=100
Answer is 5... A
Answer: A
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit?
Options:
A)20000
B)22000
C)24000
D)25000
E)30000
Rationale: SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000
E
Answer: E
Question: Pipe A that can fill a tank in an hour and pipe B that can fill the tank in 15 are opened simultaneously when the tank is empty. Pipe B is shut 15 minutes before the tank overflows. When will the tank overflow?
Options:
A)40 mins
B)35 mins
C)30 mins
D)32 mins
E)36 mins
Rationale: The last 15 minutes only pipe A was open. Since it needs 1 hour to fill the tank, then in 15 minutes it fills 1/4th of the tank, thus 3/4 of the tank is filled with both pipes open.
The combined rate of two pipes is 1 + 4 = 5 tanks/hour, therefore to fill 3/4th of the tank they need (time) = (work)/(rate) = (3/4)/5 = 3/20 hours = 15 minutes.
Total time = 15 + 15 = 30 minutes.
Answer: C
Answer: C
Question: Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 1 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank.
Options:
A)37/20
B)1/2
C)1/4
D)1
E)5/6
Rationale: A+B =6/5 ; A+C =3/2 ,B+C =1 ; ADD THEN 2*(A+B+C) = 6/5+3/2+1 =37/10
A+B+C = 37/20 HRS
A
Answer: A
Question: What is the difference between the place value of 5 in the numeral 15295?
Options:
A)5005
B)495
C)4995
D)505
E)4115
Rationale: Difference between the place values of 5 = 5000-5 = 4995
Answer is C
Answer: C
Question: In a certain game, a player begins with a bag containing tiles numbered 1 through 9, each of which has an equal probability of being selected. The player draws one tile. If the tile is even, the player stops. If not, the player draws another tile without replacing the first. If this second tile is even, the player stops. If not, the player draws a third tile—without replacing either of the first two tiles—and then stops. What is the probability that at the conclusion of the game, the sum of the tiles that the player has drawn is odd?
Options:
A)5/18
B)13/36
C)3/8
D)5/8
E)23/36
Rationale: player begins with containing tiles 1 to 10 and have equal probability of selecting means
Proabability of selecting one number =1/10. here 5 even numbers and 5 odd numbers are there.
Next , player draws one title , if number is even player stops or otherwise title is odd without replacement
player draws second title.
If second title is even , player stops or title is odd without replacement player draws third title.
in third title , without replacement of first and second title, player draws and stops it.
the sum of tilte probability is odd. here two conditions are possible.
1st condition is
1st title is odd+ 2nd title is even stops= probability of selecting one title is 1/10*5c1.
Here are we are not selecting 1st condition as even stops because sum of tile is odd.
Here 5 odd numbers are there we can select 1out of 5 odd numbers.
without replacement of fist we select second tilte is even. is 5/10*5c1/9c1.
here we are selecting one number out of remaining 9 numbers. so probability is 5/18.
we are selecting 1 even number out of 5.
2nd condition is 1stodd without replacement,2nd odd without replacement and 3rd one also odd to get odd as sum of title.
Then probability is 5/10*4/9*3/8=1/12.
Finally sum of probability of two conditions is 5/18+1/12
=5/8.
so option D is correct.
Answer: D
Question: The probability is 1/2 that a certain coin turns up heads on any given toss. If the coin is tossed seven times, what is the probability that the coin turns up tails on at least one of the tosses?
Options:
A)7/8
B)15/16
C)31/32
D)63/64
E)127/128
Rationale: P(7 heads)= 1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128.
P(at least one tail)=1-1/128=127/128.
The answer is E.
Answer: E
Question: 5 goats’s and 10 hens are brought for Rs.2500. If the average price of a hen be Rs.50. What is the average price of a goat.
Options:
A)425
B)375
C)350
D)400
E)500
Rationale: Explanation:
Average price of a hen = Rs.50
total price of 10 hens = 10*50 = Rs.500
But total price of 5 goats and 10 hens = Rs. 2500
Total price of 5 goats is = 2500 - 500
= 2000
Average price of a goat = 2000/5
= Rs. 400
Answer: D
Answer: D
Question: The price of sugar is increased by 4%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure?
Options:
A)(300/103) %
B)(400/104) %
C)(100/107)%
D)(7/100)%
E)(100/700)%
Rationale: Old price = $100 (assume);
Old consumption = 1 kg (assume).
New price = $104.
We want the spendings to remain at $100.
(New consumption)*104 = 100 --> (New consumption) = 100/104 kg.
Percent decrease = Change/Original *100 = (1 - 100/104)/1*100 = 400/104%.
Answer: B.
Answer: B
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 14%?
Options:
A)20%
B)26%
C)42%
D)29%
E)22%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 86
2/3 SP1 = 86
SP1 = 129
100 --- 29 => 29%
Answer: D
Answer: D
Question: A reduction of 5% in the price of oil enables a house wife to obtain 10kgs more for Rs.5000, what is the reduced price for kg?
Options:
A)23
B)27
C)25
D)35
E)15
Rationale: 5000*(5/100) = 250 ---- 10
? ---- 1 => Rs.25
Answer:C
Answer: C
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 5:6then find the smallest number?
Options:
A)22/3
B)19/3
C)20/3
D)25/3
E)24/3
Rationale: 2:3
2x + 10 : 3x + 10 = 5 : 6
6[2x + 10] = 5[3x + 10]
12x + 60 = 15x + 50
15x -12x = 60 - 50
3x = 10, then X=10/3
Then the first number is = 2
2x = 10
Option C
Answer: C
Question: Solve the equation:
|(2x + 1)2 - 4x2 - 2| - 3|4x – 1| = - 6
Options:
A)-1/2
B)1/2
C)-3/4
D)3
E)None
Rationale: Solution:
|(2x + 1)2 - 4x2 - 2| – 3|4x -1| = - 6 <=>
|4x2 + 4x + 1 - 4x2 - 2 | - 3|4x - 1| = - 6 <=>
|4x – 1| - 3|4x – 1| = - 6 <=> -2|4x – 1| = - 6 <=>
|4x – 1| = 3 <=> 4x - 1 = 3 or 4x - 1 = -3
Therefore x = 1 or x = -1/2
Answer A
Answer: A
Question: How many positive integers less than 500 can be formed using the numbers 1,2,3,and 5 for digits, each digit being used only once.
Options:
A)22
B)34
C)73
D)26
E)11
Rationale: Single digit numbers = 4
Double digit numbers = 4 x 3 = 12
Three digit numbers = 3 x 3 x 2 x 1 = 18
Total = 34
Answer:B
Answer: B
Question: A, B and C enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4. After 2 months, A withdraws half of his capital and after 10 months, a profit of Rs. 378 is divided among them. What is B's share ?
Options:
A)144
B)265
C)177
D)156
E)199
Rationale: Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.
Let their initial investments be 6x, 2x and 3x respectively.
A : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.
B's share = Rs. (378 * 8/21) = Rs. 144.
Answer: A
Answer: A
Question: The LCM of two numbers is 2310 and HCF is 61. If one of the numbers is 210. Then what is the other number ?
Options:
A)715
B)671
C)330
D)582
E)465
Rationale: First number * Second Number = LCM * HCF
Other number = 2310 * 61 / 210 = 11*61 = 671
ANSWER :B
Answer: B
Question: Three integers are at random chosen between 0 and 9 inclusive. What is the probability Q that each number is different ?
Options:
A)A.18/25
B)B.4/5
C)C.81/100
D)D.9/10
E)E.1
Rationale: Number of ways of choosing the 3 integers without restriction = 10 * 10 * 10
Number of ways of choosing the 3 integers so that the 3 integers are different = 10 * 9 * 8
Probability Q= 10 * 9 * 8/10 * 10 * 10 = 72/100 = 18/25
Answer: A
Answer: A
Question: If n = 3^10 – 2^10 which of the following is NOT a factor of n?
Options:
A)43
B)437
C)23
D)19
E)373
Rationale: 3^10 - 2^10
= (3^5)^2 - (2^5)^2
=(3^5 + 2^5)(3^5- 2^4)
=(405+32(405-32)
=437*373
=19*23*373
Therefore, 43 is Not a factor of n.
A
Answer: A
Question: A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 60 meters, what is the height of the building (in meters)?
Options:
A)20
B)24
C)28
D)32
E)36
Rationale: The height:length ratio will be equal in both cases.
18 / 45 = x / 60
x = 24
The answer is B.
Answer: B
Question: If the volume of two cubes are in the ratio 27:1, the ratio of their edges is:
Options:
A)3:1
B)3:2
C)3:5
D)3:7
E)None of these
Rationale: Explanation:
Let the edges be a and b of two cubes, then
a3/b3=27/1
=>(a/b)3=(3/1)3
a/b=3/1
=>a:b=3:1
Option A
Answer: A
Question: The length of a train and that of a platform are equal. If with a speed of 72 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
Options:
A)600
B)799
C)719
D)750
E)712
Rationale: Speed = [72 * 5/18] m/sec = 20 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 20 Ã¨ x = 20 * 60 / 2 = 600
Answer: A
Answer: A
Question: Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 11km apart, if they walk in the same direction?
Options:
A)15 hours
B)16 hours
C)17 hours
D)20 hours
E)22 hours
Rationale: The relative speed of the boys = 5.5kmph â€“ 5kmph
= 0.5 kmph
Distance between them is 11 km
Time = Distance/Speed
Time=11km / 0.5 kmph = 17 hrs
answer :E
Answer: E
Question: A certain kind of fuel is 1515high octane and 4545regular octane. If high octane costs three times as much as regular octane, what fraction of the cost of the fuel is due to the high octane?
Options:
A)1/5
B)2/3
C)3/7
D)3/5
E)4/5
Rationale: let x be the amount of fuel
high octane = x/5
regular = 4x/5
price of regular = y
price of high octante = 3y
cost of high octane in the fuel = 3y * x/5
total cost = 3y * x/5 + 4x/5 * y
% = cost of high octante / total cost
= 3/7
Answer is C
Answer: C
Question: One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 8 robots altogether, if the robots build only one robot at a time?
Options:
A)70 min
B)94 min
C)110 min
D)131 1/7 min
E)146 1/7 min
Rationale: First the 2 robots work at the rate of
1 + 1/2 = 3/2
so they complete one robot in 2/3 rd of an hour = 40 minutes - (1)
Now the 3 robots work together at the rate of
1 + 1/2 + 1/2 = 4/2 = 2/1
so they complete one robot in 1/2 an hour,i.e 30 minutes - (2)
Now the 4 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2 = 5/2
so they complete one robot in 2/5th of an hour - (3)
Now the 5 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2+1/2 = 3
so they complete one robot in 1/3th of an hour - (4)
Now the 6 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2=7/2
so they complete one robot in 2/7th of an hour - (5)
Now the 7 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2=9/2
so they complete one robot in 2/9th of an hour - (6)
And now we have 8 robots
So Total = (1) + (2) + (3)+(4)+(5) + (6) = 146 1/7minutes
Answer - E
Answer: E
Question: Rice weighing 35/2 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each container? (Note that 1 pound = 16 ounces)
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: 35/2 ÷ 4 = 35/8 pounds in each container
35/8 pounds * 16 ounces / pound = 70 ounces in each container
The answer is D.
Answer: D
Question: Oil cans x and y are right circular cylinders and the height and radius of y are each twice those of x. If the oil in can x filled to capacity sells for $3, how much does the oil in y sell for if y is only half filled?
Options:
A)$11
B)$12
C)$13
D)$14
E)$18
Rationale: formula for vol of a cyl is PI*r^2*h
so Vy = 8*Vy
y when half filled will cost 4 times x so ans is B
Answer: B
Question: What is the area of a square field whose diagonal of length 22 m?
Options:
A)287
B)269
C)270
D)242
E)230
Rationale: d2/2 = (22 * 22)/2
= 242
Answer:D
Answer: D
Question: If the average of t, b, c, 14 and 15 is 12. What is the average value of t, b, c and 29
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: t+b+c+14+15 = 12*5 = 60
=>t+b+c = 60-29 = 31
t+b+c+29 = 31+29= 60
Average = 60/4 = 15
Answer D
Answer: D