divelab/Sys2Bench huggingface dataset:
Question: In a barrel of juice there is 60 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?
Options:
A)3:2.
B)1:1.
C)3:1.
D)4:3.
E)3:4.
Rationale: Juice barrel : beer Barrel = 60:80 i.e. 3:8
price of Juice : Price of Beer = 3 : 4
so for 6/8 costs 3/4, ie 6J / 8B = 3/4.
Solving for J/B, we get 2:2=1:1
Answer B.
Answer: B
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required?
Options:
A)34
B)40
C)68
D)88
E)None
Rationale: Solution
We have:L =20 ft and lb = 680 sq.ft	b = 34ft
Length of fencing	= (l + 2b)
= (20 + 68)ft
= 88 ft.
Answer D
Answer: D
Question: A river 2m deep and 45 m wide is flowing at the rate of 3 kmph the amount of water that runs into the sea per minute is?
Options:
A)4500 M3
B)4580 M3
C)I8500 M3
D)4900 M3
E)4700 M3
Rationale: Explanation:
(3000 * 2 * 5)/60 = 4500 M3
Answer: Option A
Answer: A
Question: You and your friend spent a total of $19 for lunch. Your friend spent $3 more than you. How much did your friend spend on their lunch?
Options:
A)$9
B)$3
C)$4
D)$6
E)$11
Rationale: My lunch = l, my friends lunch = l+3
(l)+(l+3)=19
l+l+3-3=19-3
2l=16
l=8
My friends lunch l+3 = 8+3=$11, the answer is E
Answer: E
Question: A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations F are possible?
Options:
A)3
B)4
C)5
D)6
E)F=8
Rationale: The combinations could be F{(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6),(48,5),(60,4),(80,3),(120,2),(240,1)}
Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with.
{(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)}
Hence 8..E
Answer: E
Question: Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 21 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel?
Options:
A)54
B)66
C)68
D)60
E)63
Rationale: E
63
It takes 3 hours for the friends to meet; so the pigeon flies for 3 hours at 21 MPH = 63 miles
Answer: E
Question: Two wheels are connected via a conveyor belt. The larger wheel has a 36cm diameter and the smaller wheel has a 24cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per hour in terms of r?
Options:
A)1280π
B)75r
C)48r
D)90r
E)(64π)/3
Rationale: Interesting to note that the larger wheel has a diameter of 36 (6*6) while the smaller one has a diameter of 24 (6*4)...
If the large wheel has a diameter of 36 and the small wheel, 24, then their circumferences are 36pi and 24pi respectively. In order for them to move the conveyor belt at the same rate, the smaller wheel would need to rotate 1.5 times as fast as the larger wheel. Lets say the large wheel makes 10 revolutions per minute, the smaller wheel would need to make 10*1.5 = 15 revolutions per minute. If the large wheel makes 10 revolutions per minute it makes 600 per hour. Therefore, the smaller wheel would need to make 600*1.5 = 900 revolutions per hour.
If r = 10, then the answer choice must be d.
D. 90r
Answer: D
Question: Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work?
Options:
A)12 days
B)5 days
C)8 days
D)11 days
E)6 days
Rationale: Answer: Option D
(5 + x)/20 + 5/25 = 1 => x = 11 days
Answer: D
Question: Ajay can complete a piece of work in 4 days. Balu takes double the time taken by Ajay, Charan takes double that of Balu, and Danush takes double that of Charan to complete the same task. They are paired in groups of two each. One pair takes two thirds the time needed by the second pair-to complete the work. Which is the first pair?
Options:
A)A, B
B)A, C
C)B, C
D)A, D
E)None of these
Rationale: Time taken by Ajay, Balu, Charan, Dhanush is 4 days, 8 days, 16 days and 32 days respectively.
Therefore, grouping Ajay and Dhanush work will be two third of the work that will be completed by grouping Balu and Charan.
ANSWER:D
Answer: D
Question: A Bell Curve (Normal Distribution) has a mean of − 1 and a standard deviation of 1/8 . How many integer values M are within three standard deviations of the mean?
Options:
A)0
B)1
C)3
D)6
E)7
Rationale: Got the question correctly -- the second item -- [highlight]bthe list of elements in the set is required.[/highlight] is not required.
With the new information, there is only one integer value (-1) that is between (-1.375, -0.625) i.e., falls within the three 3 SD range.B
Answer: B
Question: What is the units digit of 2222^(555)*3333^(222)?
Options:
A)0
B)2
C)4
D)6
E)8
Rationale: Each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits.
Here's another way to organize the information.
We're given [(2222)^333][(3333)^222]
We can 'combine' some of the pieces and rewrite this product as....
([(2222)(3333)]^222) [(2222)^111]
(2222)(3333) = a big number that ends in a 6
Taking a number that ends in a 6 and raising it to a power creates a nice pattern:
6^1 = 6
6^2 = 36
6^3 = 216
Etc.
Thus, we know that ([(2222)(3333)]^222) will be a gigantic number that ends in a 6.
2^111 requires us to figure out thecycleof the units digit...
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
So, every 4powers, the pattern of the units digits repeats (2, 4, 8, 6.....2, 4, 8, 6....).
111 = 27 sets of 4 with a remainder of 3....
This means that 2^111 = a big number that ends in an 8
So we have to multiply a big number that ends in a 6 and a big number that ends in an 8.
(6)(8) = 48, so the final product will be a gigantic number that ends in an 2.
Final Answer:
B
Answer: B
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
Options:
A)7
B)8
C)5
D)2
E)4
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer:B
Answer: B
Question: A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.20. For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount. What is the total for a book on the third day it is overdue?
Options:
A)$0.60
B)$0.70
C)$0.80
D)$0.90
E)$1.00
Rationale: 1st day fine - 0.2
2nd day fine - 0.2*2 = 0.4 (as doubling gives lower value)
3rd day fine - 0.4+3 = 0.7 (as doubling gives higher value)
Answer: B.
Answer: B
Question: The sides of a rectangle are in the ratio of 6 : 5 and its area is 1331 sq.m. Find the perimeter of rectangle.
Options:
A)121
B)123
C)125
D)122
E)126
Rationale: Let 6x and 5x be sides of the rectangle
6x × 5x = 1331
11xpower2 = 1331
xpower2 = 1331/11 = 121 => x = 11
Length = 6x = 6 × 11 = 66
Breadth = 5x => 5 × 11 = 55
Perimeter = 2 (l+b) => 2 (66+55) = 121 m
Answer is A.
Answer: A
Question: A CAN FINISH A WORK IN 21 DAYS AND B CAN DO THE SAME WORK IN15 DAYS. B WORKED FOR 10 DAYS AND LEFT THE JOB. IN HOW MANY DAYS, A ALONE CAN FINISH THE REMAINING WORK?
Options:
A)5
B)5 1/2
C)7
D)8
E)NONE OF THESE
Rationale: B'S 10 DAY'S WORK=(1/15*10)=2/3 REMAINING WORK = (1-2/3)=1/3
NOW, 1/18 WORK IS DONE BY A IN 1 DAY
1/3 WORK IS DONE BY A IN (21*1/3)=7 DAYS.
CORRECT OPTION:C
Answer: C
Question: The volume of a large cube is 125 cubic inches. A new
shape is formed by removing a smaller cube from one
corner of the large cube. The surface area of this new
shape in square inches is
Options:
A)120
B)150
C)180
D)225
E)250
Rationale: Note that the surface area of the shape is the same as the surface area of the
large cube. Also, the large cube has side 5, and surface area 6 × 5-2round = 150.
correct answer B
Answer: B
Question: The first four numbers in a regular sequence are 4, 10, 22, and 46. What is the next number in the sequence?
Options:
A)94
B)54
C)176
D)82
E)190
Rationale: it is a good Q to learn to pick up number properties in the given set, even if we do not get a Q on these line in actuals..
when we see the sequence 4, 10, 22, 46, we see that each succeeding number is some value more than twice the previous number..
10=2*4+2..
22=2*10+2..
and so on..
so next number= 2*46+2=94..
A
Answer: A
Question: What least number must be added to 1056, so that the sum is completely divisible by 23 ?
Options:
A)23
B)24
C)12
D)2
E)6
Rationale: 23) 1056 (45
92
---
136
115
---
21
---
Required number = (23 - 21)
= 2
ANSWER D
Answer: D
Question: A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 6 runs. His new average is:
Options:
A)46
B)50
C)52
D)54
E)30
Rationale: Let average for 10 innings be x. Then,
(10x + 108)/11 = x + 6
= 11x + 66 = 10x + 108
= x = 42.
New average = (x + 6) = 48 runs.
ANSWER A
Answer: A
Question: How many four-digit numbers that do not contain the digits 2, 3, 4, 5, 6, 7, or 8 are there?
Options:
A)30
B)36
C)42
D)48
E)54
Rationale: The 1st digit can be filled up by the numbers: {1,9} = 2 ways
The 2nd digit can be filled up by the numbers: {0,1,9} = 3 ways
The 3rd digit can be filled up by the numbers: {0,1,9} = 3 ways
The 4th digit can be filled up by the numbers: {0,1,9} = 3 ways
The total number of such four-digit numbers is 2*3*3*3 = 54
The answer is E.
Answer: E
Question: How many three letter words are formed using the letters of the word THREE?
Options:
A)A)117
B)B)118
C)C)119
D)D)120
E)E)121
Rationale: The number of letters in the given word is five.
The number of three letter words that can be formed using these four letters is 5P4
= 5 * 4 * 3*2 = 120.
Answer:D
Answer: D
Question: In a pair of fractions, fraction A is twice the fraction B and the product of two fractions is 2/25. What is the value of fraction A?
Options:
A)1/5
B)1/25
C)2/5
D)Data inadequate
E)None of these
Rationale: A = 2B => B = 1/2 A, so, AB = 2/25
1/2 A2 = 2/25
A2 = 4/25
A = 2/5
ANSWER:C
Answer: C
Question: The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?
Options:
A)28882
B)27772
C)23123
D)Rs.13500
E)28811
Rationale: P = (184*106) / [6 2/3 * 6 2/3 *(300*6 2/3)]
P = 13500
Answer: D
Answer: D
Question: What is the maximum number Q of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?
Options:
A)36
B)32
C)24
D)21
E)15
Rationale: 27 cubic centimetre cubes gives side = 3cm
so if:
L*W*H is 9*12*8, then max. cube we can have are 3*4*2 = 24
L*W*H is 9*8*12, then max. cube we can have are 3*2*4 = 24
L*W*H is 12*8*9, then max. cube we can have are 4*2*3 = 24
L*W*H is 12*9*8, then max. cube we can have are 4*3*2 = 24
L*W*H is 8*12*9, then max. cube we can have are 2*4*3 = 24
L*W*H is 8*9*12, then max. cube we can have are 2*3*4 = 24
In all cases we get Q=24 cubes.
Ans. C
Answer: C
Question: In a can, there is a mixture of milk and water in the ratio 3:2. If the can is filled with an additional 6 liters of milk, the can would be full and the ratio of milk and water would become 2:1. Find the capacity of the can?
Options:
A)36
B)34
C)32
D)30
E)28
Rationale: Let C be the capacity of the can.
(3/5)*(C-6)+6=(2/3)*C
9C-54+90=10C
C=36
The answer is A.
Answer: A
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
Options:
A)2:5
B)2:8
C)2:4
D)2:1
E)2:2
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2:5
Answer: A
Answer: A
Question: To mail a package, the rate is 40 cents for the first pound and 5 cents for each additional pound. Two packages weighing 4 pounds and 6 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
Options:
A)Combined, with a saving of 20 cents
B)Combined, with a saving of 35 cents
C)Separately, with a saving of 5 cents
D)Separately, with a saving of 15 cents
E)Combined, with a saving of 25 cents
Rationale: 4 pounds cost = 40+3*5 = 55
6 pounds cost = 40+5*5 = 65
Total = 120
10 pounds cost = 40+ 9*5 =85 dif. 35
Answer : B
Answer: B
Question: Twenty eight years ago,a father was three times as old as his son.Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is :
Options:
A)120
B)176
C)168
D)105
E)86
Rationale: Let the present ages of the father and son be 2x and x years respectively.
then,(2x-28)=3 (x-28)
x=56.
Required sum =(2x+x)=3x=168 years.
Answer is C
Answer: C
Question: In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 8720 votes were polled, then how many valid votes did B get?
Options:
A)1888
B)2999
C)2834
D)2777
E)2991
Rationale: Let the total number of votes polled in the election be 100k.
Number of valid votes = 100k - 20% (100k) = 80k
Let the number of votes polled in favour of A and B be a and b respectively.
a - b = 15% (100k) => a = b + 15k
=> a + b = b + 15k + b
Now, 2b + 15k = 80k and hence b = 32.5k
It is given that 100k = 8720
32.5k = 32.5k/100k * 8720 = 2834
The number of valid votes polled in favour of B is 2834.
Answer: C
Answer: C
Question: The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.04. There are 40 brand A widgets, 35 brand B widgets, 25 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x?
Options:
A)0.05
B)0.055
C)0.07
D)0.1
E)0.2
Rationale: Given probability of defective items in each brand,
So, the number of items defective in brand A=x*40, in brand B=0.06*35 and brand C=0.04*25
Total number of widgets=40+35+25=100
the probability that the widget selected is defective is 0.053=(x*40+0.06*35+0.04*25)/100
=> 40x+2.1+1=5.3
=>40x = 2.2
>x=2.2/40=0.055
Ans B
Answer: B
Question: Rachel drove 40 1/4 kilometres in 45 minutes. What was her average rate of speed in kilometres per hour?
Options:
A)52
B)52 2/3
C)53
D)53 2/3
E)54 1/3
Rationale: D = 40(1/4) = 161/4
T = 3/4
S = D/T = 53 2/3
Answer = D
Answer: D
Question: What number must be added to 6, 16 and 8 to get an average of 13?
Options:
A)23
B)22
C)44
D)33
E)55
Rationale: B
22
Answer: B
Question: A box contains four silver coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the coin tossed is also a head.
Options:
A)3/5
B)4/5
C)2/5
D)1/5
E)3/4
Rationale: There are four ways (2 heads in one two-headed coin and 2 heads in the other two-headed coin)
How many ways can you get heads from this entire set of coins? There are five ways (four as identified above and one from the normal coin)
Therefore probability = (number of ways to get heads from a two-headed coin)/(number of ways to get heads from any coin)
= 4/5
B
Answer: B
Question: There are 3 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them?
Options:
A)90
B)120
C)45
D)180
E)200
Rationale: Number of ways of selecting 2 fiction books = 3C2
Number of ways of selecting 2 non fiction books = 6C2
3C2 * 6C2 = 3 * 15 = 45
Answer: C
Answer: C
Question: total 85 matches are conducted in Knockout match type. How many players will be participated in that tournament?
Options:
A)85
B)81
C)53
D)82
E)84
Rationale: 84 players
ANSWER:E
Answer: E
Question: If the sum of two numbers is 22 and the sum of their squares is 404, then the product of the numbers is
Options:
A)40
B)44
C)80
D)88
E)90
Rationale: Sol.
Let the numbers be x and y.
Then, (x+y) = 22 and x2 + y2 = 404.
Now, 2xy = (x+y)2 - (x2 + y2)
= (22)2 - 404 = 484 - 404 = 80
xy = 40.
Answer A
Answer: A
Question: Worker A takes 10 hours to do a job. Worker B takes 15 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
Options:
A)40 days
B)40/9 days
C)39/9 days
D)6 days
E)60/9 days
Rationale: A's one hour work = 1/10.
B's one hour work = 1/15.
(A+B)'s one hour work = 1/10+1/15 = 5/30 = 1/6.
Both A & B can finish the work in 6 days
D
Answer: D
Question: Each child has 5 crayons and 14 apples. If there are 10 children, how many crayons are there in total?
Options:
A)22
B)65
C)12
D)36
E)50
Rationale: 5*10=50.Answer is E.
Answer: E
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
Options:
A)3
B)6
C)8
D)7
E)9
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer: A
Answer: A
Question: Find the invalid no.from the following series 15, 16, 34, 105, 425, 2124, 12756
Options:
A)16
B)34
C)105
D)425
E)12755
Rationale: 2nd term = (1st term) * 1 + 1 = 15 *1 + 1 = 16.
3rd term = (2nd term) * 2 + 2 = 16 * 2 + 2 = 34
4th term = (3th term) *3 + 3 = 34 * 3 + 3 = 105
5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424
6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125
5th term should 424 instead of 425.
D
Answer: D
Question: which number replaces the question mark and completes the puzzle ?
2 + 2 = 4
3 + 3 = 18
4 + 4 = 48
6 + 6= ?
Options:
A)135
B)150
C)185
D)180
E)190
Rationale: D
180
2 + 2 = 4 {2 * 2 * 1}
3 + 3 = 18 {3 * 3 * 2}
4 + 4 = 48 {4 * 4 * 3}
6 + 6 = 180 {6 * 6 * 5}
Answer: D
Question: What is the are of an equilateral triangle of side 16 cm?
Options:
A)64√8 cm2
B)64√2 cm2
C)62√3 cm2
D)64√3 cm2
E)44√3 cm2
Rationale: Area of an equilateral triangle
= √3/4 S2
If S = 16, Area of triangle
= √3/4 * 16 * 16
= 64√3 cm2;
Answer: D
Answer: D
Question: A man deposited Rs 50000 in bank at 8% simple interest in 5 years ago. Now he decided to divide total amount among his 7 sons. How much money will get each son?
Options:
A)15000
B)8000
C)12000
D)16000
E)10000
Rationale: i = (50000*5*8)/100
i = 20000
Each son will get = (50000+20000)/7 = 10000
Answer: E
Answer: E
Question: If m/63 is an integer, then each of the following must be an integer EXCEPT
Options:
A)4
B)3
C)5
D)11/2
E)2
Rationale: Now plug m =63 into the answer choices:
A. (63- 28)/7 =5. This is an integer
B. (63+ 21)/7 = 12. This is an integer
C. 14(63)/98 = 9. This is an integer
D. (63^2 - 49)/49 =80. This is an integer
E. (63+ 14)/14 = 11/2. This is NOT an integer
Answer: D
Answer: D
Question: A company charges a fixed rental of Rs. 350 per month. It allows 200 calls free per month. Each call is charge at Rs. 1.4 when the number of calls exceed 200 per month and it charges Rs. 1.6 when the number of calls exceeds 400 per month and so on. A customer made 150 calls in February and 250 calls in march. By how much percent each call is cheaper in March than each call in February.
Options:
A)28%
B)25%
C)18.5%
D)16%
E)None of these
Rationale: Solution: Charge per call in February = 350/150 = 7/3 = 2.33
Charge per call in March = [350+(50*1.4)]/250 = 420/250 = 42/25 = 1.68
% Cheaper call rate in March = [(2.33-1.68)/2.33]*100 = 28%.
Answer: Option A
Answer: A
Question: 456.62+7.523+59.6=?
Options:
A)163.45
B)523.743
C)385.69
D)4896.35
E)782.96
Rationale: 456.62
7.523
59.6
----------
523.743
Answer is B
Answer: B
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 140 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)19 sec
B)38 sec
C)36 sec
D)16 sec
E)11 sec
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 140 = 360 m.
Time taken = 380/10 = 38 sec.
Answer: B
Answer: B
Question: A person starting with Rs.64 and making 6 bets, wins three times and loses 3times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for half the money remaining at the time of the bet, then the final result is?
Options:
A)Rs.37
B)Rs.56
C)Rs.65
D)Rs.76
E)Rs.81
Rationale: As the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order).
The overall resultant will remain same.
So final amount with the person will be (in all cases):
=64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)==64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)= Rs 2727
Hence the final result is:
64−27=3764−27=37:
A loss of Rs.37
A
Answer: A
Question: If the sides of a triangle are 21 cm, 19 cm and 5 cm, what is its area?
Options:
A)42.25 cm2
B)57.5 cm2
C)42.5 cm2
D)47.5 cm2
E)52.5 cm2
Rationale: The triangle with sides 21 cm, 19 cm and 5 cm is right angled, where the hypotenuse is 21 cm.
Area of the triangle
= 1/2 * 19 * 5
= 47.5 cm2
Answer: D
Answer: D
Question: The maximum number of students among them 1345 pens and 775 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is:
Options:
A)91
B)10
C)6
D)5
E)None of these
Rationale: Explanation:
Required number of students = H.C.F of 1345 and 775 = 5. Answer: D
Answer: D
Question: 3 people, Amy, Beth, and Cassie, have speeds of 3 mph, 4 mph and 6 mph respectively. They run a race in which Beth gives Amy a head start of 2 hrs. If both Beth and Cassie overtake Amy at the same time, what head start did Cassie give Amy?
Options:
A)3 hours
B)4 hours
C)5 hours
D)9 miles
E)10 miles
Rationale: Question clearly states that A started first. B started after 2 hours and we need to determine When did C start.
As per the question, we know that All three meet at the same point.
So, we can determine when did A and B meet. The point they will meet would be the same at which C will be present at that time.
So,
A and B will meet after t = 6/(4-3) = 6 hours.
In these 6 hours, B would have covered 4*6=24 miles.
=> C would also have covered 24 miles and that would be in 24/6=4 hours.
Thus, C started 2 hours after B or 4 hours after A. hence, answer is B.
Answer: B
Question: Set #1 = {A, B, C}
Set #2 = {K, L, M, N, O, P}
There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel?
Options:
A)1/6
B)1/3
C)4/9
D)2/3
E)5/6
Rationale: So Not a vowel in Set-1 : 2/3
And not a vowel in Ser-2:5/6
Now,
2/3∗5/6=5/9
This is for not a vowel.
Then for at least one vowel will be = 1−5/9=4/9
Answer will be C.
Answer: C
Question: P is a set of four numbers 1, 2, 3 and 1. In every step, one is added to any two numbers in the set P. In how many such steps is it possible to make all the four numbers in the set P equal?
Options:
A)4
B)5
C)6
D)1
E)2
Rationale: If all the four numbers are equal, then their sum in the end of the process must be multiple of 4.
Now the sum of the given numbers is equal to 7. Each time we are adding 1 to two of any two numbers, so the sum increases by 2 each time. So the sum never becomes a multiple of 4 as odd + even = always odd.
Answer:A
Answer: A