divelab/Sys2Bench huggingface dataset:
Question: A train travelling at a speed of 75 mph enters a tunnel 3 miles long. The train is mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
Options:
A)2.5 min
B)3 min
C)3.2 min
D)3.5 min
E)3.8 min
Rationale: Total distance travel by train is 4 miles
and speed of the train is 75 miles per hour
so time is distance by speed = (4/75) hours
den we should change to minits then (4/75)*60 = 3.2
ANSWER:C
Answer: C
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 18 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel?
Options:
A)54
B)66
C)80
D)36
E)96
Rationale: A
54
It takes 3 hours for the friends to meet; so the pigeon flies for 3 hours at 18 MPH = 54 miles
Answer: A
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter =5300	/26.50 m = 200 m.
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m.
answer : C
Answer: C
Question: Seats for Maths, Physics and Biology are in the ratio of 5 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?
Options:
A)2 : 3 : 4
B)6 : 7 : 8
C)6 : 8 : 9
D)Cannot be determined
E)None of these
Rationale: Reqd ratio 5 × 140⁄100 : 7 × 150⁄100 : 8 × 175⁄100
= 5 × 140 : 7 × 150 : 8 × 175 = 2 : 3 : 4
Answer A
Answer: A
Question: Laxmi goes 6 km towards South-East from her office.Then she goes 15 km turning to West. After this she goes 6 km towards North-West and in the end she goes 11 km towards East. How far is she from her office ?
Options:
A)10 km
B)11 km
C)4 km
D)6 km
E)8 km
Rationale: Explanation:
From the above fig we can observe that distance between Laxmi and her office is 15-11 = 4 kms.
ANSWER IS C
Answer: C
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 24 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
Options:
A)288
B)540
C)877
D)278
E)178
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 24 + 21 = 45
T = 12
D = 45 * 12 = 540
Answer: B
Answer: B
Question: A can do a piece of work in 3 hours; B and C together can do it in 2 hours, which A and C together can do it in 2 hours. How long will B alone take to do it?
Options:
A)6hours
B)3hours
C)2hours
D)5hours
E)4hours
Rationale: A's 1 hour work = 1/3;
(B + C)'s 1 hour work = 1/2;
(A + C)'s 1 hour work = 1/2
(A + B + C)'s 1 hour work = (1/3 + 1/2) = 5/6
B's 1 hour work = (5/6 - 1/2) = 1/3
B alone will take 3 hours to do the work.
Answer:B
Answer: B
Question: The average age of 15 students of a class is 16 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is?
Options:
A)22years
B)24years
C)26years
D)28years
E)30years
Rationale: Age of the 15th student
=[15 * 16 - (14 * 5 + 16 * 9)]
= (240 - 214) = 26 years.
Answer:C
Answer: C
Question: Tomy's age 14 years hence will be thrice his age four years ago. Find Tomy's present age?
Options:
A)12 years
B)13 years
C)15 years
D)17 years
E)18 years
Rationale: Let MTomy's present age be 'x' years.
x+ 14 = 3(x- 4)
=> 2x = 26 => x = 13 years.
B
Answer: B
Question: A test has 100 questions. Each question has 5 options, but only 1 option is correct. If test-takers mark the correct option, they are awarded 1 point. However, if an answer is incorrectly marked, the test-taker loses 0.25 points. No points are awarded or deducted if a question is not attempted. A certain group of test-takers attempted different numbers of questions, but each test-taker still received the same net score of 40. What is the maximum possible number of such test-takers?
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: A correct answers get you 1 point, an incorrect answer gets you MINUS 1/4 point and a skipped question gets you 0 points. Since there are 200 total questions, there are a variety of ways to get a total of 40 points.
Let C be the number of correct answers and let I be the number of incorrect answers.
To get 40 points, a test taker must have at least 40 correct answers. Then C=> 40.
For every correct question above 40, the test taker has 4 incorrect answers.
Then, the I = 4*(C - 40).
Also, I + C <= 100. Thus 5C <= 260 and so C <= 52.
Then 40 <= C <= 52 and C can have 13 possible values.
The answer is E.
Answer: E
Question: If a,b,c,d,e are five consecutive odd integers,then what is their average?
Options:
A)a+4
B)abcde/5
C)5(a+b+c+d+e)
D)a+8
E)a+6
Rationale: b=a+2,c=a+4,d=a+6 and e=a+8
Required average = (a+a+2+a+4+a+6+a+8)/5=a+4
Answer is A
Answer: A
Question: A worker earns $24 on the first day and spends $18 on the second day. The worker earns $24 on the third day and spends $18 on the fourth day. If this pattern continues, on which day will the worker first reach a net total of $72?
Options:
A)9
B)12
C)17
D)21
E)24
Rationale: Every two days, the net total is $6.
After 16 days, the worker will have $48.
On day 17, the worker will receive $24 for a net total of $72.
The answer is C.
Answer: C
Question: 34.	The side surface of a cylinder is rolled with a rectangular plate. If the perimeter of the circular base Is 6 feet, and the diagonal of the rectangular plate was 10 ft. What is height of the of the cylinder?
Options:
A)7
B)10
C)8
D)12
E)15
Rationale: Think of a Pringles can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both, one side and thehypothenuse use pythagoreans theorem or properties of 3-4-5 triangles to solve for the other side, 8. Correct answer C.
Answer: C
Question: Siddharth wants to borrow Rs.6000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
Options:
A)Rs.21.60
B)Rs.21.69
C)Rs.21.87
D)Rs.21.68
E)Rs.21.19
Rationale: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.6,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 6,000{ [1 + 6/100]2 - 1 - 12/100}
= 6,000 {(1.06)2- 1 - 0.12} = 6,000(1.1236 - 1 - 0.12)
= 6,000 (0.0036) = 6 * 3.6 =Rs.21.60
Answer:A
Answer: A
Question: The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
Options:
A)14 years
B)17 years
C)18 years
D)12 years
E)11 years
Rationale: 9 * 2
= 181
Answer:C
Answer: C
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 180. The amount of the bill is
Options:
A)1200
B)1764
C)1680
D)1354
E)None of these
Rationale: Explanation:
Let P.W. be Rs.x.
Then, S.I. on Rs. x at 16% for 9 months = Rs. 180.
x Ã— 16 Ã— (9/12) Ã— (1/100) = 180 or x = 1500.
P.W. = Rs. 1500.
Sum due = P.W. + T.D. = Rs.(1500
180) = Rs. 1680.
Answer: C
Answer: C
Question: On a certain date, Pat invested $5,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $20,000, in how many years, the total value of the investment plus interest will increase to $30,000?
Options:
A)15
B)16
C)18
D)20
E)24
Rationale: if i were to choose during the test, would go for 18 or 20. probably 18 cuz it wont take too long to get the value doubled....
I found a method: Rule of 72.
Given an x% return, it takes 5,000 to quadralope 12 years.
So according to the rule: 72/x is the no of years 5,000.00 took to double 10,000.00.
Again, 10,000.00 took to double 20,000.00 same (72/x) no of years.
72/x+ 72/x = 12
x = 12% (though rate here is not very much required).
Again, 20,000.00 takes the same (72/x) no of years to double 30,000.00.
72/x = 6 years.
So altogather:
5,000 - 10,000 = 6 years
10,000 - 20,000 = 6 years
20,000 - 30,000 = 3 years
Answer A 15 years.
Answer: A
Question: Every year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 9/10, what is the probability that Taylor makes exactly one basket in three tries?
Options:
A)3^5/10^3
B)3^4/10^3
C)3^3/10^3
D)3^2/10^3
E)3^4/10^4
Rationale: Probability of basket = 1/10
Probability of no basket = 9/10
Required probability= 3* (1*9*9/1000)
= 3^5/10^3
A is the answer
Answer: A
Question: there is a equilateral triangle whose area is A.another triangle is formed by joining the mid points.this process is continued.find the sum of these areas.
Options:
A)A/3
B)2A/3
C)A
D)4A/3
E)5A/3
Rationale: Area of equilateral triangle =(root(3)/4)*a^2=A(given)
side of triangle=a
now side is a/2
then total area A+A/4 +A/16-------
A/1-(1/4)=A*4/3 is total area
ANSWER:D
Answer: D
Question: If 2x + y = 7 and x + 2y = 5, then (2x + 2y)/3 =
Options:
A) 3
B) 4/3
C) 17/5
D) 18/5
E) 4
Rationale: 2*(x+2y = 5) equals 2x+4y=10
2x+4y=10
- 2x + y= 7
= 3y=3
Therefore Y = 1
Plug and solve...
2x + 1 = 7
2x=6
x=3
(2*3+2*1)/3= (6+3)/3
=9/3
=3
A
Answer: A
Question: A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number?
Options:
A)5
B)8
C)9
D)10
E)11
Rationale: Solution
Let the number be x.	Then, 3(2x+9) = 75
‹=› 2x+9 = 25
‹=›2x = 16
Answer B
Answer: B
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 the amountby which he might have fallen short.
Options:
A)30
B)40
C)50
D)60
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
Question: The ratio of the volumes of two cubes is 512 : 729. What is the ratio of their total surface areas?
Options:
A)1:22
B)81:12
C)41:46
D)41:19
E)84:12
Rationale: Ratio of the sides = ³√512 : ³√729
= 8 : 9
Ratio of surface areas = 82:92
= 41:46
Answer: C
Answer: C
Question: A coin is tossed until sequence HTH appears (H denotes the fall of heads, T denotes the fall of tails). What is the probability P that the game will end after the fourth throw?
Options:
A)1/16
B)3/32
C)1/8
D)3/16
E)1/4
Rationale: Another approach:
Two likely scenarios would be : HHTH or THTH
for each of the scenarios probability would be 1/16
So Probablilty P is 1/16 + 1/16 = 1/8.C
Answer: C
Question: The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages (in years)
Options:
A)12, 14, 18
B)14, 20, 36
C)16, 12, 14
D)16, 28, 36
E)None
Rationale: Sol.
Let thier present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56 ⇔ 20x = 80 ⇔ x = 4.
∴ Their present ages are 16 years, 28 years and 36 years respectively.
Answer D
Answer: D
Question: Set X consists of 10 integers and has median of 10 and a range of 10. What is the value of the greatest possible integer that can be present in the set?
Options:
A)32
B)37
C)C.40
D)20
E)50
Rationale: Note that both median and range do not restrict too many numbers in the set. Range is only concerned with the smallest and greatest. Median only cares about the middle.
Quick check of each option starting from the largest:
(E) 50
Range of 20 means the smallest integer will be 30. So 20 cannot lie in between and hence cannot be the median.
(D) 43
Range of 20 means the smallest integer will be 23. So 20 cannot lie in between and hence cannot be the median.
(C) 40
Range of 20 means the smallest integer will be 20. 20 can lie in between such as:
20, 20, 20, 20, 20, 20, 20, 20, 20, 20
This is possible. Hence it is the greatest such number.
Answer (D)
Answer: D
Question: At a Halloween party, 2/5 of the people were dressed as vampires, 1/3 were dressed as ghosts; everyone else at the party, were equally dressed as Pirates, Robin Hood, Fairies, and Princesses. If all of the Fairies leave the party, and the people who just arrived to the party are all dressed as ghosts, doubling the number of ghosts at the party, what proportion of the people at the party are vampires?
Options:
A)6/19
B)5/18
C)5/26
D)1/2
E)3/7
Rationale: Vampires = 2/5 = 6/15
Ghosts = 1/3 = 5/15
Pirates + Robin Hoods + Fairies + Princesses = 1 - (5/15 + 6/15) = 4/15, so each = 1/15
If Ghosts doubled (2)(5) = 10, and now Fairies = 0; then, total = 6 + 10 + 1 + 1 + 1 + 0 = 19. 6 are Vampires => proportion = 6/19.
Answer: A
Answer: A
Question: When n is divided by 18, the remainder is 6. When n is divided by 11, the quotient is equal to Z, and the remainder is equal to 6. Z must be divisible by which of the following numbers?
Options:
A)16
B)17
C)18
D)19
E)20
Rationale: N = 18 q + 6
N = 11 z + 6
Equating
18 Q + 6 = 11z+6
11z=18q
11z/18 = q
since q is an integer Z must be divisible by 18.
Hence C
Answer: C
Question: Tlaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement. Given these choices, how many candle + flower groupings can she select?
Options:
A)54
B)72
C)96
D)144
E)432
Rationale: Tlaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement. 2 candles from 4 candles: 4C2: 6
8 flowers from 9 flowers: 9C8 : 9
So total grouping
9*6= 54.
Answer is A.
Answer: A
Question: In a class, 6 students can speak Tamil, 15 can speak Gujarati and 6 can speak H. If two students can speak two languages and one student can speak all the three languages, then how many students are there in the class?
Options:
A)20
B)21
C)22
D)23
E)24
Rationale: T = 6
G = 15
H = 6
students can speak two languages (suppose Tamil & Gujarati) = 2
student can speak all the three languages = 1
student can speak only Tamil language = 6-2-1 = 3
student can speak only Gujarati language = 15-2-1 = 12
student can speak only H language = 6-1 = 5
So, Total number of student = 2+1+3+12+5 = 23
ANSWER:D
Answer: D
Question: Divide 2379 into 3 parts so that their amounts after 2, 3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The first part is:
Options:
A)759
B)792
C)818
D)828
E)None of these
Rationale: Let the parts be x, y and [2379 – (x + y)].
x + (x × 2 × 5⁄100) = y + (y × 3 × 5⁄100)
= z + (z × 4 × 5⁄100)
⇒ 11x⁄10 = 23y⁄20 = 6z⁄5 = k ⇒ x = 10k⁄11, y = 20k⁄23, z = 5k⁄6
But x + y + z = 2379.
⇒ 10k⁄11 + 20k⁄23 + 5k⁄6 = 2379
⇒ 1380 k + 1320 k + 1256 k = 2379 × 11 × 23 × 6
⇒ k = 2379×11×23×6/3965=3×11×23×6/5
∴ x = (10/11×3×11×23×6/5)=828
Hence, the first part is 828.
Answer D
Answer: D
Question: Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?
Options:
A)5
B)9
C)11
D)13
E)15
Rationale: Explanation:
x + y = 15
2x – 3y = 5
x = 10 y = 5
A)
Answer: A
Question: How many three digits numbers greater than 600 can be formed by using the digits 4,5,6,7,8?
Options:
A)45.
B)55.
C)65.
D)85.
E)75.
Rationale: Clearly repetition of digits allowed. Since the three digits number greater than 600 will have 6,7 or 8 at hundreds place. So hundreds place can be filled in 3 ways. Each of ten's and one's place can be filled in 5 ways. Hence, total number of required number =3x5x5 =75. Answer : E
Answer: E
Question: What is the greatest of 3 consecutive integers whose sum is 39?
Options:
A)14
B)15
C)16
D)17
E)18
Rationale: 39 / 3 = 13
The three numbers are 12, 13, and 14.
The answer is A.
Answer: A
Question: The average weight of 10 oarsmen in a boat is increased by 1.8kg when one of the crew, who weight 53kg is replaced by a new man. Find the weight of the new man.
Options:
A)59kg
B)62kg
C)74kg
D)85kg
E)71kg
Rationale: Total weight increased = 1.8*10 = 18kg
Weight of the new man = 53+18 = 71 kg
Answer is E
Answer: E
Question: Ann and Bob drive separately to a meeting. Ann's average driving speed is greater than Bob's avergae driving speed by one-third of Bob's average driving speed, and Ann drives twice as many miles as Bob. What is the ratio E of the number of hours Ann spends driving to the meeting to the number of hours Bob spends driving to the meeting?
Options:
A)8:3
B)3:2
C)4:3
D)2:3
E)3:8
Rationale: Say the rate of Bob is 3mph and he covers 6 miles then he needs 6/3=2 hours to do that.
Now, in this case the rate of Ann would be 3+3*1/3=4mph and the distance she covers would be 6*2=12 miles, so she needs 12/4=3 hours for that.
The ratio E of Ann's time to Bob's time is 3:2.
Answer: B.
Answer: B
Question: What is the area of a square field whose diagonal of length 22 m?
Options:
A)288
B)289
C)242
D)112
E)178
Rationale: d2/2 = (22 * 22)/2
= 242
Answer: C
Answer: C
Question: How many 5 letter words ( with or without meaning) can be formed using all the following 5 letters P,Q,R,S,and W so that letter P is to the left of letter R?
Options:
A)70
B)50
C)60
D)90
E)100
Rationale: Two positions can be selected out of 5 positions in 5C2 ways = 10 ways.
And the remaining 3 letters can be placed in 3 posions in 3! Ways = 6 ways.
So the final Answer = number of ways letters P and R can be arranged x number
of ways the other 3 letters can be arranged
Final Answer = 10 x 6 = 60 ways
C
Answer: C
Question: In a group of ducks and cows, the total number of legs are 28 more than twice the no. of heads. Find the total no.of buffaloes.
Options:
A)11
B)12
C)14
D)16
E)18
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 28
=> 2x = 28 => x = 14
C
Answer: C
Question: Susan weighs m pounds more than Anna does, and together they weigh a total of n pounds. Which of the following represents Anna’s weight in pounds?
Options:
A)(n - m)/2
B)(n + m)/2
C)n/2 - m
D)2n − m
E)n − 2m
Rationale: Let Anna's weight = a
Susan's weight = a + m
Together their weight is 2a + m = n
2a = n-m
Hence a = #(n-m)/2#
ANSWER:A
Answer: A
Question: The sum of three integers is 33. The largest integer is 3 times the middle integer, and the smallest integer is 23 less than the largest integer. What is the product of the three integers?
Options:
A)192
B)203
C)214
D)225
E)236
Rationale: Let x be the middle integer. Then the largest is 3x and the smallest is 3x - 23.
3x - 23 + x + 3x = 33
x = 8
The three integers are 1, 8, and 24.
The product is 1*8*24 = 192
The answer is A.
Answer: A
Question: If a:b=1:2 and b:c=3:4 find a:b:c?
Options:
A)3:5:8
B)3:6:8
C)3:7:8
D)3:6:4
E)3:6:9
Rationale: a:b = 1:2, b:c = 3:4
1:2
3:4
(a = 1 × 3 = 3, b = 2 × 3 = 6 and c = 2 × 4 = 8)
(a = a × b, b = b × b and c = b × c)
a:b:c = 3:6:8
B
Answer: B
Question: By selling a watch for Rs.640/-, a man loses 20% what is that watch cost price?
Options:
A)Rs. 600/-
B)Rs. 700/-
C)Rs. 800/-
D)Rs. 850/-
E)Rs. 900/-
Rationale: 80 % ------> 640 (80 * 8 = 640)
100 % ------>800 (100 * 8 = 800)
Cost price = Rs. 800/-
C)
Answer: C
Question: A football coach must choose 3 freshers from a team of 12players. How many different ways can the coach choose the freshers?
Options:
A)220
B)650
C)729
D)800
E)890
Rationale: Choose 3 starters from a team of 12 players. Order is not important.
\inline {\color{Black} 12C_{3}}= 220
A
Answer: A
Question: In the first round of the elections, the only two candidates got exactly the same number of votes. During the second round, 24,000 votes switched from the first candidate to the second one. The total number of votes remained the same in both rounds, and no other votes switched sides. If, in the second round, the winning candidate got four times as many votes as the other candidate, how many people have voted in each round?
Options:
A)15,000
B)25,000
C)80,000
D)50,000
E)60,000
Rationale: Let A be the first candidate and B be the second one.
Given x+24000 = 4(x-24000) => x = 40000
2x = 80000
IMO option C.
Answer: C
Question: Find the probability that a number selected from numbers 1, 2, 3,..., 40 is a prime number, when each of the given numbers is equally likely to be selected?
Options:
A)10/40
B)12/40
C)8/40
D)3/40
E)7/40
Rationale: Let X be the event of selecting a prime number.
X = {2, 3, 5, 7, 11, 13, 17, 19,23,29,31,37}
n(X) = 12,
n(S) = 40
Hence, the required probability is 12/40.
ANSWER:B
Answer: B
Question: If logX = (logY)/2 = (logZ)/5, then X4.Y3.Z-2 =?
Options:
A)2
B)10
C)1
D)0
E)3
Rationale: (log X)/1 = (logY)/2 = (logZ)/5 = K
=> logX = K, log Y = 2k, log Z = 5K
Thus, log(X4.Y3.Z-2) = 4logX +3logY - 2logZ = 0.
=> X4.Y3.Z-2 = 1.
ANSWER:C
Answer: C
Question: In the quiet town ofNothintodothere are 850 inhabitants, 400 are unemployed and 300 are somnambulists. If half of the somnambulists are unemployed, how many are employed and are not somnambulists?
Options:
A)50.
B)100.
C)150.
D)200.
E)300.
Rationale: Total = 850
unemployed=400
employed=850-400=450
som=300
unemployed som = 300/2=150
employed som = 150
employed that are not som = 450-150=300
Answer : E
Answer: E
Question: In how many ways can the letters of word TREATMENT be arranged such that all the vowels as well as all the Consonants always appear together?
Options:
A)9!
B)3!*6!*2!
C)5!*5!
D)5!*4!*2!
E)6!*4!
Rationale: Since all the vowels and consonants have to be together there can only be there are 3! way to order the vowels and 6! to order the consonants. But they must be together either vowels come first or consonants so you multiply by 2.
So 3!6!2! (B)
Answer: B
Question: The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
Options:
A)156
B)144
C)165
D)182
E)716
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 6 = 144.
Answer: B
Answer: B
Question: If the median of a list of numbers is m, the first quartile of the list is the median of the numbers in the list that are less than m. What is the first quartile of the list of numbers 42, 24, 30, 22, 26, 27, 33 and 35 ?
Options:
A)33
B)28
C)27
D)24
E)25
Rationale: It is given that a quartile is the middle number of all numbers less than median..
so lets arrange the number in ascending order- 42, 24, 30, 22, 26, 27, 33 and 35
22, 24, 26, 27, 30, 33, 35, 42,...
numbers less than median are 22, 24, 26, 27..
the median of these numbers = center of 24 and 26 = 25
E
Answer: E
Question: While driving from A-ville to B-town, Harriet drove at a constant speed of 110 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 140 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town?
Options:
A)138
B)148
C)150
D)162
E)168
Rationale: 5hr = 300min.
If harriet spend equal hrs on each leg she will spend 150min on each. Since speed A-B is less than speed B-A and distance on each leg is the same, time spent on A-B is more than 150min, which mean we can eliminate ans. A, B and C.
Now let plug in ans. D or E and verify which one give same distance on each leg.
E. t= 168min
* leg A-B ---> d = 110.168/60 = 18480/60
* leg B-A ----> d = 140*132/60 = 18480/60
so the correct ans. isE
Answer: E