divelab/Sys2Bench huggingface dataset:
Question: In a friendship gang Andrew has 8 gang, in how many ways can he invite one or more of the gang to his house?
Options:
A)234
B)255
C)265
D)267
E)272
Rationale: Andrew can select one or more than one of his 8 gang.
=> Required number of ways = 28 – 1= 255.
B
Answer: B
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is?
Options:
A)0.5922
B)0.5904
C)0.5287
D)0.1288
E)0.5919
Rationale: Explanation:
P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
Answer: B
Answer: B
Question: A can do a piece of work in 10 days, B in 15 days. They work together for 5 days, the rest of the work is finished by C in two more days. If they get Rs. 3000 as wages for the whole work, what are the daily wages of A, B and C respectively (in Rs):
Options:
A)300, 200, 252
B)300, 200, 250
C)300, 200, 259
D)300, 200, 251
E)300, 200, 212
Rationale: Explanation:
A's 5 days work = 50%
B's 5 days work = 33.33%
C's 2 days work = 16.66% [100- (50+33.33)]
Ratio of contribution of work of A, B and C =
= 3 : 2 : 1
A's total share = Rs. 1500
B's total share = Rs. 1000
C's total share = Rs. 500
A's one day's earning = Rs.300
B's one day's earning = Rs.200
C's one day's earning = Rs.250
Answer: B) 300, 200, 250
Answer: B
Question: 60 percent of movie theatres in Town X have 3 screens or less. 20% of those theatres sell an average of more than $300 worth of popcorn per showing. 50 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing. What percent of all the stores on the street have 4 or more screens and sell an average of more than $100 worth of popcorn per day?
Options:
A)12
B)18
C)32
D)40
E)44
Rationale: Lets take numbers here.
Assume that the total number of movie theaters in the town = 100
Then number of movie theaters with 3 screens or less = 60
=> Number of movie theaters with 4 screens or more = 40
Movie theaters with 3 screens or less selling popcorn at more than $300 = 20% of 60 = 12
Number of movie theaters selling popcorn at $300 or less = 56
=> Number of movie theaters selling popcorn at more than $300 = 100-56 = 44
Of these 44 theaters, 12 are those with 3 screens or less
Therefore 12 (44-12) must be those with four screens or more
A is the answer
Answer: A
Question: The average of 11 numbers is 10.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is
Options:
A)21.5
B)11.5
C)61.5
D)41.5
E)31.5
Rationale: Middle numbers = [(10.5 x 6 + 11.4 x 6) - 10.9 x 11]
= (131.4 - 119-9) = 11.5.
Answer: B
Answer: B
Question: The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
Options:
A)3
B)4
C)5
D)6
E)9
Rationale: Let the ten's digit be x and unit's digit be y.
Then, (10x + y) - (10y + x) = 36
9(x - y) = 36
x - y = 4.
Answer: Option B
Answer: B
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 40 with him, what was the average amount with the group before his joining the group?
Options:
A)s.17
B)s.16.66
C)s.15.50
D)s.29.33
E)s.19
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 40. So, the amount with remaining 6 people = 140 - 40 = Rs. 100
The average amount with them = 16.66
= Rs.16.66.
Answer:B
Answer: B
Question: Distance between Sumter and Columbia is 48 miles, and there is a bridge crossing a river at the midpoint between the two towns. A man from Sumter and a man from Columbia start walking toward each other. The man who started in Sumter traveled uniformly with average speed 4 mph. The man from Columbia started an hour later, and in an attempt to make up lost time began jogging at 6 mph. After two hours, however, the Columbia man needed to rest for an hour before he could resume at the same pace. Where will the two men meet?
Options:
A) On the Columbia side, 4 miles away from the bridge
B) On the Sumter side, 6 miles away from the bridge
C) On the Columbia side, 6 miles away from the bridge
D) On the Sumter side, 4 miles away from the bridge
E) On the bridge
Rationale: Since the question asks where Sumter and Columbia men will meet each other, we know the answer will involve distance and location.
In such questions, look for a symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same.
Here the average speed of the Sumter man is 4 mph and distance is 48 miles. So this means that A would take a total of 48/4 = 12 hours to cover the distance from Sumter to Columbia. So, if the Columbia man's speed were also 4, both men travel for 6 hours to meet in the middle.
Since we know the Columbia man started late, the rate for his first hour is 0, followed by two hours of 6 mph. The Columbia man then has to rest for an hour before continuing, so we know the pattern of 0, 6, 6, will continue. This means, for each three-hour period, the Columbia man will average 4 mph. Since the 6 hours before the Sumter man reached the bridge can be divided by 3, then both men will be traveling at the same average rate.
The correct answer is (E).
Answer: E
Question: In a LAB experiment, a 100 ml compound of element X and element Y needs to be increased to 180 ml by adding some quantity of element X, and some quantity of element Y. If the original compound contains 30% of element X, how much (in ml) of element Y must be added so that element X will be exactly one third of the resulting mixture ?
Options:
A)50 ml
B)100/3 ml
C)20 ml
D)20/3 ml
E)10 ml
Rationale: There are 0.3*100=30 ml of element X in the initial solution.
We need X to be 1/3rd of 180 ml in the resulting solution, so 60 ml. Thus out of 80 ml of solution added, 30 must be X (in order it to become 60 ml) ans the remaining 50 must be Y.
Answer:A
Answer: A
Question: The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 15 percent, what was the annual interest rate last year?
Options:
A)14.04%
B)15.04%
C)13.64%
D)12.04%
E)10.04%
Rationale: let i = interest rate
i(this year) = i(last year) + 0.1i(last year) = 1.1i(last year)
15 = 1.1 x i(last year)
i(last year) = 15/1.1 = 150/11 = 13.64 %
Answer : C
Answer: C
Question: If the average of a sequence of consecutive multiple of 18 is 153, and the greatest term is 270, how many terms F in the sequence are smaller than the average?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Let the sequence have N terms starting 18*K
--> 18K, 18(K+1), 18(K+2), .... , 18(K+N-1) is the sequence.
The sum of the sequence is
---> 18K + 18(K+1) + 18(K+2) + .... + 18(K+N-1) =18*(K+(K+1)+...+(K+N-1)) = 18*(N*(2K+N-1)/2).
So the average is
153=[18*(N*(2K+N-1)/2)]/N = 18*(2K+N-1)/2 = 9 *(2K+N-1) ---> by cancelling 9 we get 2K+N-1=17 --> 2K+N=18 ---*).
On the other hand, since the greatest term is 270, 18(K+N-1)=270 --> by cancelling 18 we get K+N-1=15 --> K+N=16 ---**).
By *), **) we have K=2, N=14.
Since 153/18 = 8.5, 18*8<153<18*9. So the number of terms F which are smaller than the average is 18*2, 18*3, ..... ,18*8 ---> 7. The answer is C.
Answer: C
Question: A store reduced the price of all items in the store by 10% on the first day and by another 10% on the second day. The price of items on the second day was what percent of the price before the first reduction took place?
Options:
A)80.0
B)80.9
C)81.0
D)81.1
E)81.9
Rationale: consider price of the all items as $100
after a initial reduction of 10% price becomes = 0.9 *100 = $ 90
after the final reduction of 10% price becomes = 0.9* 90 = $ 81
price of all items on second day is 81% of price on first day
correct answer option C
Answer: C
Question: The length of the train which is moving at 54km/hr, can crosses a bridge of length 245 m in 30 sec, is ?
Options:
A)260 m.
B)345 m.
C)130 m.
D)245 m.
E)145 m.
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of train be x metres. Then, (245 + x)/30
= 25/2 => 2(245 + x)=750
130 = x
= 130 m.
Answer:C
Answer: C
Question: What is the greatest value of n such that 4^n is a factor of 25! ?
Options:
A)6
B)5
C)7
D)4
E)3
Rationale: Pretty simple, really.
If m = 7, then 4m = 28, which is 14x2, both of which are included in 25!
Since 7 is the largest number here, its the answer.
Answer is C
Answer: C
Question: Find the last term of a G.P whose first term is 9 and common ratio is ( 1/3 ) if the sum of the terms of the G.P is ( 40/3 )
Options:
A)1/3
B)2/5
C)1/4
D)2/3
E)4/5
Rationale: Sum of the G.P . = ( First term - r * last term)/1 – r
40/3 = 9 – 1/3 ( last term ) / 2/3
Last term = ( -40/3*2/3+9 ) * 3 = - 80/3 + 27 = 1/3
ANSWER:A
Answer: A
Question: Simplify:1397 x 1397
Options:
A)9157109
B)1956109
C)1951609.
D)1951709
E)1951702
Rationale: 1397 x 1397	= (1397)2
= (1400 - 3)2
= (1400)2 + (3)2 - (2 x 1400 x 3)
= 1960000 + 9 - 8400
= 1960009 - 8400
= 1951609.
Answer is C
Answer: C
Question: The three sides of an acute angled triangle (all in cms) are 12, 19 and j. How many integer values can j take?
Options:
A)23
B)22
C)15
D)8
E)7
Rationale: In acute angle triangles all angles in the triangle should be less than 90.
The maximum length of j can be when it is the hypotenuse of the triangle.
So, j= sqrt(12^2 + 19^2) = 22.5 (approx)
The maximum length of j can be when side of length 12 is the hypotenuse of the triangle.
So, j = sqrt (19^2 - 12^2) = 14.7 (approx)
So, j>14.7 and j<22.5.
Hence, possible values for j can be 15,16,17,18,19,20,21 and 22. Total 8 values.
Answer D.
Answer: D
Question: One hour before John started walking from P to Q, a distance of 13 miles, Ann had started walking along the same road from Q to P. Ann walked at a constant speed of 3 miles per hour and John at 2 miles per hour. How many miles had Ann walked when they met?
Options:
A)6 miles
B)8,4 miles
C)9 miles
D)9,6 miles
E)12 miles
Rationale: Ann walks from Q to P at a speed of 3 miles/hr for one hour. She covers 3 miles in 1 hour and now distance between John and Ann is 13 - 3 = 10 miles.
Ann walks at 3 mph and John at 2 mph so their relative speed is 3+2 = 5 mph.
They have to cover 10 miles so it will take them 10/5 = 2 hours to meet.
In 2 hrs, Ann would have covered 2 hrs * 3 miles per hour = 6 miles.
Adding this to the 3 miles she covered before John, Ann covered a total of 3 + 6= 9 miles.
Answer (C)
Answer: C
Question: From a group of 5 managers (Joon, Kendra, Lee, Marnie and Noomi), 2 people are randomly selected to attend a conference in Las Vegas. What is the probability that Marnie and Noomi are both selected?
Options:
A)0.1
B)0.2
C)0.25
D)0.4
E)0.6
Rationale: (1/6)*(1/5)+(1/6)*(1/5)=2/30=1/15
ANS:A
Answer: A
Question: Working simultaneously and independently at an identical constant rate, 5 machines of a certain type can produce a total of x units of product P in 8 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?
Options:
A)30
B)18
C)16
D)12
E)8
Rationale: 5 machines do x units in 8 days
we have x/8 => rate of the 5 machines
we know that we need to have 3x units in 4 days
therefore, we need to get to 3x/4 rate of the machines.
rate of one machine is x/8*1/5 = x/40.
now, we need to know how many machines need to work simultaneously, to get 3x done in 4 days.
3x/4 work needs to be done by machines that work at x/40 rate.
let's assign a constant Y for the number of machines:
(x/40)*y = 3x/4
y = 3x/4 * 40/x
cancel 4 with 40, and x with x and get -> 30. Answer choice A
Answer: A
Question: During the last four years, a large truck company purchased diesel at rates of $1.1, $1.4, $1.8 and $2.1 per gallon. What was the mean cost of diesel over the four-year period if the company spends the same amount of dollars on diesel each year?
Options:
A)$2.5
B)$2.55
C)$1.51
D)$3.25
E)$3.0
Rationale: finding the Harmonic mean here.
HM = 4/(1/12 + 1/14 + 1/18 + 1/21) = 15.07
C
Answer: C
Question: How many revolutions will a circular wheel make to travel a distance of 3 km, given that the radius is 2.4 m?
Options:
A)11085.7
B)15085.7
C)35085.7
D)15015.7
E)15083.7
Rationale: 2 * 22/7 * 2.4 * x = 15085.7
x = 1000
Answer: A
Answer: A
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1260, find the loss %?
Options:
A)16%
B)18%
C)17%
D)78%
E)28%
Rationale: 1500 ---- 240
100 ---- ? => 16%
Answer:A
Answer: A
Question: If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 5 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour?
Options:
A)1/9
B)29/180
C)26/143
D)3/20
E)39/121
Rationale: 50 apprentices can finish the job in 4 hours,thus:
10 apprentices can finish the job in 4*5 = 20 hours;
In 1 hour 10 apprentices can finish 1/20 of the job.
30 journeymen can finish the same job in 4,5 hours,thus:
15 journeymen can finish the job in 5*2 = 10 hours;
In 1 hour 15 journeymen can finish 1/10 of the job.
Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/10=3/20 of the job.
Answer: D.
Answer: D
Question: The L.C.M of two numbers is 48. The numbers are in the ratio 1:4. The sum of numbers is:
Options:
A)28
B)30
C)40
D)50
E)60
Rationale: Let the numbers be 1x and 4x.
Then, their L.C.M = 4x. So, 4x = 48 or x = 12.
The numbers are 12 and48.
Hence, required sum = (12+ 48) = 60.
ANSWER:E
Answer: E
Question: Find the compound interest on Rs. 10,000 in 2 years at 4% per annum, the interest being compounded half-yearly.
Options:
A)Rs 824.32
B)Rs 822.32
C)Rs 700
D)Rs 900
E)Rs 624.00
Rationale: Principal = Rs. 10000; Rate = 2% per half-year; Time = 2 years = 4 half-years.
Amount =
Rs [10000 * (1+(2/100))4] = Rs(10000 * (51/50) * (51/50) * (51/50) * (51/50))
= Rs. 10824.32.
:. C.I. = Rs. (10824.32 - 10000) = Rs. 824.32.
ANSWER A Rs 824.32
Answer: A
Question: John had a stock of 700 books in his bookshop. He sold 50 on Monday, 82 on Tuesday, 60 on Wednesday, 48 on Thursday and 40 on Friday. What percentage of the books were not sold?
Options:
A)26.5%
B)50%
C)46.5%
D)56.5%
E)60%
Rationale: Let N be the total number of books sold. Hence
N = 50 + 82 + 64 + 78 + 135 = 280
Let M be the books NOT sold
M = 700 - N = 700 - 280 = 420
Percentage
Books not sold / total number of books = 420/700= 0.60 = 60%
correct answer E
Answer: E
Question: There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
Options:
A)72
B)48
C)64
D)24
E)8
Rationale: Let's say that Models of Europe are represented by E1 and E2 respectively
Let's say that Models of South America are represented by S1 and S2
Let's say that Models of North America are represented by Na and N2
So we have to define the total ways of entries of E1 E2 S1 S2 N1 N2
We have to keep E1 E2 together and similarly N1 N2 together and similarly S1 S2 together so make three groups of two models from same region each
Arrangement of these three Group can be done in 3! ways
Arrangement of Models within Group can be done in 2!x2!x2! ways
i.e. Total Ways of Arranging the models so that they are grouped as per region together = (3!)*(2!x2!x2!) = 6*8 = 48
Answer: Option B
Answer: B
Question: Pat, Kate, and Mark charged a total of 117 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate?
Options:
A)18
B)36
C)72
D)90
E)65
Rationale: 65
all u do is do
2:1:6=>2x+x+6x=117=>x= 13
26:13:78
78-13=65
Answer E
Answer: E
Question: In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors S?
Options:
A)2
B)3
C)5
D)6
E)8
Rationale: I like to put the numbers in prime factors so it is easier and faster to visualize.
14*n/60
If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have
(2*7*n)/(2^2*3*5)
Simplifying
7*n/(2*3*5)
The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7.
The number could be 2*3*5, or 2*3*5*2, or 2*3*5*.....
However to be less than 200 we can not add any prime number.
2*3*5 = 120
If we added the next prime factor 7, we would have S=2*3*5*7 = 840
Thus, answer B
Answer: B
Question: Peter invests a sum of money and gets back an amount of $ 830 in 3 years . David invests an equal amount of money and gets an amount of $854 in 4 years. If both amounts were invested at the same rate (simple interest ) What was the sum of money invested ?
Options:
A)670
B)664
C)698
D)758
E)700
Rationale: Since both Peter and David invested the same amount of money at the same rate, they would earn same interest per year.
David invested for one year more than Peter and hence he got interest amount for one more year.
Interest earned per year = Amount received by David - Amount received by Peter = 854 - 830 = 24
Interest earned for 3 years = 24*3 = 72
Amount invested = 830 - 72 = 758
Answer: D
Answer: D
Question: What is the probability of getting sum 10 with the help of three dice?
Options:
A)1/2
B)1/4
C)1/6
D)1/8
E)1/10
Rationale: the following has 6 permutations.
(1, 3, 6),(1, 4, 5),(2, 3, 5)
Each of the following has 3 permutations.
(2, 2, 6),(2, 4, 4),(3, 3, 4)
the total possibility = 6*3 + 3*3 = 27
total no. of outcomes = 6*6*6 = 216
probability = 27/216 = 1/8 = 0.125
ANSWER:D
Answer: D
Question: A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 7 consecutive spaces in a random direction, what is the probability T the piece ends no more than 7 spaces from the square numbered 49?
Options:
A) 7%
B) 8%
C) 14%
D) 15%
E) 28%
Rationale: OA is E
required prob is 7 spaces any side of 49.
so total 14 spaces are required in 7 moves which can be achieved by max 7 move on any side
so total spaces = 28
probability T= 28%.E
Answer: E
Question: 70% of the employees in a multinational corporation have VCD players, 75 percent have microwave ovens, 90 percent have ACs and 85 percent have washing machines. At least what percentage of employees has all four gadgets?
Options:
A)(a) 15%
B)(b) 5%
C)(c) 10%
D)(d) 20%
E)(e) 25%
Rationale: so 30% employees don't have VCD devices.
25% employees don't have MO
10% employees don't have ACs
15% employees don't have WM
Summ of employees that don't have some device = 30%+25%+10%+15% = 80% < 100%
So definitely at least 20% employees have 4 devices.
ans: D
Answer: D
Question: I. 9a2 + 18a + 5 = 0,
II. 2b2 + 13b + 20 = 0 to solve both the equations to find the values of a and b?
Options:
A)If a > b
B)If a ≥ b
C)If a < b
D)If a ≤ b
E)If a = b or the relationship between a and b cannot be established.
Rationale: I. 9a2 + 3a + 15a + 5 = 0
=>(3a + 5)(3a + 1) = 0 => a = -5/3, -1/3
II. 2b2 + 8b + 5b + 20 = 0
=>(2b + 5)(b + 4) = 0 => b = -5/2, -4
a is always more than b.
a > b.
ANSWER:A
Answer: A
Question: Griffin has a bag of marbles that contains 7 black marbles and 5 red marbles. If he removes 3 marbles at random without replacing any of the marbles, what is the probability that all 3 marbles selected will be red?
Options:
A)1/22
B)2/33
C)3/44
D)4/55
E)5/66
Rationale: P(3 red marbles) = 5/12*4/11*3/10 = 1/22
The answer is A.
Answer: A
Question: If $5,000 is invested in an account at a simple annual rate of r percent, the interest is $250. When $19,000 is invested at the same interest rate, what is the interest from the investment?
Options:
A)$700
B)$750
C)$800
D)$950
E)$900
Rationale: -> 250/5,000=5% and 19,000*5%=950.
Thus, D is the answer.
Answer: D
Question: A motor cyclist participant of a race says "We drove with the speed of 10 miles an hour one way, but while returning because of less traffic we drove on the same route with 20 miles per hour." What was their average speed in the whole journey?
Options:
A)13.3 miles/hour
B)12 miles/hour
C)11 miles/hour
D)13 miles/hour
E)14 miles/hour
Rationale: 2xy/x+y=13.3 miles/hour
ANSWER:A
Answer: A
Question: At a certain school 55% of the students join a band, 25% play a sport and 20% both join the band and play a sport. if a randomly selected student is a member of the band, what is the probablility that the student also plays a sport?
Options:
A)1) 3/4
B)2)4/5
C)3)2/5
D)4)1/2
E)5)1/5
Rationale: This is the way to approach the question:
25% of the students join a band => 25% of the students either only join a band or both join a band and play sports
25% of the students play sports => 25% of the students either only play sports or both play sports and join a band
If a randomly selected student is a member of the band, then probability that the student also plays a sport = percentage of cases in which the student can do both/percentage of cases in which the student can just play sports or do both
=20%/25% = 4/5
The answer is therefore (B)
Answer: B
Question: Find the value of y: y² + y − 2.
Options:
A)-1 and 2
B)-2 and -1
C)-2 and 1
D)1 and 2
E)0 and 2
Rationale: That quadratic is factored as follows:y² + y − 2 = (y − 1)(y + 2).Now, it is easy to see that the first factor will be 0 when y = 1Now, it is easy to see that the second factor will be 0 when y = -2The solutions are:x	=	-2 and 1 C
Answer: C
Question: A train 100 m long crosses a platform 125 m long in 15 sec; find the speed of the train?
Options:
A)91.2 kmph
B)61.9 kmph
C)45.9 kmph
D)61.2 kmph
E)71.2 kmph
Rationale: D = 100 + 155 = 255
T = 15
S = 255/15 * 18/5 = 61.2 kmph
ANSWER:D
Answer: D
Question: 2^2*3^3*2^3*3^2*2^2 =
Options:
A)3^5*2^5
B)2^9*3^4
C)2^4*3^9
D)5^8
E)6^10
Rationale: 2^2*3^3*2^3*3^2*2^2 =
A) 3^5*2^5
B) 2^9*3^4
C) 2^4*3^9
D) 2^7*3^5
E) 6^10
If the base is same, powers are added so that follows D) 2^7*3^5.
Hence the answer is D
Answer: D
Question: A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. The maximum marks are
Options:
A)600
B)500
C)400
D)300
E)None of these
Rationale: Explanation :
Given that the student got 125 marks and still he failed by 40 marks
=> The minimum pass mark = 125 + 40 = 165
Given that minimum pass mark = 33% of the total mark
=> Total Mark × (33/100) = 165
=> Total Mark = 16500/33 = 500
Answer : Option B
Answer: B
Question: If the mean of numbers 28, x, 42, 78, 82 and 104 is 62, then what is the mean of 128, 255, 511, 1023 and x?
Options:
A)395
B)275
C)391
D)415
E)365
Rationale: The mean of numbers 28, x, 42, 78 and 104 is 62: 28+x+42+78+82+104=62*6 --> x=38;
So, the mean of 128, 255, 511, 1023 and x is (128+255+511+1023+38)/5=391.
Answer: C.
Answer: C
Question: A rotameter is a device that measures flow of liquid and gases. When measuring liquid phase flows, 2.5 inches represent 60 liters per minute of liquid. With gas measurements the rotameter moves 50% of the movement he moves with the liquid phase. How many liters of gas passed through the rotameter if it measured 4 inches?
Options:
A)176
B)192
C)202
D)218
E)284
Rationale: In case of liquid- 2.5 inches represents 60 lit/min.
In case of gas- 50% of 2.5 inches represents 60 lit/min
1.25 inches represents 60 lit /min
4 inches will represent 60*4/1.25= 192
B is the answer
Answer: B
Question: Mr. X is rewriting legislation to unevenly split $6,000,000 in funds to towns in his district. There are 5 counties in his district. What is the least amount of money he could spend to equally distribute the funds per county?
Options:
A)$1,100,200
B)$1,250,000
C)$1,000,200
D)$1,200,000
E)none of the above
Rationale: This problem requires us to divide our main amount by 5.
Since the current amount is easily divisible by 5, as in anything that is either a multiple of 5 or 10 could be divided to an exact, whole number.
And by dividing our amount, we get the answer.
Correct option: D
Answer: D