MU-NLPC/Calc-aqua_rat huggingface dataset:
A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?	Choose the correct choice from the following choices.
A) 278	B) 166	C) 151	D) 270	E) 109

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Time= 26 sec.   Let the length of the train be x meters.   Then, (x + 250)/26 = 20   x = 270 m.   Answer:270
Answer: D
One of the following numbers can be marked out as the odd one out. can you find which one?
1) 680986879
2) 716089780
3) 820670987
4) 932967879	Choose the correct choice from the following choices:  A) The odd number is 680986879  B) The odd number is 820670987  C) The odd number is 716089780  D) The odd number is 932967879  E) None

Solution: Correct Answer : The odd number is 820670987   if you add up the first three digits of all the numbers, it adds up to 14 except for second option 820670987
Answer: B
At an M&M factory, two types of M&Ms are produced, red and blue. The M&Ms are transported
individually on a conveyor belt. Anna is watching the conveyor belt, and has determined that
four out of every five red M&Ms are followed by a blue one, while one out of every six blue
M&Ms is followed by a red one. What proportion of the M&Ms are red?  Choose the correct choice from the following:
A) 1/29	B) 2/29	C) 3/29	D) 4/29	E) 5/29

Solution: Suppose that the fraction of red M&Ms is fr and the fraction of blue M&Ms   is fb. Then the probability that Anna sees a red one emerge next is fr. This probabil-   ity can also be expressed using conditional probabilities as fr = P(blue)P(red after blue) +   P(red)P(red after red), or fr = fb(1=6) + fr(1=5). Likewise, we find fb = fr(4=5) + fb(5=6).   Solving the system of equations gives fb = 24   29 and fr =5/29   correct answer 5/29
Answer: E
If 5x + 3 = 10x – 22, what is the value of x? Select the correct option:
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: solve for x:   5x+3=10x-22   25=5x   5=x   correct answer 5)5
Answer: E
If each term in the sum R=a1+a2+a3+...+an either 2 or 22 and the sum equals 100, which of the following could be equal to n? Select the correct option:
A) 38  B) 39  C) 40  D) 41  E) 42

Solution: Min value of 'n' can be 10 i.e 4*22+6*12=R => 22+22+22+22+2+2+2+2+2+2= 
22+22+22+22+2+2+2+2+2+2 = 100
100   Since we don't have 10 in the options proceed further, (10-1)+22/2=> 20 digits, which is again not in the options    (20-1) + 22/2= 
 (20-1) + 22/2 = 30
30 digits ( not in options)   (30-1) + 22/2= 
(30-1) + 22/2 = 40
40 digits   Hence 40.
Answer: C
The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 32,000 locusts?
Choose the correct choice from the following answers: A) 2 B) 4 C) 6 D) 8 E) 9

Solution: - 4 hours: 1,000   -2 hours: 2,000   Now: 4,000   + 2 hours: 8,000   + 4 hours: 16,000   + 6 hours: 32,000   Answer : 6
Answer: C
The price of a book is increased from $300 to $330. What is the % of increase in its price? Choose the correct answer:
A) 10%	B) 20%	C) 30%	D) 35%	E) 45%

Solution: Explanation: Change in the price = Rs 330 – Rs 300   = Rs 30   Percentage of increase = Change in the price Initial Price   * 100.   Percentage increase in price =( 30 / 300   ) *100 = 10%   10%
Answer: A
The 44 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees?  Choices.
A) 4  B) 6  C) 8  D) 9  E) 10

Solution: The formula is Total = 4+B+C - sum of exactly two + 2*all three + neither   21+18+19-x-2*5=44   solving for x you get 4   4nswer 4
Answer: A
A and B together can do a piece of work in 2 days. If A alone can do the same work in 22 days, then B alone can do the same work in?	Choose the correct choice from the following answers.
A) 0.35 days B) 0.45 days C) 0.55 days D) 0.25 days E) 0.15 days

Solution: 0.45 days = 1/2 – 1/22 =0.45 days   ANSWER:0.45 days
Answer: B
A farmer wishes to start a 100 sq. m. rectangular vegetable garden. Since he has only 30 meter barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. Then find the dimension of the garden.
Choose the correct choice from the following options
A) 20 m * 58 m	B) 20 m * 7 m	C) 20 m * 5 m	D) 80 m * 5 m	E) 20 m * 1 m

Solution: From the question, 2b+l = 30   => l = 30-2b   Area=100m2=>l×b=100=>b(30−2b)=100b2−15b+50=0=>(b−10)(b−5)=0   Area=100m2=>l×b=100=>b(30−2b)=100b2−15b+50=0=>(b−10)(b−5)=0   b = 10 or b = 5   when b = 10 then l = 10   when b = 5 then l = 20   Since the garden is rectangular so we will take value of breadth 5.   So its dimensions are 20 m * 5 m   Answer: 20 m * 5 m
Answer: C
The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is? Choose one
A) 27 B) 82 C) 245 D) 288 E) 232

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.   Answer:245
Answer: C
A, B and C invest in a partnership in the ratio: 7/2, 4/3, 6/5. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 27,000, then what is B's share in the profit?
Choose the correct choice from the following:
A) Rs. 2000 B) Rs. 3000 C) Rs. 4000 D) Rs. 5000 E) None of these

Solution: Explanation :   Ratio of the initial investment = 7/2 : 4/3 : 6/5   = 105 : 40 : 36   From this ratio, we can assume that actual initial investments of A, B and C   are 105x, 40x and 36x respectively   A increases his share 50% after 4 months. Hence the ratio of their investments =   (105x * 4) + (105x * 150/100 * 8) : 40x * 12 : 36x : 12   = 105 + (105 * 3/2 * 2) : 40*3 : 36 * 3   = 105 * 4 : 40 *3 : 36 * 3   = 35 * 4 : 40 : 36   = 35 : 10 : 9   B's share = total profit * (10/54) = 27,000 * 10/54 = 5000. Answer : Option Rs. 5000
Answer: D
A polling company surveyed a certain country, and it found that 35% of that country’s registered voters had an unfavorable impression of both of that state’s major political parties and that 20% had a favorable impression only of Party A. If one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of Party B, then what percentage of the country’s registered voters have a favorable impression of both parties (assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only)?	Select
A) 15
B) 20
C) 30
D) 35
E) 45

Solution: Assume the total pool of registered voters = 100, so 35 of the country’s registered voters had an unfavorable impression of both of that state’s major political parties and 20 had a favorable impression only of Party A   let x = # of voters with a favorable impression of both parties   let 2x = # of voters with a favorable impression only of Party B   so unfavorable A and favorable B # of voters = 2x-x = x   35+x = number of unfavorable A   20+ 35+x = 100   55+x=100   x=45   ANSW45R:45
Answer: E
In 16 minutes, the minute hand gains over the hour hand by Choose one.
A) 16°  B) 80°  C) 88°  D) 96°  E) None of these

Solution: In 1 hour, the minute hand gains 330° over the hour hand.   i.e. in 60 minute, the minute hand gains 330° over the hour hand.   ∴ In 16 minutes, the minute hand gains over the hour hand by 330°⁄60 × 16° = 88°   Answer 88°
Answer: C
A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?  Select
A) 11 B) 18 C) 19 D) 12 E) 15

Solution: A:18 = 2:3   18:C = 2:5   A:18:C = 4:6:15   6/25 * 75= 
6/25 * 75 = 18
18   Answer: 18
Answer: B
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
Pick:
A) 10 days  B) 12 days  C) 15 days  D) 20 days  E) 25 days

Solution: A's 2 day's work = 1	x 2 =	1	.   20	10   (A + B + C)'s 1 day's work = 1	+	1	+	1 =	6	=	1	.   20	30	60	60	10   Work done in 3 days = 1	+	1 =	1	.   10	10	5   Now,	1	work is done in 3 days.   5   Whole work will be done in (3 x 5) = 15 days.   Option 15 days
Answer: C
What is the greatest positive integer E such that 3^E is a factor of 9^10?	Choose the correct choice from the following choices:
A) E=5
B) E=9
C) E=10
D) E=20
E) 30

Solution: What is the greatest positive integer E such that 3^E is a factor of 9^10?   9^10 = (3^2)^10 = 3^20   D. 20
Answer: D
A parking garage rents parking spaces for $10 per week or $35 per month. How much does a person save in a year by renting by the month rather than by the week? Choose the correct choice from the following answers.
A) $100 B) $160 C) $220 D) $240 E) $260

Solution: 10$ per week!   An year has 52 weeks.   Annual charges per year = 52* 10= 
52* 10 = 520
520$   35$ per month!   An year has 12 months.   $100nnual charges per year= 12 * 35= 
12 * 35 = 420
420$    520 - 420= 
 520 - 420 = 100
100   $100ns $100
Answer: A
How many arrangements of the letters of the word CONTINUES can be made, without changing the place of the vowels in the word?
Pick one:
A) 130
B) 140
C) 150
D) 120
E) 110

Solution: O,I,E,U fixed. Consonants can be arrangements in 5P5 = 5! = 120 ways   Option '120'
Answer: D
A train with 120 wagons crosses John who is going in the same direction, in 36 seconds. It travels for half an hour from the time it starts overtaking the John ( he is riding on the horse) before it starts overtaking the Mike(who is also riding on his horse) coming from the opposite direction in 24 seconds. In how much time (in secs) after the train has crossed the Mike do the John meets to Mike?	Pick.
A) 2534 s	B) 5435 s	C) 7645 s	D) 7456 s	E) 3576 s

Solution: Let the length of the train be L metres and speeds of the train Arun and Sriram be R, A and S respectively, then   ---------- (i)   and ---------(ii)   From eq.(i) and (ii)   3(R - A ) = 2 (R + K)   R = 3A + 2K   In 30 minutes (i.e 1800 seconds), the train covers 1800R (distance) but the Arun also covers 1800 A (distance) in the same time. Therefore distance between Arun and Sriram, when the train has just crossed Sriram   = 1800 ( R - A) - 24 ( A + K)   Time required =   = (3600 - 24)= 
(3600 - 24) = 3_576
3576 s   3576 s
Answer: E
A train passes a station platform in 48 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?	Select the correct option
A) 476 m  B) 420 m  C) 440 m  D) 407 m  E) 402 m

Solution: Speed = [54 * 5/18] m/sec   = 15 m/sec.   Length of the train = (15 * 20)= 
(15 * 20) = 300
300 m.   Let the length of the platform be x meters.   Then, x + 300 / 48= 15   x + 300 = 720   x =420 m.   Answer: 420 m
Answer: B
What was the day of the week on 17th June 1998?	Options
A) Monday	B) Sunday	C) Wednesday	D) Friday	E) Tuesday

Solution: Explanation:   17 Jun 1998 = (1997 years + period from 1-Jan-1998 to 17-Jun-1998)   We know that number of odd days in 400 years = 0   Hence the number of odd days in 1600 years = 0 (Since 1600 is a perfect multiple of 400)   Number of odd days in the period 1601-1900   = Number of odd days in 300 years   = 5 x 3 = 15 = 1   (As we can reduce perfect multiples of 7 from odd days without affecting anything)   Number of odd days in the period 1901-1997   = 73 normal years + 24 leap year   = 73 x 1 + 24 x 2 = 73 + 48= 
73 + 48 = 121
121= (121 - 7 x 17) = 2 odd days   Number of days from 1-Jan-1998 to 17-Jun-1998   = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31(may) + 17(Jun)   = 168 = 0 odd day   Total number of odd days = (0 + 1 + 2 + 0)= 
(0 + 1 + 2 + 0) = 3
3   3 odd days= Wednesday   Hence 17th June 1998 is Wednesday.   Answer: Option Wednesday
Answer: C
If p is an odd integer and q is an even integer, which of the following must be an even integer?  Choose the correct choice from the following answers.
A) 2q-p
B) 3p+q
C) 2p+3q
D) 4(p+q)
E) p+q^2

Solution: p is odd; for this assume p=1   q is even; for this assume q = 2   (2*2)-1= 
(2*2)-1 = 3
3 Odd    (3*1)+2= 
 (3*1)+2 = 5
5 Odd   (2*1)+(3*2)= 9 Odd   4(1+2) = 12 Even   1+(2^2) = 5 Odd   Answer:4(p+q)
Answer: D
Which of the following cannot be the sum of 2 different prime numbers?  Choose the most appropriate option.
A) 10	B) 13	C) 14	D) 15	E) 19

Solution: Option A: 10 = 7 + 3. Sum of 2 different prime numbers.   Option B: 13 = 11 + 2. sum of 2 different prime numbers   Option C: 4 = This is not a sum of 2 different prime numbers.   Option D: 15 = 13 + 2. Sum of 2 different prime numbers   Option E: 19 = 17 + 2. Sum of 2 different prime numbers   14orrect Option: 14
Answer: C
A man buys $50 shares in a company which pays 10% dividend. If the man gerts 12.5% on his investment, at what price did he buy the shares?  Choices.
A) 37.5
B) 40
C) 50
D) 48
E) 52

Solution: Dividend on 1 share = $(10/100*50)= 
(10/100*50) = 5
$5   $12.5 is an income on an investment of $100   $5 is an income on an investment of $  (100*2/25*5)= 
  (100*2/25*5) = 40
40   Thus, cost of 1 share=$40   ANSWER 40
Answer: B
All of the stocks on the over-the-counter market are designated by either a 6-letter or a 7-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
Choose the correct choice from the following:
A) a. 2(26^5)  B) b. 26(26^4)  C) c. 27(26^4)  D) d. 26(26^5)  E) e. 27(26^6)

Solution: no of different stocks for 6-letter code = 26^6   no of different stocks for 7-letter code = 26^7   total = 26^6 + 26^7 = 26^6(26+1) = 27(26^6)   [Reveal]Spoiler:   Option e. 27(26^6)
Answer: E
There are 418 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 8 : 11, then how many nurses are there in the hospital?	Select:
A) 152 B) 209 C) 242 D) 171 E) 181

Solution: Given,   The ratio of the doctors to the nurses is 8 : 11   Number of nurses = 11/19 x 418 = 242   ANSWER:242
Answer: C
Two-third of two-fifth of three-fourth of a number is 36. What is the square root of four-fifth of that number? Choose the correct choice from the following:
A) 9
B) 12
C) 14
D) 16
E) 20

Solution: Explanation:   We have, 2/3 * 2/5 * 3/4 * X = 36   X = 180   Now, 4/5 * X = 4/5 * 180= 
4/5 * 180 = 144
144   √144= 12   ANSWER: 12
Answer: B
A grocer has a sale of Rs. 5921, Rs. 5468, Rs. 5568, Rs. 6088 and Rs. 6433 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 5900? Choices.
A) 4902  B) 4922  C) 5922  D) 5924  E) 5928

Solution: Total sale for 5 months = Rs. (5921 + 5468 + 5568 + 6088 + 6433) = Rs. 29478.   Required sale = Rs. [ (5900 x 6) - 29478 ]   = Rs. (35400 - 29478)   = Rs. 5922.   ANSWER:5922
Answer: C
Four packages have an average weight of 14.5 pounds. What is the minimum possible weight of the heaviest package in pounds if the median is 12 pounds?  Select the correct option.
A) 25 B) 24 C) 23 D) 22 E) 21

Solution: Let us denote the weights of the packages in pounds by a, b, c, d naming from the lightest one to the heaviest one. The median is 12 pounds. Therefore (b + c) / 2 = 12.   b + c = 24   The average is 14.5 pounds. Therefore (a + b + c + d) / 4 = 14.5.   a + (b + c) + d = 58   a + 24 + d = 58   a + d = 34   The weight a must be no greater than 12, since 12 is the median. Therefore the minimum possible weight of the heaviest package is 34 – 12 = 24 pounds (all the other packages would weigh 12 pounds in this case).   Answer: 24
Answer: B
The average price of 10 books is Rs.12 while the average price of 8 of these books is Rs.11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what is the price of each of these two books?	Pick one:
A) Rs. 5, Rs.7.50
B) Rs. 8, Rs. 12
C) Rs. 16, Rs. 10
D) Rs. 12, Rs. 14
E) NOne

Solution: Solution:   Total cost of 10 books = Rs. 120   Total cost of 8 books = Rs. 94   => The cost of 2 books = Rs. 26   Let the price of each book be x and y.   => x + y = 26 ---------------- (1)   (160/100)y+y =26   On Solving for y, we get   y = 10.   Now, Substituting y = 10 in (1) we get,   x + 10 = 26   x = 16.   So the price of each book is Rs. 16 and Rs. 10 respectively.   Answer: Option Rs. 16, Rs. 10
Answer: C
If the operation ∆ is defined by a ∆ b = (b - a)^2/a^2 for all numbers a and b, and a ≠ 0, then what is the result when we evaluate this expression: (-4) ∆ (4 ∆ −4) ?
Choose the correct choice from the following answers:
A) 2
B) 4
C) 6
D) 8
E) 10

Solution: (-4) ∆ (4 ∆ −4) =   (-4) ∆ (8^2/4^2) =   (-4) ∆ (4) =   (-8^2) / (-4)^2 = 4   The answer is 4.
Answer: B
The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact? Pick:
A) 18/35  B) 18/35  C) 18/39  D) 18/31  E) 18/32

Solution: If both agree stating the same fact, either both of them speak truth of both speak false.   Probability = 3/5 * 4/7 + 2/5 * 3/7   = 12/35 + 6/35 = 18/35   18/35nswer: 18/35
Answer: A
In a sample of Christ college students, 30 percent are third year students and 90 percent are not second-year students. What fraction of those students who are not third-year students are second-year students?  Options.
A) 3/4 B) 2/3 C) 4/7 D) 1/2 E) 1/7

Solution: = 10/70. = 1/7   my answer is 1/7 too
Answer: E
A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slips back 20 feet before he again starts climbing in the beginning of the next hour. If he begins his ascent at 8.00 a.m., at what time will he first touch a flag at 120 feet from the ground? Choose the correct choice: A) 4 p.m. B) 5 p.m. C) 6 p.m. D) 7 p.m. E) None of these

Solution: A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slips back 20 feet before he again starts climbing in the beginning of the next hour.   It means monkey climbs effectively 10 ft in 1 hr.   so it climbs 90 ft in 9 hrs .   balance 30 ft is covered in 10th hr.   So total it will take 10 hrs.   Monkey will touch 120 ft flag at 8+10 = 1800 hrs or 6 PM.   ANSWER:6 p.m.
Answer: C
An article costing rs.160 is sold at 15% discount on a mark-up price. What is the selling price after
discount?  Choose the correct choice from the following:
A) 106  B) 116  C) 126  D) 136  E) 146

Solution: Rs. 136   160-(160*15/100)=160*85/100= 
160*85/100 = 136
136   ANSWER:136
Answer: D
For dinner at a restaurant, there are x + 1 choices of appetizers, y + 1 main courses, and z choices of dessert. How many total possible choices are there if you choose 1 appetizer, 1 main course, and 1 dessert for your meal?
Answers:	A) x + y + z + 1	B) xyz + xz	C) xyz+xz+yz+z	D) xyz + 1	E) xyz + 1/2

Solution: x +1 appetizers,   y + 1 main courses,   z dessert   Required: 1 appetizer, 1 main course, and 1 dessert   Number of ways possible = (x+1)xyz+xz+yz+z1*(y+1)xyz+xz+yz+z1*zxyz+xz+yz+z1 {Nxyz+xz+yz+z1 = N! / (N-1)!*1! = N}   Hence, number of ways = (x+1)(y+1)z = (yz+z)(x+1)=xyz+xz+yz+z   xyz+xz+yz+zorrect Option: xyz+xz+yz+z
Answer: C
In a race of length L metres, Johnson beats Lewis by X metres and Greene by Y metres, By how many metres does Lewis beat Greene in the same race ? (X<Y)	Pick one
A) L(L-Y) / L-X B) L(Y-X) / L-X C) L-Y D) X-Y E) X+Y

Solution: As the time is constant, the ratio of distances will be the same as the ratio of speeds.   If Sj,Sl,Sg are the speeds of Johnson, Lewis, and Greene respectively, then   Sj/Sl = L/(L-X)   and Sj/Sg = L/(L-Y)   => Sg/Sl = (L-Y)/(L-X)   Therefore the speeds of Lewis and Greene are in the ratio (L-X)/(L-Y)   When Lewis finishes the race, the time run by him and Greene are same   => The ratio of the speeds of Lewis and Greene will be the same as the ratio of distances run by them.   => Distance run by Greene when Lewis finishes the race = (L-Y)/(L-X) * L   => Lewis beats Greene by L - L*(L-Y)/(L-X) = L [ 1 - (L-Y)/(L-X)] = L (Y-X) / (L-X)   Option (L(Y-X) / L-X) is therefore correct.
Answer: B
A green grocer received a boxful of tomatoes and on opening the box found that several had gone bad. He then counted them up so that he could make a formal complaint and found that 68 were mouldy, which was 16 per cent of the total contents of the box. How many tomatoes were in the box? Answers
A) 336 B) 425 C) 275 D) 235 E) 689

Solution: 425   425   (68 Ã· 16) Ã— 100
Answer: B
Find the perimeter and area of the rectangle of length 15 cm and breadth 13 cm. Choose the correct choice:  A) 71 cm2  B) 121 cm2  C) 141 cm2  D) 195 cm2  E) 221 cm2

Solution: length = 15 cm, breadth = 13 cm   Perimeter of rectangle = 2 (length + breadth)   = 2 (15 + 13) cm   = 2 × 28 cm   = 56 cm   We know that the area of rectangle = length × breadth   = (15 × 13) cm22   = 195 cm2   ANSWER : 195 cm2
Answer: D
6 points are marked on a straight line and another 7 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?
Choose the correct answer.
A) 21 B) 281 C) 168 D) 196 E) 364

Solution: Solution: select 2 from 6 and one from 7 + select 2 from 7 and 1 from 6   6C2*7C1 + 7C2*6C1   = 281   Answer : 281
Answer: B
A Contractor employed a certain number of workers to finish constructing a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the scheduled time, so he at once doubled the no of workers and thus he managed to finish the road on the scheduled time. How much work he had been completed, before increasing the number of workers?  Choose the most appropriate option
A) 14 9/7 % B) 14 2/7 % C) 14 2/3 % D) 14 2/5 % E) 54 2/7 %

Solution: Explanation:   Let he initially employed x workers which works for D days and he estimated 100 days for the whole work and then he doubled the worker for (100-D) days.   D * x +(100- D) * 2x= 175x   => D= 25 days   Now , the work done in 25 days = 25x   Total work = 175x   therefore, workdone before increasing the no of workers = \frac{25x}{175x}\times 100=14\frac{2}{7} %   Answer: 14 2/7 %) 14 2/7 %
Answer: B
A train running at the speed of 120 km/hr crosses a pole in 18 seconds. What is the length of the train?  Choose the correct choice from the following answers: A) 560 B) 570 C) 580 D) 590 E) 600

Solution: Speed=(120 x(5/18)m/sec	=(100/3)m/sec.   Length of the train = (Speed x Time).   Length of the train =	((100/3)x 18)m = 600 m   600
Answer: E
In an examination, 25% of total students failed in Hindi, 40% failed in English and 35% in both. The percentage of these who passed in both the subjects is :
Options
A) 10% B) 20% C) 30% D) 40% E) 50%

Solution: pass percentage = 100 - (25+40-35) = 100-70= 
100-70 = 30
30   ANSWER:30%
Answer: C
A set of 11 positive integers has an average of 20. Which of the following is the greatest possible value for the median of this set?	Choose the correct choice from the following options:	A) 25	B) 30	C) 35	D) 45	E) 46

Solution: for the median to bé max , we should take all the values below meadian to be the lowest and the remaining values to be the same..   here 1 is the lowest value(positive int) số thẻ lowest 5 int will equal 5..   remaining 6= 20*11-5=215..   therefore each valueof these 6 int =215/6=35   ans 35
Answer: C
here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?	Choose one.
A) 1234
B) 4512
C) 1800
D) 1203
E) 4512

Solution: 5 subjects can be arranged in 6 periods in 6P5 ways.   Any of the 5 subjects can be organized in the remaining period (5C1 ways).   Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.   Total number of arrangements   = 6P5× 518001 /2!=1800   Ans: 1800
Answer: C