MU-NLPC/Calc-aqua_rat huggingface dataset:
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?  Choose the correct choice from the following choices
A) 25200	B) 33232	C) 23228	D) 29982	E) 20822

Solution: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)   =7C3X4C2   = 210.   Number of groups, each having 3 consonants and 2 vowels = 210.   Each group contains 5 letters.   Number of ways of arranging 5 letters among themselves   = 5!   = 120   Required number of ways = (210 x 120) = 25200.   25200nswer: 25200
Answer: A
If 12 men or 20 women can do a piece of work in 54 days, then in how many days can 9 men and 12 women together do the work? Pick one:
A) 22 days	B) 88 days	C) 40 days	D) 55 days	E) 44 days

Solution: Given that 12m = 20w => 3m = 5w   9 men + 12 women = 15 women + 12 women = 27 women   20 women can do the work in 54 days. So, 27 women can do it in   (20 * 54) /27= 
  (20 * 54) /27 = 40
40 days.   Answer: 40 days:
Answer: C
On tuesday Morning, Chris receives tickets to a baseball game that will be played at 8pm on the next evening that it does not rain. However, Chris is only in town until Thursday morning, at which point he must fly to another city. If there is a 30% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game? Choose the correct choice from the following answers: A) 36% B) 91% C) 66% D) 80% E) 84%

Solution: Chris won't be able to attend the game if it be raining on Monday eveningandTuesday evening. The probability of that is 0.3*0.3 = 0.09. So, the probability that he will be able to attend is 1 - 0.09 = 0.91.   Answer: 91%.
Answer: B
How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5412, 6336  Select the correct option:
A) 4
B) 5
C) 6
D) 7
E) 8

Solution: A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.   Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.   Each one of remaining 5 is divisible by each one of 11, 3 and 4 and therefore, by 132.   ANSWER:5
Answer: B
Current age of Bruce and Tomy r in the ratio of 5:4 respectively. 3 years hence, the ratio of their ages will become 11:9 respectively. What is Tomy 's present age in years?  Choose the correct choice from the following.
A) 12 years	B) 16 years	C) 24 years	D) 32 years	E) 36 years

Solution: Let the present ages of Bruce and Tomy be 5x years and 4x years respectively.   Then, 5x + 3 = 11   4x + 3 9   9(5x + 3) = 11(4x + 3)   45x + 27 = 44x + 33   45x - 44x = 33 - 27= 
33 - 27 = 6
6.   Anand's present age= 4x = 24 years.   24 years
Answer: C
In traveling from a dormitory to a certain city, a student went 1/3 of the way by foot, 1/4 of the way by bus, and the remaining 5 kilometers by car. What is the distance, in kilometers, from the dormitory to the city? Choose the correct choice from the following answers.
A) 13	B) 17	C) 42	D) 15	E) 12

Solution: Whole trip = distance by foot + distance by bus + distance by car   x = 1/2x + 3/5x + 5   x - 1/2x - 3/5x = 5   x = 12km   Option: 12
Answer: E
How many different arrangements are possible to place seven different books on a shelf if all three math books must be placed next to each other? Select the correct option:
A) 120	B) 148	C) 360	D) 540	E) 720

Solution: Let the 3 math books be M1,M2,M3 while the rest be A,B,C,D for a total of 7 different books.   Consider 3 math books to be 1 collective item (=M1M2M3 = M , as they need to be together). Thus, number of arrangements of 3 different books (M1M2M3)= 3P3 = 3!   Total number of arrangements of M,A,B,C,D = 5P5= 5!   Thus, The total possible arrangements will be : M1M2M3 ABCD = 5!*3! = 720, 720 is the correct answer
Answer: E
John bought 9.25m of cloth for $444. Find the cost price per metre. Answers
A) 48  B) 47  C) 58  D) 56  E) 54

Solution: Cloth bought by John = 9.25 m   Cost of 9.25 m = $444   Cost per metre = 444 ÷ 9.25   The cost of the cloth per metre = $ 48   48nswers: 48
Answer: A
A certain team has 15 members, including Joey. A three-member relay team will be selected as follows: one of the 15 members is to be chosen at random to run first, one of the remaining 14 members is to be chosen at random to run second, and one of the remaining 13 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?  Choose the correct choice from the following answers
A) 1/1320  B) 1/132  C) 1/110  D) 1/12  E) 2/15

Solution: Total outcomes= 15*14*13   Favorable Outcomes= 14*1*13 and 14*13*1   P=2*14*13*1/15*14*13   P=2/15   Ans 2/15
Answer: E
Employee A work from 01:00 to 08:45 (24 hour clock) on each of the five days this week. Next week, he is scheduled to work the same total hours, but will work a compressed 4 day work schedule. If he starts work at 01:00 next week, what time will he finish each day?  Select the correct option:
A) 09:04 B) 10:41 C) 10:45 D) 11:56 E) 16:19

Solution: working hours between 01:00 - 08:45 for 5 days are 7:45*5 (5 days) = 38:45   same total hours are to be scheduled for 4 days,   so 38:45/4 = 10:41   ANSWER:10:41
Answer: B
A certain restaurant offers 4 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?  Choose one:  A) 8  B) 12  C) 15  D) 21  E) 14

Solution: As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain:   A. 2 kinds of cheese and 2 kinds of fruits --> 4C2*2C2=6*1= 
6*1 = 6
6   B. 1 kind of cheese and 1 kind of fruit --> 4C1*2C1=4*2= 
4*2 = 8
8   A+B=6+8= 
6+8 = 14
14   Answer: 14.
Answer: E
If 5 machines can produce 20 units in 10 hours, how long would it take 10 machines to produce 100 units?	Pick
A) 25  B) 30  C) 35  D) 24  E) 96

Solution: 5 machines would produce 100 units in 50 hours. Increasing the amount of machines by 2 would mean dividing 50 hours by 2.   50/2= 
50/2 = 25
25   25nswer : 25
Answer: A
A certain vehicle is undergoing performance adjustments during a set of three trials on an 8-mile track. The first time it travels around the track at a constant rate of p miles per minute, the second time at a constant rate of p^2 miles per minute, and the third time at a constant rate of p^3 miles per minute. If the vehicle takes the same time to travel the first 18 miles of these trials as it does to travel the last 8 miles, how many minutes does it take to complete all three trials (not counting any time between trials)? Select the correct option:
A) 18
B) 36
C) 60
D) 96
E) 112 minutes

Solution: The first journey takes 18 miles whereas the last journey takes 8 miles.   r1= p   r2=p^2   and r3= p^3 so we set up a table like   r x t = d   p x t1 = 8   p^2 x t2= 8   p^3 x t3 = 2 (because 18-16)   so the time taken to complete each leg individually amounts to t1 + t2 + t3 = (8/p) + (8/p^2) + (2/p^3). ----> (equation 1)   On the other hand, the time taken to complete the last leg of miles is (8/p^3) ---> (equation 2) because p^3 is the speed on the last leg. Since both the times are equal, equate them to get:   (8/p) + (8/p^2) + (2/p^3) = (8/p^3)   Taking the LCM of the Left hand equation and solving both these equations gives us the value of p=1/2 and p= (-3/2) Since p can not be negative, we have p=1/2 as our value.   Now put this value in the time taken to finish each trial which is the sume of (8/p) + (8/p^2) + (8/p^3) and it will become   16+32+64= 
  16+32+64 = 112
112 minutes.   Option 112 minutes is the correct answer.
Answer: E
Of the two square fields, the area of the one is 1 hectare, while anothe one is broader by 1%. There differences in area is: Choose the correct choice from the following answers
A) 201 m(power)2  B) 220 m(power)2  C) 211 m(power)2  D) 219 m(power)2  E) 205 m(power)2

Solution: 201 m(power)2rea of one square field = 10000 m(power)2   10000 × 1 = 10000   Side of this field = √10000 m = 100 m   Side of another square = 101 m   Difference of areas = [ 101(power)2 - 100(power)2 ] m(power)2   [101+100][101-100] m(power)2   (201)(1) m2 = 201 m(power)2   201 m(power)2nswer is 201 m(power)2.
Answer: A
Evaluate: 19 + sqrt(- 2 + 12Ã—6Ã·9) =?  Choose the correct option:	A) 51	B) 53	C) 55	D) 57	E) 59

Solution: According to order of operations, inner brackets first where 12x6Ã·9 is first calculated since it has a multiplication and a division.   12x6Ã·9 = 72Ã·9 = 8   Hence   19 + sqrt(- 2 + 12Ã—6Ã·9) = 19+ sqrt(- 2 + 8)   = 19 + sqrt(6) = 19 + 36= 
19 + 36 = 55
55   correct answer 55)55
Answer: C
How many ways are there to arrange the letters in the word tenant ?	Choices.
A) 1
B) 360
C) 3780
D) 7560
E) 11340

Solution: 6 total words, 2N   = 6! / 2! = 360. Answer 360
Answer: B
A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.300 when the rate to profit rises from 5 to 7 percent. Find the Capital of B? Select
A) 3377 B) 2899 C) 3750 D) 2778 E) 1991

Solution: A:B:3750 = 2/3:1/6:1/6 = 4:1:1   x * 2/100 * 2/3 = 300   B capital = 22500*1/6= 
22500*1/6 = 3_750
3750   Answer: 3750
Answer: C
How many integers are between 2 and 57/7, inclusive?  Options
A) 5 B) 7 C) 9 D) 10 E) 12

Solution: 57/7 = 8.xx   We are not concerned about the exact value of 57/7 as we just need the integers.   The different integers between 2 and 57/7 would be 2,3, 4, 5, 6, 7, 8.   Total number of integers = 7   Option 7
Answer: B
In how many ways 4 Indians and 3 Englishmen can be seated in a row so that they are alternate?  Pick one:
A) 120  B) 96  C) 144  D) 202  E) 256

Solution: number of ways = 4!*3! = 144   Answer is 144
Answer: C
On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 45 centimeters assuming that 1-inch is 2.54 centimeters?
Choices
A) 174.2
B) 212
C) 283
D) 296
E) 282.4

Solution: 1.5 inch = 2.54*1.5 cm.   So, 2.54*1.5 represents 24 miles.   So for 45 cm.:   45/(2.54*1.5) = x / 24 ---> x = 24*45/(3.81) = 283   Answer will be 283.
Answer: C
The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?	Options: A) 1:3 B) 2:5 C) 3:2 D) 9:4 E) 4:2

Solution: Explanation:   Let C.P. = Rs. 5x and S.P. = Rs. 7x.   Then, Gain = Rs. 2x   Required ratio = 2x : 5x = 2:5   Answer: Option 2:5
Answer: B
The sum of the ages of 4 children born at the intervals of 5 years each is 58 years. what is the age of the youngest child ? Pick one.
A) 7
B) 8
C) 10
D) None of these
E) Cannot be determined

Solution: Explanation:   Let x = the youngest child. Each of the other four children will then be x+5, x+10, x+15   We know that the sum of their ages is 58 .   so, x+(x+5)+(x+10)+(x+15) = 58   x= 7   The youngest child is 4 years old.   7nswer: 7
Answer: A
The average of nine numbers is 17. The average of first four numbers is 20 and the average of last four numbers is 16. What is the middle number?
Select the correct option:
A) A)7
B) B)8
C) C)9
D) D)10
E) E)11

Solution: The total of nine numbers = 9X17 = 153   The total of first 4 and last 4 numbers is = 4 X 20+4 X 16 = 144   So, the middle number is  (153 - 144 )= 
 (153 - 144 ) = 9
9   9
Answer: C
Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?  Answers:
A) 10 sec  B) 30 sec  C) 40 sec  D) 20 s  E) 50 sec

Solution: D   Relative speed = (42 + 30) * 5/18 = 4 * 5= 
4 * 5 = 20
20 mps.   Distance covered in passing each other= 120 + 280= 
120 + 280 = 400
400 m.   The time required= d/s = 400/20= 
400/20 = 20
20 s
Answer: D
A certain company charges $6 per package to ship packages weighing less than 2 pounds each. For a package weighing 2 pounds or more, the company charges an initial fee of $6 plus $2 per pound. If the company charged $28 to ship a certain package, which of the following was the weight of the package, in pounds?	Choose the correct option:
A) 7
B) 9
C) 11
D) 13
E) 15

Solution: Let the weight of the package be X.   2X + 6= 28   X = 11   The answer is 11.
Answer: C
A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?	Choose the correct choice from the following:
A) 31 8/7 years
B) 31 5/7 years
C) 31 5/8 years
D) 35 5/7 years
E) 31 3/7 years

Solution: Required Average = [(67 * 2) + (35 * 2 ) + (6 * 3)]/(2 + 2 + 3)   = (134 + 70 + 18)/7 = 31 5/7 years.   Answer: 31 5/7 years
Answer: B
34.96 + 240.016 + 23.98 = ?	Choose one: A) 298.956 B) 298.694 C) 289.496 D) 289.469 E) 298.964

Solution: 34.96   240.016   + 23.98   --------   298.956   298.956nswer is 298.956.
Answer: A
M is a certain set of numbers with an average (arithmetic mean) of 10 and a standard deviation of 2. Q is a subset of M consisting of 5 terms. Exactly 80% of the numbers in Q are located within 2 standard deviations from the average of M. Which of the following could Q be?
Select the correct option.
A) {1, 4, 5, 10, 14} B) {1, 6, 7, 10, 12} C) {1, 5, 5, 10, 16} D) {1, 5, 7, 10, 18} E) {6, 6, 7, 10, 12}

Solution: Exactly 80% of the numbers in Q, so 4 out of 5 numbers are from 10 - 2*{SD} = 6 to 10 + 2*{SD} = 14.   A. {1, 4,5, 10, 14} --> only 2 numbers are in this range. Discard.   B. {1,6, 7, 10, 12} --> 4 numbers are in this range. OK.   C. {1,5, 5, 10, 16} --> only 1 number is in this range. Discard.   D. {1,5, 7, 10, 18} --> only 2 numbers are in this range. Discard.   E. {6, 6, 7, 10, 12} --> all 5 numbers are in this range. Discard.   Answer: {1, 6, 7, 10, 12}.
Answer: B
Mudit's age 48 years hence will be thrice his age four years ago. Find Mudit's present age?
Select the correct option
A) 12 B) 19 C) 27 D) 18 E) 30

Solution: Explanation:   Let Mudit's present age be 'm' years.   m + 48 = 3(m - 4)   => 2m = 60 => m = 30 years.   Answer:30
Answer: E
The total marks obtained by a student in Mathematics and Physics is 60 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.  Choose the correct option:  A) 40  B) 28  C) 29  D) 26  E) 20

Solution: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.   Given , M + C = 60 and C - P = 20 M + C / 2   = [(M + P) + (C - P)] / 2   = (60 + 20) / 2= 
(60 + 20) / 2 = 40
40.   40nswer:40
Answer: A
In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what X percent of all the people in Smithtown are left-handed women?	Choose the correct answer
A) 50%
B) 40%
C) 25%
D) 20%
E) 10%

Solution: looking at the ratio we can take total number of people=20..   ans 5/20 or 25% 25%
Answer: C
A sink has 12 liters of water some quantity of water is taken out. If the remaining water is 6 liters less then the water taken out then quantity of water taken out is.	Options.
A) 5 liters	B) 6 liters	C) 7 liters	D) 8 liters	E) 9 liters

Solution: Let x liter water taken out   Total=Water taken out + remaining water   12=x+(x-6)   18=2*x   x=9 liters   ANSW9 litersR:9 liters
Answer: E
10 men can cut 10 trees in 2 hours. If 2men leave the job, how many trees will be cut in 3 hours?  Pick one
A) 12  B) 15  C) 16  D) 18  E) 20

Solution: 10 men - working 2 hrs - cut 10 trees   1men - working 1hr - cuts = 10/10*2   Thus 8 men - working 3hrs - cut = 10*8*3 / 10*2 = 12 trees   12nswer is 12
Answer: A
A number Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |Y|<3?
Choose the correct choice from the following:
A) 1/7  B) 3/7  C) 2/5  D) 3/11  E) 4/7

Solution: |X||X| can take 7 values.   To get |X|<2|X|<2 ( i.e., −2<x<+2−2<x   ⇒ P(|X|<2)= Favourable CasesTotal CasesP(|X|<2)= Favourable CasesTotal Cases   = 3/7   3/7
Answer: B
Two spinning machines A and B can together produce 3,00,000 m of cloth in 10 hour, if machine B alone can produce the same amount of cloth in 15 hour, then how much cloth can machine A produce alone in 10 hour? Select:	A) 2,00,000 m	B) 1,00,000 m	C) 1,50,000 m	D) 50,000 m	E) None of these

Solution: Explanation :   According to the question, machines A and B together produces 30,000 m of cloth in 1 hour.   And,machine B alone can produce 20,000 m cloth in 1 hour.   So, Machine A can produce (30,000 - 20,000) = 10,000 m cloth in 1 hour.   Hence, in 10 hour Machine A can produce 10 x 10,000 = 1,00,000 m of cloth.   Answer : 1,00,000 m
Answer: B
January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?  Choose the correct choice.
A) Saturday	B) Monday	C) Tuesday	D) Friday	E) Sunday

Solution: The year 2007 is an ordinary year. So, it has 1 odd day.   day of the year 2007 was Monday   day of the year 2008 will be 1 day beyond Monday   Hence, It will be Tuesday.   Answer is Tuesday.
Answer: C
Amy has two decks of 54 cards each: Deck 1 and Deck 2. She takes 8 black cards from Deck 2 and adds them to Deck 1 and shuffles it thoroughly. She now picks a card from the newly formed pack of cards. If the probability of either picking a red ace or a king from the newly formed pack is greater than 1/8, what is the probability that Amy picks a black king or a red Jack from the new pack? Select:
A) 1/6 B) 1/8 C) 1/9 D) 1/10 E) 1/12

Solution: Your solution is correct answer should be 1/12.   1/12
Answer: E
225 mtrs long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees?
Choose the correct option:
A) 10
B) 12
C) 14
D) 16
E) 18

Solution: 26 trees have 25 gaps between them,   Required distance (225/25) = 10   10
Answer: A
Select the non termination decimal among the following.	Choose the correct choice from the following options.
A) 2/5
B) 3/4
C) 4/5
D) 19/3
E) 9/10

Solution: D. Non terminating decimal means that 19/3 = 6.3333333 and so on.
Answer: D
The cost of 16 packets of salt,each weighing 900 grams is Rs. 28.What will be the cost of 27 packets,if each packet weight 1 kg ?
Pick one
A) Rs.52.50  B) Rs.56  C) Rs.58.50  D) Rs.64.75  E) None of these

Solution: Solution   Let the required cost be Rs. x. Then,   More packets, More cost (Direct Proportion)   More weight, More cost (Direct Proportion)   ∴ (16 × 900 × x) = (27 × 1000 × 28) ⇔ x =(27x1000x28)/16x900=105/2= 
105/2 = 105/2 = around 52.5
52.50 .Rs.52.50nswer Rs.52.50
Answer: A
On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 330 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
Choose one.
A) 237	B) 287	C) 197	D) 660	E) 720

Solution: Explanation:   Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.   2x/(x - 330) = 2 + 2(extra)   => 2x - 660 = x => x = 660.   Answer: 660
Answer: D
A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?	Choices
A) 22 1/2 kmph
B) 2 2 1/8 kmph
C) 2 2 1/0 kmph
D) 2 2 1/2 kmph
E) 2 2 2/2 kmph

Solution: 100 --- 10 2 2 1/2 kmphS = 10   ? ---- 1   75 ---- 15 US = 5   ? ----- 1 S = (10 - 5)/2   = 2 2 1/2 kmph   Answer: 2 2 1/2 kmph
Answer: D
What is the units digit of (44^4)(33^5)(21^6)? Select
A) 0 B) 2 C) 4 D) 6 E) 8

Solution: The units digit of 44^4 is the units digit of 4^4 which is 6.   The units digit of 33^5 is the units digit of 3^5 which is 3.   The units digit of 21^6 is the units digit of 1^6 which is 1.   The units digit of 6*3*1 is 8.   The answer is 8.
Answer: E
In a 8*8 chess board, what is the total number of squares refer model?
Choose the correct choice from the following answers:
A) 201 B) 202 C) 203 D) 204 E) 205

Solution: 1x1 8 8 64   2x2 7 7 49   3x3 6 6 36   4x4 5 5 25   5x5 4 4 16   6x6 3 3 9   7x7 2 2 4   8x8 1 1 1   total 204   ANSWER:204
Answer: D
A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.	Choose the most appropriate option
A) 1900  B) 1750  C) 10300  D) 8600  E) 8000

Solution: 65 * 6 : 84 * 5 : 100 * 3   26:28:20   C share = 74000 * 95/100 = 7030 * 20/74= 
7030 * 20/74 = 1_900
> 1900   1900NSWER 1900
Answer: A
At a small company, 61 percent of the employees are women, and 60 percent of the employees are married. If 2/3 of the men are single, what fraction of the women are married?  Choose the correct choice from the following options.
A) 5/16	B) 1/3	C) 9/20	D) 47/61	E) 5/7

Solution: Lets take total employees are 100.   Given that,Total Women= 61 and Total Married = 60.   Total Men = 100 - 61= 
100 - 61 = 39
39 and Single men= 2/3*39= 
2/3*39 = 26
26.   Married men= total men - single men = 39 - 26= 
39 - 26 = 13
13.   Married women= Total married - Married men = 60 - 13= 
60 - 13 = 47
47.   Fraction of women are married= Married women / Total Women = 47 / 61 = 5/7. ANS 47/61
Answer: D
The perimeter of a semi circle is 144 cm then the radius is?  Select:
A) 88
B) 28
C) 61
D) 86
E) 21

Solution: 36/7 r = 144   => r = 28   Answer:28
Answer: B
There are 45 apples and 40 oranges in stock and packs are to be filled with equal number of same type of fruits such that minimum number of packs are used. There are 20 places on the shelf to display fruits so what will be the number of empty places to display fruits?  Choose the correct choice from the following options
A) 3  B) 4  C) 5  D) 6  E) 7

Solution: k is the integer that represents the number of fruit in a pack   ak= 45 --> k = 45/a   bk= 40 --> k = 40/b   45/a = 40/b --> 9b = 8a and then min (a+b) = 17   20 -17= 
20 -17 = 3
3 empty shelf places   3NSWER: 3
Answer: A
A man can row upstream at 34 kmph and downstream at 48 kmph, and then find the speed of the man in still water?	Options
A) 29	B) 92	C) 41	D) 32	E) 23

Solution: US = 34   DS = 48   M = (48 + 34)/2= 
(48 + 34)/2 = 41
41   Answer:41
Answer: C
A and B can separately do apiece of work in 20 and 15 days respectively. They worked together for 6 days, after which B was replaced by C. If -the work was finished in next 4 days, then the number of days in which C alone could do the work will be  Choose the correct choice from the following answers:
A) 60
B) 40
C) 35
D) 30
E) 65

Solution: A and 40s one day work= 1/20+1/15=7/60   A and 40s six day work=(7/60)*6=7/10   remaining work=1-7/10=3/10   A and Cs 4 day work=(A and Cs 1 day work)*4= (1/20+1/x)*4=3/10 (remaining work)   x=40   Cs one day work=40   ANSWER:40
Answer: B
If x < y < z and y-x > 3, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?  Choose one.
A) 7 B) 6 C) 8 D) 9 E) 10

Solution: We have:   1) x<y<z 2)="" y-x="">3   3) x</y<z>=2k (x is an even number)   4) y=2n+1 (y is an odd number)   5) z=2p+1 (z is an odd number)   6) z-x=? least value   z-x=2p+1-2k=2p-2k+1=2(p-k)+1 - that means that z-x must be an ODD number.   we are asked to find the least value, so we have to pick the least numbers   since y is odd and x is even, y-x must be odd. since y-x>3, the least value for y-x must be 5, the least value for x must be 2, and, thus, the least possible value for y must be 7 (y-2=5, y=7)   2<7<z, since z is odd, the least possible value for z is 9   z-x=9-2= 
9-2 = 7
7   7nswer 7
Answer: A
How long does a train 110 m long running at the speed of 54 km/hr takes to cross a bridge 132 m length? Select the correct option.
A) 12.9 sec B) 12.1 sec C) 17.9 sec D) 16.13 sec E) 14.9 sec

Solution: Speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/sec   Total distance covered= 110 + 132= 
110 + 132 = 242
242 m.   Required time= 242/15 = 16.13 sec.   Answer: 16.13 sec
Answer: D