MU-NLPC/Calc-aqua_rat huggingface dataset:
Buses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday, what is the earliest day G on which the buses leave at the same time.
Options: A) G=Tuesday B) G=Wednesday C) G=Thursday D) G=Sunday E) G=The busses will never leave at the same time

Solution: The answer is E.   I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide.   Alternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.G=The busses will never leave at the same time
Answer: E
There are two positive integers a and b.What is the probability that a+b is odd/
Answers
A) 3/2 B) 6/7 C) 1/2 D) 7/2 E) 4/5

Solution: s=adding two numbers is (even+even),(even+odd),(odd+odd),(odd+even)   n(s)=4   e=(even+odd),(odd+even) are the points in the event.   n(e)=2   p(e)=n(e)/n(s)   =2/4   =1/2   Answer is option 1/2
Answer: C
Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 2 kg more than Peter. Together the three of them picked 26 kg of chestnuts. How many kilograms did each of them pick?
Select the correct option
A) 6, 8 and 12	B) 12, 8 and 6	C) 8, 6 and 12	D) 12, 6 and 8	E) 6, 12 and 8

Solution: Let x be the amount Peter picked. Then Mary and Lucy picked 2x and x+2, respectively. So   x+2x+x+2=26   4x=24   x=6   Therefore, Peter, Mary, and Lucy picked 6, 12, and 8 kg, respectively.   So answer is 6, 12 and 8.
Answer: E
A coin is tossed live times. What is the probability that there is at the least one tail? Choose the correct choice from the following options
A) 31/32  B) 31/36  C) 31/27  D) 31/28  E) 31/18

Solution: Let P(T) be the probability of getting least one tail when the coin is tossed five times.   = There is not even a single tail.   i.e. all the outcomes are heads.   = 1/32 ; P(T)   = 1 - 1/32   = 31/32   31/32nswer: 31/32
Answer: A
If 70 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
Choose the correct choice
A) 45%	B) 40%	C) 35%	D) 30%	E) 25%

Solution: 70% answered the first question correctly and 20% answered neither correctly.   Then 10% missed the first question but answered the second question correctly.   Then the percent who answered both correctly is 55% - 10% = 45%.   The answer is 45%.55  - 10= 
55  - 10 = 45
45%.   The answer is 45%.
Answer: A
3 men and 8 women complete a task in same time as 6 men and 2 women do. How much fraction of work will be finished in same time if 4 men and 5 women will do that task.	Options:
A) 13/14 B) 13/10 C) 13/18 D) 13/16 E) 13/11

Solution: 3 m + 8 w = 6 m + 2 w   3 m = 6 w   1 m = 2 w   Therefore 3 m + 8 w = 14 w   4 m + 5 w =13 w   13/14nswer is 13/14   13/14nswer: 13/14
Answer: A
Find the surface area of a 12 cm x 4 cm x 3 cm brick. Select.
A) 84 cu cm. B) 124 cu cm. C) 164 cu cm. D) 192 cu cm. E) None

Solution: Sol.   Surface area = [2(12 x 4 + 4 x 3 + 12 x 3)]   = (2 x 96)   = 192 cu cm.   Answer 192 cu cm.
Answer: D
A merchant marks his goods up by 40% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount?  Select
A) 21%
B) 26%
C) 69%
D) 31%
E) 19%

Solution: Let the price be 100.   The price becomes 140 after a 40% markup.   Now a discount of 10% on 140.   Profit=126-100   26%   answer 26%
Answer: B
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? Choose the correct option.
A) 33  B) 289  C) 48  D) 77  E) 12

Solution: Relative speed = 45 + 30= 
45 + 30 = 75
75 km/hr.   75 * 5/18= 125/6 m/sec.   Distance covered = 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000 * 6/125= 
1000 * 6/125 = 48
48 sec.   Answer: 48
Answer: C
The H.C.F. of two numbers is 20 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
Choose the most appropriate option:
A) 276 B) 299 C) 322 D) 345 E) 280

Solution: Clearly, the numbers are (20 x 13) and (20 x 14).   Larger number = (20 x 14) = 280. Answer: Option 280
Answer: E
A man's speed with the current is 12 km / hr and the speed of the current is 2 km / hr. The man's speed against the current i
Choose the correct choice from the following choices:
A) 8 km / hr
B) 9 km / hr
C) 10 km / hr
D) 12.5 km / hr
E) None

Solution: Sol.   Man's rate in still in water = (12- 2) km / hr = 10km / hr.   Man's rate against the current = (10 - 2) km / hr = 8 km / hr.   8 km / hrnswer 8 km / hr
Answer: A
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The
present age of his son is
Choose the correct choice from the following:
A) 20 years
B) 21 years
C) 22 years
D) 24 years
E) 26 years

Solution: Explanation:   Let the son's present age be x years. Then, man's present age = (x + 24) years   => (x + 24) + 2 = 2(x + 2)   => x + 26 = 2x + 4   So, x = 22   Answer: Option 22 years
Answer: C
If f(x)=4x−1 and g(x)=2x+1 for all integers, which of the following is a possible value of g(f(x))?
Select:	A) -23	B) -17	C) 0	D) 8	E) 20

Solution: g(f(x)) = 2*f(x)+1 = 2*(4x-1)+1 = 8x-1   Of these five options, only -17 has the form 8x-1.   The answer is -17.
Answer: B
In a tree, 1/5 of the birds are robins while the rest are bluejays. If 1/2 of the robins are female and 2/5 of the bluejays are female, what fraction of the birds in the tree are male?
Choose the correct choice from the following answers.
A) 9/25	B) 12/25	C) 17/25	D) 29/50	E) 33/50

Solution: The fraction of birds that are male robins is (1/2)(1/5)=1/10.   The fraction of birds that are male bluejays is (3/5)(4/5)=12/25.   The total fraction of male birds is 1/10 + 12/25 = 29/50.   The answer is 29/50.
Answer: D
The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?
Choose the correct choice from the following options:
A) 12 a.m	B) 13 a.m	C) 14 a.m	D) 11 a.m	E) 16 a.m

Solution: D   11 a.m   Suppose they meet x hrs after 8 a.m. Then,   (11 a.mistance moved by first in x hrs) + [11 a.mistance moved by second in (x - 1) hrs] = 330   60x + 75(x - 1) = 330 => x = 3   So, they meet at (8 + 3) i.e., 11 a.m.
Answer: D
A man can row his boat with the stream at 36 km/h and against the stream in 8 km/h. The man's rate is?	Answers:
A) 1 kmph
B) 6 kmph
C) 7 kmph
D) 14 kmph
E) 9 kmph

Solution: Explanation:   14 kmphS = 36   US = 8   S = ?   S = (36 - 8)/2= 
(36 - 8)/2 = 14
14 kmph   Answer: 14 kmph
Answer: D
The avg weight of A,B & C is 50 kg. If D joins the group, the avg weight of the group becomes 53 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 51 kg. What is the weight of A?
Select the correct option.
A) 56  B) 65  C) 73  D) 89  E) 90

Solution: A + B + C = 3 *50= 
3 *50 = 150
150   A + B + C + D= 4 * 53= 
4 * 53 = 212
212 ---- (i)   So, D= 62& E = 62 + 3= 
62 + 3 = 65
65   B + C + D +E= 51 * 4= 
51 * 4 = 204
204 --- (ii)   From Eq. (i) & (ii)   A-E= 212 – 204 = 8   A = E +8 = 65 + 8= 
65 + 8 = 73
73   Answer : 73
Answer: C
Ifaequals the sum of the even integers from 2 to 120, inclusive, andbequals the sum of the odd integers from 1 to 119, inclusive, what is the value of a - b ?
Select:
A) 60	B) 10	C) 19	D) 20	E) 21

Solution: This is a solution from Beatthegmat:   even numbers:   (120-2)/2 + 1= 
(120-2)/2 + 1 = 60
60 even integers.   (120+2)/2= 
(120+2)/2 = 61
61 is the average of the even set.   sum= avg*(#of elements) = 61*60= 
61*60 = 3_660
3660= a   odd numbers:   (119-1)/2 + 1= 
(119-1)/2 + 1 = 60
60 odd integers.   (119+1)/2= 
(119+1)/2 = 60
60 is the average of the odd set.   sum= avg*(#of elements) = 60*60= 
60*60 = 3_600
3600= b   a-b = 3660 - 3600= 
3660 - 3600 = 60
60. 60nswer : 60
Answer: A
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 correct choice from the following answers.
A) 288	B) 1900	C) 1287	D) 1271	E) 2788

Solution: 65 * 6 : 84 * 5 : 100 * 3   26:28:20   C share = 74000 * 95/100 = 7030 * 20/74= 
7030 * 20/74 = 1_900
> 1900   Answer: 1900
Answer: B
Rebecca's annual income is $15,000 and Jimmy's annual income is $18,000. By how much must Rebecca's annual income increase so that it constitutes 50% of Rebecca and Jimmy's combined income?  Choose the correct answer:	A) 7000	B) 6000	C) 5000	D) 4000	E) 3000

Solution: total rebecca = x+15000; total = x+15000+18000   x+15000/x+33000 = 50/100 therefore x =3000   3000
Answer: E
48 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
Select
A) 66
B) 26
C) 42
D) 27
E) 21

Solution: x/7 = y/9 => x:y = 7:9   7/16 * 48= 
7/16 * 48 = 21
21   Answer: 21
Answer: E
If x, y and z are three different positive integers whose sum is prime, which of the following statements could be true?  Select
A) x + y = z	B) Each of x + 3, y + 3, and z + 3 is prime.	C) Each of x + y, x + z, and y + z is prime.	D) The average (arithmetic mean) of x, y, and z is prime.	E) Each of x, y, and z is prime.

Solution: the question asks could be!!!!   this means that if at least one option works, it is the answer.   3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that Each of x, y, and z is prime. is the answer.
Answer: E
The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group? Choose the most appropriate option: A) Rs.19 B) Rs.29 C) Rs.15 D) Rs.10 E) Rs.13

Solution: Total members in the group = 7   Average amount = Rs. 20   Total amount with them = 7 * 20   = Rs. 140   One number has Rs. 50. So, the amount with remaining 6 people   = 140 - 50 = Rs. 90   The average amount with them = 90/6   = Rs.15.   Answer:Rs.15
Answer: C
Solve the given two equations and find the inequality of X and Y. (a) x^2-1=0 and (b) y^2+4y+3=0
Answers:
A) If x>y B) If x>=y C) If x<y D) If x<=y E) x=y or relationship cannot be established

Solution: Solution:-   X=+1,-1 and Y= -1,-3   Comparing we get X>=Y   If x>=y
Answer: B
A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? Choose the correct choice from the following answers.
A) 7 sec
B) 6 sec
C) 4 sec
D) 5 sec
E) 9 sec

Solution: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr   [66 * 5/18] m/sec = [55/3] m/sec.   Time taken to pass the man = [110 * 3/55= 
110 * 3/55 = 6
6 sec   Answer:6 sec
Answer: B
AB + CD = RRR, where AB and CD are two-digit numbers and RRR is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
Choose one.
A) 1  B) 3  C) 7  D) 9  E) Cannot be determined

Solution: AB and CD are two digit integers, their sum can give us only one three digit integer of a kind of RRR it's 111.   So, A=1. 1B+C9=111   Now, C can not be less than 9, because no to digit integer with first digit 1 (mean that it's<20) can be added to two digit integer less than 90 to have the sum 111 (if C9<90 meaning C<9 C9+1B<111) --> C=9   Answer: 9.
Answer: D
Working together, printer A and printer B would finish the task in 40 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 4 pages a minute more than printer A ?  Choose the correct option
A) 250
B) 375
C) 450
D) 480
E) 500

Solution: 40*A + 40*B = x pages   in 40 mins printer A will print = 40/60 * x pages = 2/3*x pages   thus in 40 mins printer printer B will print x - 2/3*x = 1/3*x pages   Also it is given that printer B prints 4 more pages per min that printer A. In 40 mins printer B will print 160 more pages than printer A   thus 2/3*x - 1/3*x = 160 => x = 480 pages   Answer: 480
Answer: D
A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
Choose the correct choice from the following answers:
A) 65
B) 24
C) 52
D) 77
E) 82

Solution: Explanation:   Let the ten's and unit's digit be x and 8/x respectively.   Then,   (10x + 8/x) + 18 = 10 * 8/x + x   9x2 + 18x - 72 = 0   x2 + 2x - 8 = 0   (x + 4)(x - 2) = 0   x = 2   So, ten's digit = 2 and unit's digit = 4.   Hence, required number = 24.   Answer: 24
Answer: B
A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so?  Choose one
A) 6 ½ sec	B) 6 ½ sec	C) 9 ½ sec	D) 8 ½ sec	E) 7 ½ sec

Solution: 8 ½ sec   8 ½ sec   8 ½ sec = 170   S = 72 * 5/18= 
72 * 5/18 = 20
20 mps   T= 170/20 = 8 ½ sec
Answer: D
Walking at 8KMPH From Point W to Point railway station, mike will miss the train by 5 minutes. If he walks at 10KMPH he will reach the station by 5 minutes early.What is the distance between Point W to Railway station?
Answers:
A) A)9KM
B) B)6.66KM
C) C)7.25KM
D) D)12.40KM
E) E)13KM

Solution: Since time differences given are in minutes so let's convert speed in Km per minute   8 kmph = 8/60 km per minute = (2/15) km per minute   10 kmph = 10/60 km per minute = (1/6) km per minute   Let, Time of train to depart from station = t minutes   Distance between Point W and Railway Station = Speed*Time = (2/15)*(t+5)   Distance between Point W and Railway Station = Speed*Time = (1/6)*(t-5)   i.e. (2/15)*(t+5) = (1/6)*(t-5)   i.e. 12t+60 = 15t - 75   i.e. 3t = 135   i.e. t = 45 minutes   i.e. Distance = (1/6)*(t-5) = (1/6)*(45-5) = 40/6 = 20/3 Km = 6.66 Km   Answer: Option 6.66KM
Answer: B
A carpenter is building a frame for a wall painting. The painting is in the shape of a rectangle. If the sides of the rectangle are in the ratio of 3:2 and the shorter side has a length of 22 inches, how many inches of framing material does the carpenter need to frame the painting? Choose the correct choice from the following options:
A) 12  B) 22 1/2  C) 37 1/2  D) 50  E) 28

Solution: (22/2) ( 2+3) * 2 = 28 =28
Answer: E
The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked the second cow in the second year?  Choose the correct choice from the following options.
A) 4730 lt
B) 4356 lt
C) 7665 lt
D) 2314 lt
E) 6545 lt

Solution: Let x be the amount of milk the first cow produced during the first year. Then the second cow produced (8100−x) litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of 15% or 10%   So 8100+15/100⋅x+10/100⋅(8100−x)=9100   Therefore 8100+320x+110(8100−x)=9100   120x=190   x=3800   Therefore, the cows produced 3800 and 4300 litres of milk the first year, and 4370 and 4730 litres of milk the second year, respectively.   correct answer 4730 lt
Answer: A
X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?
Choices: A) 7 B) 6 C) 3 D) 4 E) None of these

Solution: Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000   Let investment period of Z be x months.   Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)   = 240 : 300 : 30x = 8 : 10 : x   The share of Z in the annual profit of Rs. 50000 is Rs. 14000.   => [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7   => 25x = 7x + (18 * 7) => x = 7 months.   Z joined the business after (12 - 7) months. i.e., 5 months.   ANSWNone of theseR:None of these
Answer: E
The surface of a cube is 96sq cm. Find its volume?  Choose the correct choice from the following:
A) 8cc
B) 9cc
C) 2cc
D) 4cc
E) 64cc

Solution: 6a2 = 96 = 6*16   a = 4 => a3 = 64cc   Answer: 64cc
Answer: E
A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is: Choose the correct choice from the following options.
A) 3	B) 8	C) 2	D) 1	E) 9

Solution: E   9   Let the required number of revolutions made by larger wheel be x.   Then, More cogs, Less revolutions (Indirect Proportion)   14 : 6 :: 21 : x <-> 14 x x = 6 x 21   x = (6 x 21)/14   x = 9
Answer: E
It takes 3 workers a total of 12 hours to build a giant machine with each worker working at the same rate. If 4 workers start to build the machine at 11:00 AM, and one extra worker per hour is added beginning at 3:00 PM, at what time will the machine be complete?	Choose the correct choice from the following choices:	A) 5:30	B) 5:45	C) 6:00	D) 6:15	E) 6:30

Solution: 3 workers build 1/12 of a machine in one hour.   1 worker builds 1/36 of a machine in one hour.   In the first 4 hours, 4 workers build 4*(1/36)*4=16/36 of a machine   From 3:00 to 4:00, 5 workers build another 5/36. The total is 21/36.   From 4:00 to 5:00, 6 workers build another 6/36. The total is 27/36.   From 5:00 to 6:00, 7 workers build another 7/36. The total is 34/36.   To build another 2/36, 8 workers need (2/8)*60 minutes which is 15 minutes.   The machine is complete at 6:15.   The answer is 6:15.
Answer: D
A meal cost $ 35.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be:  Select the correct option
A) 40-42
B) 39-41
C) 38-40
D) 37-39
E) 36-37

Solution: 10%(35.5) = 3.55   15%(35.5) = 5.325   total amount could have been 35.5+3.55 and 35.5+5.325   => could have been between 39.05 and 40.625   => approximately between 39 and 41   Answer is 39-41.
Answer: B
Which one of the following is the common factor of (47^43 + 43^43) and (47^47 + 43^47) ?  Pick.
A) (2+56)
B) (47+43)
C) (3+7)
D) (4+9)
E) (12+19)

Solution: Explanation:   When n is odd, (x^ + a^n) is always divisible by (x + a).   Each one of (47^43 + 43^43) and (47^47 + 43^47) is divisible by (47 + 43).   (47+43)
Answer: B
Eight friends met for lunch at an expensive restaurant, and everyone decided to contribute equally to the total bill of $290. If one of the friends had a coupon for 29% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay? Pick one
A) $90 B) $70 C) $45 D) $37 E) $25

Solution: 290 * 0,29 = 84   290 - 84= 
290 - 84 = 206
206   206 / 8= 25   Answer $25
Answer: E
What is the sum of the prime factors of 3 and the prime factors of 1656? Choose the correct choice from the following:  A) 35  B) 45  C) 55  D) 25  E) 65

Solution: The prime factors of 3 are 3*1   The prime factors of 1656 are 2x2x2x3x3x23   2+2+2+3+3+23= 
2+2+2+3+3+23 = 35
35. 35 is the correct answer
Answer: A
For any positive x, y and z if x is n% of y and z is m% of y then what percentage E must x be of z? Answers:
A) (n/m)%
B) (m × n)%
C) (100 / [m × n]) %
D) (100 × m/n)%
E) (100 × n/m)%

Solution: x is n% of y M(100 × n/m)%ANS x= (n/100 )* y------------------------eq1   z is m% of y M(100 × n/m)%ANS z= (m/100 )* y------------------------eq2   Find equation of xz   substitute value of y from 2nd equation into Ist equation   so x= (n/100)*(100z/m)   so x= (n/m)z   or x= (100n/m)z/100   so answer (100 × n/m)% is 100n/m %.(100 × n/m)%
Answer: E
If 105 divides into n with no remainder, which of the following must be a factor of n? Choose the correct option:
A) 2  B) 4  C) 6  D) 7  E) 11

Solution: 105 / n = k (with k an integer)   (7)(5)(3) / n = k   n must have a 7 in his prime factorization to divide 105 without remainder.   answer 7
Answer: D
Two numbers are in the ratio of 5:9. If 25 be subtracted from each, they are in the ratio of 35:59. Find the numbers?	Choose the correct choice from the following options.
A) 150,170  B) 150,270  C) 50,270  D) 180,270  E) 150,290

Solution: (5x-25):(9x-25) = 35:59   x = 30 => 150,270   ANSWER:150,270
Answer: B
On Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 70% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?  Options.
A) 36%  B) 51%  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 0.7*0.7 = 0.49. So, the probability that he will be able to attend is 1 - 0.49 = 0.51.   Answer: 51%.
Answer: B
How many 2 3/4 foot pieces of cable can be cut out of a piece that is 30 feet long? Choose the correct choice from the following answers: A) a.10 B) b.16 C) c.17 D) d.18 E) e. 20

Solution: Pretty Simple..the answer is choice (A) 10.   a.10ll that one has to do is :   1: Convert 2 3/4 into an improper fraction (11/4) or a decimal (2.75)   2: Divide 30 by 11/4 (or 2.75)   a.10nswer =10 (a.10)
Answer: A
The perimeter of one square is 44 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?  Choices
A) 13√4	B) 12.1√2	C) 23√2	D) 12√4	E) 13√9

Solution: 4a = 44 4a = 20   a = 11 a = 5   a2 = 121 a2 = 25   Combined area = a2 = 146 => a = 12.1   d = 12.1√2   Answer: 12.1√2
Answer: B
Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 9 hours. How many hours will take C alone to fill the tank?	Choose the correct choice from the following options
A) 23/2	B) 41/3	C) 49/4	D) 54/5	E) 63/6

Solution: The rate of A+B+C is 1/6 of the tank per hour.   After 2 hours, the tank is 1/3 full.   The rate of A+B is 2/3 * 1/9 = 2/27 of a tank per hour.   The rate of C is 1/6 - 2/27 = 5/54   C can fill the tank in 54/5 hours.   The answer is 54/5.
Answer: D
The difference between a number and its three-fifths is 50.What is the number?  Choose the correct choice from the following answers
A) 75
B) 100
C) 125
D) Cannot be determined
E) None of these

Solution: Suppose the number is N.   Then N - 3⁄5N = 50   ⇒ 2N⁄5 = 50   ∴ N=50×52=125   Answer.125
Answer: C
Number N is randomly selected from a set of all primes between 10 and 40, inclusive. Number Z is selected from a set of all multiples of 5 between 10 and 40 inclusive. What is the probability that N+Z is odd?	Choose the correct choice from the following answers:
A) 1/2
B) 2/3
C) 3/4
D) 4/7
E) 5/8

Solution: All primes except 2 are odd, thus N must be odd. For N + Z = odd + Z to be odd, Z must be even.   There are 7 multiples of 5 between 10 and 40, inclusive: 10, 15, 20, 25, 30, 35, and 40. Out of them 3 (15, 25, and 35) are odd.   Therefore the probability that N + Z is odd is 4/7.   Answer: 4/7.
Answer: D
A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?
Choose the correct choice:
A) 5,2 B) 6,9 C) 2,1 D) 5,8 E) 15,10

Solution: 15,10xplanation:   lb = 150   2(l + b) = 50 => l + b = 25   l – b = 5   l = 15 b = 10   Answer: 15,10
Answer: E