MU-NLPC/Calc-aqua_rat huggingface dataset:
Sides of a rectangular park are in the ratio 3: 2 and its area is 2400 sq m, the cost of fencing it at 50 ps per meter is?  Choose the correct choice from the following choices:
A) 287
B) 100
C) 125
D) 988
E) 271

Solution: 3x * 2x = 2400 => x = 20   2(60 + 40) = 200 m   200 * 1/2 = Rs.100   Answer: 100
Answer: B
Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in  Choose one
A) 1×13/17 hours  B) 2×8/11 hours  C) 3×9/17 hours  D) 4×1/2 hours  E) 5×1/2 hours

Solution: (a+b+c) can fill in (1/5+1/6-1/12) =3x9/17   ANSWER:3×9/17 hours
Answer: C
The difference of two numbers is 1335. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?  Choose the correct choice from the following: A) 240 B) 270 C) 295 D) 360 E) 264

Solution: Let the smaller number be x. Then larger number = (x + 1335).   x + 1335 = 6x + 15   5x = 1320   x = 264   Smaller number = 264.   ANSW264R 264
Answer: E
Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 3H, which of the following represents the amount that Roberta paid?
Choose the correct option:	A) D + 40	B) D + H – 1	C) D + 2H	D) 3.99H	E) 1.21D

Solution: before 3.99Hiscount price was: 1.43.99H+1.5H   After 3.99Hiscount: 1.43.99H +1.5H-.423.99H-.45H   substitute 3.99H=3H   final value: 3.99H   Ans Is 3.99H :
Answer: D
The average (arithmetic mean) of the even integers from 20 to 60 inclusive is how much greater than the average (arithmetic mean) of the even integers from 10 to 140 inclusive? Choose the correct choice from the following answers:  A) 40  B) 15  C) 35  D) 20  E) 25

Solution: So, according to A mean of a set of even numbers from 20 to 60 =(20+60)/2= 
(20+60)/2 = 40
40 and mean of a set of even numbers from 10 to 140=(10+140)/2= 
(10+140)/2 = 75
75   Difference=75-40= 
75-40 = 35
35   Answer: 35.
Answer: C
A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? Choose the correct choice from the following.
A) 22 seconds
B) 77 seconds
C) 40 seconds
D) 57 seconds
E) 57 seconds

Solution: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   = 500 * (2/25)= 
500 * (2/25) = 40
40 seconds   Answer:40 seconds
Answer: C
Find the missing value: ? - 1936248 = 1635773 Options:
A) 3572021
B) 3570221
C) 3572012
D) 3752012
E) None of them

Solution: Let x - 1936248=1635773.Then, x = 1635773 + 1936248= 
1635773 + 1936248 = 3_572_021
3572021   3572021nswer is 3572021.
Answer: A
List I: { y, 2, 4, 7, 10, 11}
List II: {3, 3, 4, 6, 7, 10}
If the median R of List I is equal to the sum of the median of list II and the mode of list II, then y equals	Choose the correct option:
A) 5
B) 7
C) 8
D) R=9
E) 10

Solution: mode of list ii =3   median R of list ii =4+6/2 =5   sum of mode + mean = 3+ 5= 
3+ 5 = 8
8   now to make 8 as the median we need to find a value of y such that if the no. of terms in list 1 are odd then y=8 else if even then 7+y /2=8   here its even so   7+y/2=8 from this y= 9 (R=9)
Answer: D
The average marks obtained by 120 cndidates in a certainexaminationis 35.if the average marks of passed candidate is 39 and that of the failedcandidates is 15,what is the number of candidates who passed the examination	Select the correct option:
A) 14 years
B) 14 years 3 month
C) 14 years 8 month
D) 14 years 9 month
E) 14 years 11 month

Solution: Let No. of passed candidates are x   So, x * 39 + (120 – x) 15= 120 * 35   x = 100   2.(a) Total increase = 8 * 2= 
8 * 2 = 16
16 years   So, total age of two women= 35 + 45 +16= 
35 + 45 +16 = 96
96   Average age of two women=96/2= 
96/2 = 48
48 years   3(d) Total decrease= 20 * 2= 
20 * 2 = 40
40 month= 3 years 4 month   So, age of new boy = 18 years – 3 years 4 month   = 14 years 8 month   14 years 8 month
Answer: C
Suppose you want to buy three loaves of bread that cost $0.50 each
and a jar of peanut butter that costs $6. A jar of jelly is $2.75, but you
donâ€™t need any jelly. You have $12. How much money will you have left
over?
Choose the correct choice from the following options:
A) $1.50	B) $2.50	C) $3.50	D) $4.50	E) $5.50

Solution: The jelly is extra information. 12.00 â€“ 3 x 0.50 â€“ 6.00 =   12.00 â€“ 1.50 â€“ 6.00 = 4.50.   You have $4.50 left.   correct answer $4.50
Answer: D
An exporter expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?  Choose the correct choice from the following answers:
A) 72	B) 90	C) 80	D) 100	E) 85

Solution: Selling price = 392   gain = 25%   cost = 100*392/122.5= 
100*392/122.5 = 320
>320   profit= 392-320= 
392-320 = 72
72   72NSWER 72
Answer: A
A statue is being carved by a sculptor. The original piece of marble weighed 190 kg. In the first week 25 percent is cut away. In the second week 15 percent of the remainder is cut away. In the third week the statue is completed when 10 percent of the remainder is cut away. What is the weight of the final statue?	Choose the correct choice from the following choices.
A) 105 kg  B) 103 kg  C) 109 kg  D) 125 kg  E) 117 kg

Solution: 109 kg   109 kg   190 Ã— 0.75 Ã— 0.85 Ã— 0.9 = 109 kg.
Answer: C
A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 884 in 4 years. The sum is:  Choose the correct option.
A) s. 608
B) s. 690
C) s. 698
D) s. 700
E) s. 760

Solution: S.I. for 1 year = Rs. (884 - 815) = Rs. 69.   S.I. for 3 years = Rs.(69 x 3) = Rs. 207.   Principal = Rs. (815 - 207) = Rs. 608.   s. 608nswer: Option s. 608
Answer: A
Of the following quadratic equations, which is the one whose roots are 2 and – 15 ? Choices.
A) x2 - 2x + 15 = 0
B) x2 + 15x - 2 = 0
C) x2 + 13x - 30 = 0
D) x2 - 30 = 0
E) None of these

Solution: Sol.   (c) Sum of roots = 2 – 15 = – 13   Product of roots = 2 × (– 15) = – 30   Required equation   = x2 - x(sum of roots) + product of roots = 0   => x2 + 13x - 30 = 0   Answer x2 + 13x - 30 = 0
Answer: C
Six students are equally divided into 3 groups, then, the three groups were assigned to three different topics. How many different arrangements X are possible? Choose the most appropriate option:
A) 30
B) 60
C) 90
D) 180
E) 540

Solution: 90 is the number of ways you can assign 3 teams formed out of 12 people to 3 different tasks.   But now you can order the 3 tasks in 3! ways. T1 T2 T3 or T2 T1 T3.... etc etc.   I was confused between 90 and 540 but since question used the wordarrangementsdecided to go with complete arrangements X including the order of tasks.   could you explain the highlighted step... i'm getting 90 = 15 * 3!   suppose the students are numbered 1,2,3,4,5,6 and tasks are X,Y and Z   one of the 15 possible ways of forming teams is 12, 34, 56. these teams can be assigned to 3 tasks in 3! = 6 ways   X--	Y--	Z   12--	34--	56   12--	56--	34   34--	12--	56   34--	56--	12   56--	12--	34   56--	34--	12   so the answer should be 15*6= 
15*6 = 90
90   But now you can fruther decide which task you want to perform first X Y or Z..90
Answer: C
1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2,__ ?
Choose the correct option
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: 1,1,2,1,2,3,1,2,3,4,1,2,__?   Looking at the series   1   12   123   1234   12(3)45   So the answer is 3.   ANSWER:3
Answer: C
The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 150 square centimeters, what is the length of the rectangle in centimeters?  Choose the correct answer
A) 15
B) 16
C) 17
D) 18
E) 19

Solution: Perimeter = 2(W+L) = 5W   3W = 2L   W = 2L/3   WL = 150   2L^2/3 = 150   L^2 = 225   L = 15 cm   The answer is 15.
Answer: A
Length of a rectangular plot is 22 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
Choose the correct choice from the following options
A) 51 m  B) 61 m  C) 71 m  D) 81 m  E) 91 m

Solution: Let breadth = x metres.   Then, length = (x + 22) metres.   Perimeter = 5300 m = 200 m.   26.50   2[(x + 22) + x] = 200   2x + 22 = 100   2x = 78   x = 39.   Hence, length = x + 22 = 61 m   61 m
Answer: B
Given x = 20o, what is the value of log5(tan x)-log5(sin x)+log5(cos x)? Choose one.
A) 0 B) 1 /2 C) 1 D) log5 2 E) log2 5

Solution: One approach is to use that   A + F = (A+B) + (C +D) + (E +F)􀀀(B +C)􀀀(D+E) = 1 + 3 +5􀀀2􀀀4 = 3:   The answer can also be obtained by taking A = 1 and solving for the remaining variables.   Since A + B = 1, we get B = 0. Since B + C = 2, we get C = 2. Continuing, we get   D = 1, E = 3, and F = 2. Thus, A + F = 1 + 2= 
1 + 2 = 3
3 is a possibility. There are other   possibilities for the variables A;B; : : : ; F (just set A equal to something else), but in any   case the sum A + F will be 3.   correct answer 0
Answer: A
When a positive integer A is divided by 5 and 11, the remainders obtained are 3 and 4, respectively. When the positive integer B is divided by 5 and 11, the remainders obtained are 3 and 4, respectively. Which of the following is a factor of (A - B)?	Select the correct option
A) 15	B) 25	C) 35	D) 45	E) 55

Solution: A = 5k+3 = 11j+4   B = 5m+3 = 11n+4   A-B = 5(k-m) = 11(j-n)   A-B is a multiple of both 5 and 11, so it is a multiple of 55.   The answer is 55.
Answer: E
Salaries of Ranjani and Sudha are in the ratio 2:3. If the salary of each in increased by Rs.4000, the new ratio becomes 40:57. What is the Sudha's present salary?	Choose the most appropriate option.
A) 34000 B) 35000 C) 37000 D) 38000 E) 36000

Solution: let the org sal of ranjani and sudha be rs.2x and rs 3x respctvily.   then,   =2x+4000/3x+4000= 40/57   cross multiply   57(2x+4000)=40(3x+4000)   6x=68000 and 3x=34000   sudhas present sal =(3x+4000)=>(34000+4000)= 
(34000+4000) = 38_000
>38000   ANSWER:38000
Answer: D
A boatman rows 96 km downstream in 8 hours with a stream speed of 4kmph. How much time will he take to cover 8km upstream?	Choose one:
A) 2 hours	B) 8 hours	C) 6 hours	D) 7 hours	E) 9 hours

Solution: Explanation:   Speed = distance/time   Speed downstream: 96 / 8 km/hr = 12kmph   Speed of stream = 4kmph   Effective speed of boat = (12-4)= 
(12-4) = 8
8kmph   Distance to be travelled upstream= 8 km   Speed upstream = boat speed-current speed   = 8-4= 
8-4 = 4
4 kmph   Time taken= distance/speed = 8/ 4= 
8/ 4 = 2
2 hours   2 hoursNSWER:2 hours   Thus it will take 2 hours to go upstream.
Answer: A
The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?	Pick.
A) 15	B) 12	C) 28	D) 36	E) 96

Solution: Explanation:   Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.   P + Q = 10 ----- (1)   (10Q + P) - (10P + Q) = 54   9(Q - P) = 54   (Q - P) = 6 ----- (2)   Solve (1) and (2) P = 2 and Q = 8   The required number is = 28   Answer 28
Answer: C
The line Z represented by which of the following equation does not intersect with the line represented by y = 3x^2+5x+1	Pick:
A) y = 2x^2+5x+1	B) y = x^2+5x+2	C) y = 3x^2+5x+2	D) y = 3x^2+7x+2	E) y = x^2+7x+1

Solution: concept of slope for linesparabolas are different. Bunuel, please correct if I am wrong. Also please help to solve this problem if its a GMAT type question.   The general form of parabolic equ. is y^2= 4ax which implies the axis is x or x^2 = 4ay where axis is y.   We have a similar form as x^2 = 4ay.   here the vertex is origin.   So if we have same values of x and y but constant term changes then we will have parallel parabolas.   This is same as for straight line Z which are parallel for different values of constant term c   ax + by +c1 = 0 and ax +by+ c2 =0   We have quadratic equations. These equations when drawn give parabolas, not lines. The question is: which of the following parabolas does not intersect with the parabola represented by y=3x^2+5x+1.y = 3x^2+5x+2
Answer: C
Mr. Evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 4 children and 5 grandchildren, then approximately what percentage of Mr. Evans estate will each grandchild receive?  Choose the correct choice:
A) 20%  B) 17%  C) 4.0%  D) 3.3%  E) 2.8%

Solution: 20/5= 
20/5 = 4
4   Answer : 4.0%
Answer: C
The average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.12000 and the average salary of the rest is Rs.6000. The total number of workers in the workshop is	Pick:
A) 20  B) 21  C) 22  D) 23  E) 24

Solution: Solution   Let the toatl number of workers be x.   Then 8000x=(12000 x 7) + 6000 (x -7)   2000x =42000   x= 21.   Answer 21
Answer: B
Ross is 20 years older than his daughter Julie. In 5 years Ross will be twice as old as Julie. What is Julies current age.  Choose the correct choice:	A) 10	B) 15	C) 20	D) 30	E) 25

Solution: Now: Julie = x, Ross =x+20   In 5 years Julie = x+5, Ross = x+20+5 or 2(x+5)   x+20+5 = 2(x+5)   x+25=2x+10   25=x+10   15=x   Julie is 15 years old, the answer is 15)
Answer: B
How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per Kg so that there may be a gain of 10 % by selling the mixture at Rs. 9.24 per Kg ? Pick.
A) 33
B) 39
C) 38
D) 63
E) 01

Solution: By the rule of alligation:   C.P. of 1 kg sugar of 1st kind C.P. of 1 kg sugar of 2nd kind   {\color{Blue} \therefore } Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.   Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind.   Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg.   Answer: 63) 63 Kg
Answer: D
A tank can supply water to a village for 20 days. If a leak at the bottom of the tank drains out 10 liters per day, the supply lasts for 15 days only. For how many days will the supply last if the leak drains out 20 liters per day?
Choose the correct choice from the following
A) 9 B) 10 C) 11 D) 12 E) 14

Solution: Losing 10 liters per day results in a loss of 150 liters in 15 days. So, those 150 liters were for 5 days, making daily consumption of the village 30 liters per day. Thus the capacity of the tank is  30*20= 
 30*20 = 600
600 liters.   Losing 20 liters plus 30 liters gives 50 liters per day. At this rate the supply will last   600/50= 
  600/50 = 12
12 days.   The answer is 12.
Answer: D
The price of a certain painting increased by 30% during the first year and decreased by 15% during the second year. The price of the painting at the end of the 2-year period was what percent of the original price?	Pick.
A) 102%
B) 105%
C) 110.5%
D) 112.5%
E) 100%

Solution: Easiest thing to do: Assume that price is 100   Price at the end of yr 1: 100+ 30 = 130   Price at the end of year 2 = 130 - 130*0.15 = 130*0.85= 
130*0.85 = 110.5
110.5   Hence required answer= (110.5/100)*100= 
(110.5/100)*100 = 110.5
110.5%   Answer is 110.5%.
Answer: C
Divide $600 among A,B in the ratio 1:2. How many $ that A get?  Choose one:
A) $50 B) $500 C) $150 D) $250 E) $600

Solution: Sum of ratio terms = 1+2= 
1+2 = 3
3   A= 600*1/3= 
600*1/3 = 200
$200   Answer is $600
Answer: E
Vanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address?	Choose the correct option: A) 1/24 B) 1/8 C) 1/4 D) 1/3 E) 3/8

Solution: Total Vanya# of ways - 4! = 24.   1/3esired:   A-Mapped to the only correct address----------x 1 way only   B-Mapped to other two incorrect addresses - x 2 ways   C-Mapped to other two incorrect addresses - x 2 ways   1/3-Mapped to other two incorrect addresses - x 2 ways   Therefore, 1*2*2*2/24 = 1/3.?
Answer: D
At a certain high school, the senior class is twice the size of the junior class. If 1/8 of the seniors and 3/4 of the juniors study Japanese, what fraction of the students in both classes study Japanese? Select:
A) 3/8
B) 3/4
C) 1/3
D) 4/5
E) 1/2

Solution: Start by deciding on a number of students to represent the number of students in the senior class. For this example I will choose 200 students. That would make the number of students in the junior class 100. Then we can find out how many students are taking Japanese in each grade and add them together. (1/8)*200=25 and   (3/4)*100= 
  (3/4)*100 = 75
75. 25+75=100. There are a total of 300 students in the junior class and senior class combined (100+200=300), and there are 100 total students in Japanese, so 100 students in Japanese / 300 total students equals 1/3 of the students in both classes that study Japanese.   Answer: 1/3
Answer: C
The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor? Pick.
A) 12 B) 17 C) 18 D) 77 E) 21

Solution: Let the length and the breadth of the floor be l m and b m respectively.   l = b + 200% of b = l + 2b = 3b   Area of the floor = 324/3= 
324/3 = 108
108 sq m   l b= 108 i.e., l * l/3 = 108   l2 = 324 => l = 18.   Answer: 18
Answer: C
The height of a triangle is decreased by 25% and its base increased by 40%. Its area will Choose one:
A) decrease by 12.5%
B) increase by 12.5%
C) decrease by 25%
D) Increase by 25%
E) Increase by 5%

Solution: Explanation :   Let the initial height be 100 and the base be 200 units.   âˆ´ Area = 1/2 x 100 x 200 = 1000sq units   Now, height = 75 units and base = 280 units   âˆ´ New area = 1/2 x 75 x 280 = 10500   âˆ´ Area is increased by (10500 - 10000)/10000 x 100   = 5%   Answer : Option Increase by 5%
Answer: E
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. If the faster train passes the slower train in 36 seconds,what is the length of each train?
Choose the correct choice from the following.
A) 25	B) 30	C) 50	D) 75	E) 40

Solution: Assume the length of each train = x   Total distance covered for overtaking the slower train = x+x = 2x   Relative speed = 46-36= 
46-36 = 10
10km/hr= (10×10)/36 = 100/36 m/s   Time = 36 seconds   2x/ (100/36) = 36   => (2x × 36 )/100 = 36   => x = 50 meter   Answer is 50.
Answer: C
A fruit seller had some Mangoes. He sells 60% and still has 20 apples. Originally, he had ? Choices
A) 10 Mangoes  B) 60 Mangoes  C) 40 Mangoes  D) 50 Mangoes  E) None

Solution: Answer   âˆµ 40% of N = 20   âˆ´ N = (20 x 100)/40 = 50   Correct Option: 50 Mangoes
Answer: D
5 persons A,B,C,D and E occupy seats in a row at random. What is the probability that A and B sit next to each other ?  Choices:	A) 3/5	B) 2/5	C) 1/5	D) 8/5	E) None of these

Solution: Explanation :   Without restriction, number of arrangements = 5! .   => Number of possible outcomes = T = 5! = 120 .   With restriction, number of arrangements = 4! x 2 .   ( i.e considering A and B together) = 48.   => Number of favourable outcomes = F = 48.   Hence,   P( A and B sit together)   => F / T   => No. of arrangements with restriction / No. of arrangements without restriction .   => 48 / 120.   => 2 / 5.   Answer : 2/5
Answer: B
A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?  Answers.
A) 247 B) 267 C) 120 D) 872 E) 267

Solution: Speed = (12/10 * 60) km/hr   = (72 * 5/18) m/sec = 20 m/sec.   Length of the train   = 20 * 6= 
20 * 6 = 120
120 m.   Answer:120
Answer: C
By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent of solution B. If 200 grams of solution A are mixed with 700 grams of solution B, then liquid X accounts for what percent of the weight of the resulting solution?	Select.
A) 1.42%  B) 1.9%  C) 10%  D) 15%  E) 19%

Solution: I think there is a typo in question.   It should have been "By weight Liquid 'X ' makes up..... "   Weight of Liquid X = 0.8 % of Weight of 1.42% + 1.8% of Weight of B   When 200gms of 1.42% and 700gms of B is mixed :   Weight of Liquid X = (0.8 * 200)/100 + (1.8* 700)/100= 
(0.8 * 200)/100 + (1.8* 700)/100 = 14.2
14.2gms   % of Liquid X in resultant mixture= (14.2/1000) *100= 
(14.2/1000) *100 = 1.42
1.42%   1.42%
Answer: A
The Delhi Express runs @ 144 kilometers per hours and it reaches destination 20 minute ahead of schedule. If it averages 100 km/hour, it reaches 24 minute behind schedule. What is the average speed it should maintain in order to reach the destination on schedule?	Choose the correct answer:
A) 250
B) 240
C) 230
D) 245
E) 235

Solution: If the destination is D kilometer and the speed in order to reach on schedule is S km/hour,   the time taken to reach on schedule is D/S hours   Thus we get two equations:   D/144 = D/S - 1/3 and   D/100 = D/S + 2/5 and   Subtracting the first equation from the second we get : 44D/14400 = 11/15   Thus D = 14400 x 11/ 44 x 15 = 240   ANSWER:240
Answer: B
At what price must an Book costing $47.50 be marked in order that after deducting 20% from the list price. It may be sold at a profit of 25% on the cost price?	Select
A) 72.5 B) 55.5 C) 64.2 D) 82.5 E) 60.5

Solution: 64.2   $62.50   64.2P = 47.50   SP = 47.50*(125/100)= 
47.50*(125/100) = 59.375
59.375   MP*(80/100)= 59.375   MP = 74.2
Answer: C
At an examination in which full marks were 500. A got 10% less than B, B got 25% more than C and C got 20% less than D. If A got 360marks, what percentage of full marks was obtained by D?
Choices.
A) 48%	B) 30%	C) 12%	D) 80%	E) 28%

Solution: A B 12% D   90 100 80 100   A D   90 ----- 100   360 ------ ? = 400   500 ------ 400   100 ------- ? => 80%   Answer: 12%
Answer: C
Calculate the value of 4.54 x 10^5 ?	Pick one
A) 454	B) 4540000	C) 454000	D) 45400	E) 4540

Solution: 4.54 x 10^5 = 4.54 x 100000 = 4540000.   Answer = 4540000
Answer: B
The expression uv+u is odd when the u and v are integers. Which of the following expressions must be even? Choose the correct option
A) u B) v C) u + v D) uv - u E) u + v^2

Solution: uv+u is odd   u and v are integers   If u were even uv+u would be even despite any value of v.   v can't be odd, so v must be even.   Ans : v
Answer: B
The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
Choose one.
A) 12  B) 15  C) 14  D) 18  E) 19

Solution: The ratio of the times taken is 2:1.   The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1)= 
(2+1)/(2-1) = 3
3/1= 
3/1 = 3
3:1   Speed of the stream= 42/3= 
42/3 = 14
14 kmph.   Answer: 14
Answer: C
Two vessels contains equal number of mixtures milk and water in the ratio 8:2 and 9:1. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture so obtained?  Choose the correct choice from the following options:
A) 1:3 B) 9:13 C) 5:11 D) 11:3 E) 17:3

Solution: The ratio of milk and water in the new vessel is = (8/10 + 9/10) : (2/10 + 1/10)   = 17/10 : 3/10 = 17:3   Answer is 17:3
Answer: E
A can do a work in 6 days. B can do the same work in 8 days. Both A&B together will finish the work and they got $1000 from that work. Find their shares? Choose the correct choice
A) 600,800  B) 500,500  C) 300,700  D) 800,200  E) 550,450

Solution: Ratio of their works 600,800:B = 6:8   Ratio of their wages 600,800:B = 3:4   600,800's share = (3/5)1000 = 600   B's share = (4/5)1000 = 800   correct option is 600,800
Answer: A