MU-NLPC/Calc-aqua_rat huggingface dataset:
If x>=y and y>1 , what is the maximum value of log (base x) -(x/y) + log (base y)x^2/y?  Choose the correct choice from the following answers.
A) -0.5  B) 0  C) 0.5  D) 1  E) 2

Solution: log -(x/y) + log ( x^2)/y => - log x/y + 2log (x/y)   x y x y   0y Formula (i) - log x/y = log y/x (ii) log y/x = log y - log x   x x x x x   log y - log x + 2{log x - log y }   x x y y   log y -1 + 2log x - 2 ==> log y + 2log x -3   x y x y   by Sub x &y as 2 by Question Condition---> Ans 1+2-3= 
1+2-3 = 0
0   ANSWER:0
Answer: B
16 children are to be divided into two groups A and B of 10 and 6 children. The average percent marks obtained by the children of group A is 75 and the average percent marks of all the 16 children is 76. What is the average percent marks of children of group B ? Choose the correct choice from the following options
A) 233/3
B) 233/8
C) 233/1
D) 233/2
E) 263/3

Solution: Required average = [(76 * 16) - (75 * 10)] / 6   = (1216 - 750)/6 = 466/3   = 233 /3.   233/3nswer: 233/3
Answer: A
Cereal A is 9% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?	Options.
A) 2:9 B) 2:5 C) 1:6 D) 1:4 E) 1:3

Solution: (9/100)A+(2/100)2:5 = (4/100)(A+2:5)   5A =22:5   => A/2:5 = 2/5   Answer is 2:5.
Answer: B
If a committee of 3 people is to be selected from among 9 married couples so that the committee does not include two people who are married to each other, how many such committees are possible? Choose the correct choice.
A) 420 B) 540 C) 550 D) 672 E) 720

Solution: You now have your Committee of 3 people. But you've selected them in an order, when order doesn't matter.   Selection #1 = Jack   Selection #2 = Susan   Selection #3 = Mary   Assume this is a good committee where Jack is not married to Susan or Mary and Susan and Mary are not married. The above committee will be the same as the following committee:   Selection #1 = Susan   Selection #2 = Mary   Selection #3 = Jack   To account for the fact that the order does not matter, we must divide out the number of ways a single committee can be the same members but in different order. 3 places = 3!, 3*2*1 = 6.   18*16*14 / 6= 
18*16*14 / 6 = 672
672. Answer 672.
Answer: D
What will $3000 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually? Choose the correct choice:	A) $4316	B) $4632	C) $4864	D) $5184	E) $5548

Solution: After one year: 1.2 * $3000   After two years: (1.2)^2 * $3000   After three years: (1.2)^3 * $3000 = $5184   The answer is $5184.
Answer: D
A man is 40 years older than his son. In six years, his age will be twice the age of his son. The present age of this son is Pick one:
A) 31 years  B) 32 years  C) 33 years  D) 34 years  E) 35 years

Solution: Explanation:   Let's Son age is x, then Father age is x+40.   => 2(x+6) = (x+40+6)   => 2x+12 = x+46   => x = 34 years   Answer: Option 34 years
Answer: D
Inland revenue paid $300 on its first 1000 watts of electricity and then $5000 on the next 10000 watts. By approximately what percent did the ratio of monies due to watts increase from the first $1000 watts to the next 10000 watts? Choose the correct choice from the following options.
A) A) 80%
B) B) 6%
C) C) 60%
D) D) 20%
E) E) 40%

Solution: First 1000 watts (3/10)   Next 10000 (5/10)   percentage increase is (difference/initial quantity)*100   (3/10)/(5/10 )* 100= 
(3/10)/(5/10 )* 100 = 60
60%   60%orrect options is 60%
Answer: C
A vendor buys 10 t-shirts at an average price of $14 per t-shirt. He then buys 15 more t-shirts at an average price of $11 per t-shirt. What is the average price S per t-shirt that the vendor paid for these purchases?	Answers.
A) $12.20  B) $12.50  C) $12.55  D) $12.70  E) $13.00

Solution: Correct Answer: A   Explanation: The relevant formula for this problem is Average S= (Sum)/(Number of Terms). Another way to look at the formula is Sum = Average x Number of Terms. For the first purchase, the vendor's sum (total cost) was $140, since 14 x 10 = 140. For the second purchase, the vendor's cost was $165, since 11 x 15 = 165. The grand sum is then $140 + $165, which equals $305. The total number of shirts purchased was 25, so to get the average price per shirt, we divide 305 by 25, which equals $12.20. As a result, the correct answer is A.   NOTE: A relative understanding of weighted average offers a shortcut to this problem. Because the true average of 11 and 14 is 12.5, but the vendor sells more shirts at the lower price than at the higher price, the weighted average must be less than $12.50; only answer choice $12.20 is a possibility.
Answer: A
A boat travels 80 km downstream in 8 hours and 48 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current. Pick.
A) 7 km/hr, 3 km/hr	B) 5 km/hr, 4 km/hr	C) 1 km/hr, 6 km/hr	D) 2 km/hr, 1 km/hr	E) 4 km/hr, 1 km/hr

Solution: Downstream speed=80km/8hrs   =10kmph   upstream speed80  /8= 
80  /8 = 10
10kmph   upstream speed=48km/12hrs   =4kmph   speed of boat48  /12= 
48  /12 = 4
4kmph   speed of boat=avg of downstream and upstream speeds   speed of boat=(10+4)/2= 
(10+4)/2 = 7
7kmph.   current speed=half of the difference of downstream and upstream speeds   currend speed=(10-4)/2= 
(10-4)/2 = 3
3kmph   ans is 7km/hr,3km/hr   7 km/hr, 3 km/hrNSWER:7 km/hr, 3 km/hr
Answer: A
Marty's Pizza Shop guarantees that their pizzas all have at least 75% of the surface area covered with toppings, with a crust of uniform width surrounding them. If you order their best seller – a circular pizza with a diameter of 16 inches – what is the maximum width you can expect to see for the crust?	Choose one:
A) 0.8 inches B) 1.1 inches C) 1.6 inches D) 2.0 inches E) 2.5 inches

Solution: Total Area = 8 * 8 * pi   Radius = 64 pi   Surface = .75 * 64 * pi = 48 pi   Radius of surface = 4 sqrt (3) ~ 6.8   Radius width = 8 - 6.8= 
8 - 6.8 = 1.2
1.2   Answer: 1.1 inches
Answer: B
The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 34 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add?	Options:
A) 17 litres B) 22.67 litres C) 11 litres D) 07 litres E) 38.67 litres

Solution: 262.85(34)+3,104.35x = 1,399.45(34 + x)   Solve the equation.   262.85(34)+3,104.35x = 1,399.45(34 + x)   8936.9+ 3,104.35x = 47,581.3 + 1,399.45x   8936.9 + 1,704.9x = 47,581.3   1,704.9x = 38,644.40   x ≈ 22.67   Answer is 22.67 litres.
Answer: B
There is a 30% chance Jen will visit Chile this year, while there is a 50% chance that she will visit Madagascar this year. What is the probability that Jen will visit either Chile or Madagascar this year, but NOT both?
Choose the correct choice from the following choices:
A) 25.0%
B) 37.5%
C) 50.0%
D) 62.5%
E) 75%

Solution: P(50.0%hile and not Madagascar) = 0.3*0.5= 
0.3*0.5 = 0.15
0.15   P(Madagascar and not 50.0%hile)= 0.5*0.7= 
0.5*0.7 = 0.35
0.35   Total probability= 0.15 + 0.35= 
0.15 + 0.35 = 0.5
0.5= 50%   The answer is 50.0%.
Answer: C
9 3/4 + 7 2/17 - 9 1/15=?  Answers
A) 7 719/1020	B) 9 817/1020	C) 9 719/1020	D) 7 817/1020	E) None of them

Solution: Given sum=9+3/4+7+2/17-(9+1/15)   =(9+7-9)+(3/4+2/17-1/15)   =7+(765+120-68/1020   =7 817/1020   Answer is 7 817/1020
Answer: D
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?	Pick:
A) 2/28  B) 2/129  C) 2/21  D) 2/20  E) 2/25

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = Â³2/21â‚‚/Â¹âµ2/21â‚‚ = (3 * 2)/(15 * 14) = 1/35   Probability that both are yellow = Â²2/21â‚‚/Â¹âµ2/21â‚‚ = (2 * 1)/(15 * 14) = 1/105   Probability that one blue and other is yellow = (Â³2/21â‚ * Â²2/21â‚)/Â¹âµ2/21â‚‚ = (2 * 3 * 2)/(15 * 14) = 2/35   Required probability = 1/35 + 1/105 + 2/35   = 3/35 + 1/105 = 1/35(3 + 1/3)   = 10/(3 * 35) = 2/21   Answer: 2/21
Answer: C
123 school girls are to be transported in small vans. Each van can carry 8 girls only. What is the smallest possible number of vans that are needed to transport all 123 school girls?
Choose the most appropriate option
A) 15 B) 16 C) 17 D) 18 E) 19

Solution: To find the number of vans, we divide 123 by 8.   123 * 8 = 15 and remainder = 3   So 15 vans are needed to transport 15 * 8= 
15 * 8 = 120
120 girls, and 1 van is needed to transport the 3 remaining girls. A total of 16 vans are needed.   correct answer 16
Answer: B
The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money? Choose the correct choice from the following options:	A) 7 months	B) 10 months	C) 9 months	D) 11 months	E) 8 months

Solution: 7*5: 5*x = 7:10   x = 10   ANSWER:10 months
Answer: B
Three archers each have an equal chance of hitting a target, and if only two of the three shoot the likelihood of the two hitting the target is 4/9 . What is the likelihood of all three men missing the target?
Pick.
A) probability is 1/27  B) 16/81  C) 8/27  D) 19/27  E) 26/27

Solution: Let the probability of an archer hitting a target be xx. Then the probability of two hitting the target will be P=x∗x=49P=x∗x=49 - -> x=23x=23, so the probability of an archer missing the target will be P=1−23=13P=1−23=13.   The probability of all three men missing the target will be P=(13)3=127P=(13)3=127.   probability is 1/27nswer: probability is 1/27.
Answer: A
When average age of 21 members are 0, how many members greater than 0? Choose one:
A) 17
B) 20
C) 21
D) 24
E) 25

Solution: Average of 21 numbers = 0.   Sum of 21 numbers (0 x 21) = 0.   It is quite possible that 20 of these numbers may be positive and if their sum is a then 21st number is (-a)   Answer is 20 (20)
Answer: B
An owner of a pizza stand sold small slices of pizza for Rs. 150 each and large slices for Rs. 250 each. One night he sold 5000 slices, for a total of Rs. 10.50 lakh. How many small slices were sold?  Choices:
A) 3000	B) 2000	C) 4000	D) 2500	E) 3500

Solution: Explanatory Answer   This question is a word problem in linear equations. The problem is solved by framing two linear equations from the information given in the question and solving them.   Let 's' be the number of small slices and 'b' the number of large slices sold on that night.   Therefore, s + b = 5000 ... eqn (1)   Each small slice was sold for Rs.150.   Therefore, 's' small slices would have fetched Rs.150s.   Each large slice was sold for Rs.250.   Therefore, 'b' large slices would have fetched Rs.250b.   Total value of sale = 150s + 250b = 10,50,000 (note the left hand side is in Rupees and hence we have to convert right hand also to Rupees from Lakhs of Rupees)   Or 150s + 250b = 10,50,000 ... eqn (2)   Multiplying equation (1) by 150, we get 150s + 150b = 7,50,000 ... eqn (3)   Subtracting eqn (3) from eqn (2), we get 100b = 3,00,000   Or b = 3000   We know that s + b = 5000   So, s = 5000 - b = 5000 - 3000= 
5000 - 3000 = 2_000
2000.   2000 small slices were sold.   Answer 2000
Answer: B
Ten years ago, a mother was four times older than her daughter. After ten years, the mother will be twice older than daughter. The present age of the daughter is  Answers.
A) 22	B) 21	C) 24	D) 20	E) 19

Solution: Let the mother’s present age be ’x’   Let the daughter’s age be ’y’;   10 years ago; (x - 10) = 4(y - 10) or x - 4y = - 30.. (1)   10 years later; (x + 10) = 2(y + 10) or x - 2y = 10.. (2)   Solving (1) & (2)   y = 20   ANSWER:20
Answer: D
In what time will Rs.1000 become Rs.1331 at 10% per annum compounded annually  Choose the correct option:
A) 2 Years	B) 3 Years	C) 4 Years	D) 5 Years	E) None of these

Solution: Explanation:   Principal = Rs.1000;   Amount = Rs.1331;   Rate = Rs.10%p.a.   Let the time be n years then,   1000(1+10100)n=1331(1110)n=13311000(1110)3=13311000   So answer is 3 years   Answer: 3 Years
Answer: B
The jogging track in a sports complex is 1000 meters in circumference. Deepak and his wife start from the same point and walk in opposite directions at 20 km/hr and 13 km/hr respectively. They will meet for the first time in?  Choose the most appropriate option:
A) 50min  B) 33min  C) 35min  D) 25min  E) 20min

Solution: Clearly, the two will meet when they are 1000 m apart   To be   20+13= 
  20+13 = 33
33 km apart, they take 1 hour   To be 1000 m apart, they take   33 * 1000/1000= 
  33 * 1000/1000 = 33
33 min.   Answer is 33min
Answer: B
In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women? Choose the correct choice from the following options
A) 63
B) 25
C) 40
D) 65
E) 98

Solution: Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) = = 63.   63NSWER 63
Answer: A
From the below series find the remainder? 1201 × 1203 ×1205 × 1207 is divided by 6? Choose the correct choice from the following options
A) 3	B) 4	C) 5	D) 6	E) 8

Solution: If you don't know the above rule, this problem is really calculation intensive.   But by applying the above rule, when 1201, 1201, 1203, 1204 divided by 6, leaves remainders 1, 3, 5, 1. The product of these remainders = 15.   When 15 is divided by 6, Remainder is 3   3
Answer: A
A plant manager must assign 12 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 2 new workers. How many different ways can she assign the new workers?  Choose the correct choice from the following choices:
A) 23760  B) 47520  C) 33000  D) 48600  E) 54000

Solution: whatever : my take selecting team of 2 out of 12 to assign to the shifts = 12C2 = 66 ways.   now 2 out of 12 means total of 6 group possible.   so putting them in shifts = counting methode: first, second, third, alt , alt   = 6*5*4*3*2*1= 
6*5*4*3*2*1 = 720
720   here alt and alt are the same: so  720/2= 
 720/2 = 360
360 ways.   total ways of selecting= (selecting 2 out of 12)*arranging those teams in shifts   = 66*360= 
66*360 = 23_760
23760   23760ns: 23760
Answer: A
In the coordinate plane, Line A has a slope of -1 and an x-intercept of 1. Line B has a slope of 5 and a y-intercept of -5. If the two lines intersect at the point (a,b), what is the sum a+b?  Choose the correct answer
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: The equation of Line A is y = -x + 1   The equation of Line B is y = 5x - 5   5x - 5 = -x + 1   x = 1   y = 0   The point of intersection is (1,0) and then a+b = 1.   The answer is 1.
Answer: B
If A= {2, 4, 6}, B= {1, 2, 5, 7}, and C= {2, 3, 4, 6}. Find A-(B U C)  Choose the correct choice from the following.
A) {1 , 2}
B) {2 ,3 ,5 }
C) { }
D) {5 }
E) None of these

Solution: Explanation :   A= {2, 4, 6},   B= {1, 2, 5, 7},   C = {2, 3, 4, 6}   Now,(B U C) = {1, 2, 5, 7} U {2, 3, 4, 6} = {1,2,3,4,5,6,7}   A-(B U C) = {2, 4, 6} - {1,2,3,4,5,6,7} = { }   Hence (C) is correct answer.   Answer : { }
Answer: C
A radio station has to choose two days of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any three of the seven weekdays can be chosen. How many different three-day combinations of the seven weekdays can be constructed? Choose the correct answer
A) 9	B) 15	C) 21	D) 35	E) 56

Solution: Behind the story, we are really being asked to evaluate 7C2. We could use the factorial formula, but above we conveniently happen to have Pascal’s Triangle written out to the seventh row. We see that 7C2, the third entry of the seventh row, is 21. Answer = 21.
Answer: C
John has on his shelf four books of poetry, four novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one poetry? Choose the most appropriate option
A) 1/2
B) 2/5
C) 3/10
D) 7/20
E) 16/45

Solution: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 4/10*4/9 + 4/10*4/9 = 16/45.   Answer: 16/45.
Answer: E
A person took some amount with some interest for 5 years, but increase the interest for 1%, he paid Rs.250/- extra, then how much amount he took?	Choose the correct choice:  A) Rs.5500/-  B) Rs.6000/-  C) Rs.4000/-  D) Rs.5000/-  E) None of these

Solution: Explanation:5 years = Rs.250/-year = 250/5Rate of Interest = 1%100/1% × 250/5 = Rs.5000/-P = Rs.5000/- Answer: Option Rs.5000/-
Answer: D
One millisecond is 0.001 of a second. The costs for a single run of a computer program are $1.07 for operating-system overhead, $0.019 per millisecond of computer time, and $4.35 for the mounting of a data tape. What is the total of these three costs for 1 run of a program that requires 1.5 seconds of computer time ? Select.
A) $7.15
B) $8.87
C) $33.92
D) $35.57
E) $39.62

Solution: Operating system overhead for 1 run = 1.07 $   Mounting of data tape = 4.35$   $33.92ost per 1 millisecond of computer time = .019 $   Total cost of 1 run of a program that requires 1.5 seconds of computer time   = 1.07 + (.019*1500) + 4.35   =1.07 + 28.5 + 4.35= 
1.07 + 28.5 + 4.35 = 33.92
33.92$   Answer $33.92
Answer: C
Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 40 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast? Choose the correct answer.
A) 10%	B) 12%	C) 15%	D) 17%	E) 20%

Solution: Lets assume that candidate got 40% votes and total votes is 100.   Candidate won = 40   Remaining = 60   To get 50%, candidate requires 10 votes from 100 which is 10% and 10 votes from 60.   10/60 = 1/6 = .166 = 16.67%   Which is approx 17%. Hence the answer is 17%
Answer: D
Two trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 36 hours respectively. The ratio of their speeds is Choose the correct option.
A) 4:1  B) 4:2  C) 4:5  D) 6:3  E) 3:6

Solution: Ratio of their speeds = Speed of first train : Speed of second train   = √36−−√9   = 6:3   Answer is 6:3.
Answer: D
If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+69)=? Pick one.
A) 3675	B) 3575	C) 3475	D) 3375	E) 3275

Solution: Explanation :   To solve this use the formula of 3675P,   Sn= (n/2)(a+l) ................(1)   To find n, use   => Tn= a+(n-1)d   => 69=1+(n-1)2   => n=35   Use value of n in (1)   then,   Sn = (35/2)(1+69) = 1225   3675ns:- 3(Sn) = 3675   3675nswer : 3675
Answer: A
The length of a train and that of a platform are equal. If with a speed of 108 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?	Choose the correct choice from the following choices.
A) 227 B) 299 C) 276 D) 750 E) 900

Solution: Speed = [108 * 5/18] m/sec = 30 m/sec; Time = 1 min. = 60 sec.   Let the length of the train and that of the platform be x meters.   Then, 2x/60 = 30 è x = 30 * 60 / 2= 
30 * 60 / 2 = 900
900   Answer: 900
Answer: E
Given that E and F are events such that P(E) = 0.16, P(F) = 0.4 and P(E n F) = 0.4,
find P (E|F) and P(F|E)
Select the correct option:
A) 1/2	B) 1/7	C) 1/4	D) 1/3	E) 1/5

Solution: Here, E and F are events   P(E|F) = P(EnF)/P(F) = 0.4/0.4= 
0.4/0.4 = 1
1   P(F|E)= P(EnF)/P(E) = 0.4/0.16 = 1/4.   1/4
Answer: C
In 1995, there are 28 days in February and there are 365 days in the year. In 1996, there are 29 days in February and there are 366 days in the year. If the date February 12, 1995 is a Wednesday, then which one of the following would the date February 12, 1996 be? Choose the correct choice from the following:  A) Thursday  B) Friday  C) Saturday  D) Sunday  E) Monday

Solution: From the information given, Feb 12, 1996 is 366 days after Feb 12, 1995.   366 days = 52 weeks and 2 more days. Therefore if Feb 12, 1995 is a Wednesday, then Feb 12, 1996 is Wednesday + 2 days = Friday   Answer: Friday
Answer: B
In a covering a certain distance, the speeds of A and B are in the ratio of 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is?	Options:
A) 2 hrs  B) 3 hrs  C) 5 hrs  D) 6 hrs  E) 4 hrs

Solution: A   Ratio of speeds = 3:4   Ratio of times taken = 4:3   Suppose A takes 4x hrs and B takes 3x hrs to reach the destination.   Then, 4x - 3x = 30/60 => x = 1/2   Time taken by 2 hrs = 4x hrs = 4 * 1/2= 
4 * 1/2 = 2
2 hrs.
Answer: A
In a workshop there are 4 kinds of beds, 2 kinds of closets, 2 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?
Choose the correct answer.
A) 168.  B) 80.  C) 56.  D) 48.  E) 72.

Solution: ways to select one shelf = 2   ways to select one bed = 4   ways to select one of the following: a chair or a closet = 7+2= 
7+2 = 9
9   ways to select all of them together= 2*4*9= 
2*4*9 = 72
72   Hence, 72. is the answer.
Answer: E
What is the average of first 21 multiples of 6 ? Options:  A) A)66  B) B)77  C) C)79  D) D)81  E) E)82

Solution: Required average = 6(1+2+....+21) / 21   (6/21)X ( (21x22) / 2 ) (because sum of first 21 natural numbers)   = 66   66
Answer: A
Machine A and machine B are each used to manufacture 550 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10% more sprockets per hour than machine A. How many sprockets per hour does machineAproduce?
Choose the correct choice from the following answers:
A) 5.5 B) 6.6 C) 60 D) 100 E) 110

Solution: time taken by B = t   time taken by A = t+10   qty produced by A = q   qty produced by B = 1.1 q   for B: t(1.1q) =550   qt=500   for A: (t+10)(q) =550   qt+10q=550   500+10q=550   q=5   so A can produce 5/hour.   then B can produce = 5(1.1)=5.5/hour.   5.5
Answer: A
Which of the following numbers is two more than the square of an odd integer?  Options
A) 14,173 B) 14,361 C) 15,131 D) 15,737 E) 15,981

Solution: If a square has an odd unit's digit, then its ten's digit must be even.   Only 15,131-2 = 15,129 satisfies this condition.   The answer is 15,131.
Answer: C
How many positive integers S less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9 ?
Choose one.
A) 19
B) 18
C) 17
D) 16
E) 15

Solution: We're asked to deal with the positive integers LESS than 20. There are only 19 numbers in that group (1 to 19, inclusive). We're asked to find all of the numbers that fit one (or more) of the given descriptions. Looking at the answer choices, we have every value form 15 to 19, inclusive, so most (if not all) of the numbers from 1 to 19 fit one (or more) of the descriptions. How long would it take you to find the ones that DON'T fit.....?   The first several should be pretty easy to find - the prompt wants us to focus on multiples of 2 and 9 (and sums of those multiples). So what ODD numbers are less than 9?   1, 3, 5, 7   None of these values fit the given descriptions. That's 4 out of 19 that we know for sure do NOT fit. 19 - 4 = 15 = 15
Answer: E
Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 16 km apart, if they walk in the same direction?  Pick:
A) 5hours
B) 6hours
C) 8hours
D) 16hours
E) 12hours

Solution: To be 2km apart they take 1 hour   To be 10km apart they take = 1/2 * 16= 
1/2 * 16 = 8
8 hours   Answer is 8hours
Answer: C