MU-NLPC/Calc-aqua_rat huggingface dataset:
The mall charges 50 cents for the first hour of parking and $3 for each additional hour until the customer reaches 4 hours, after that the parking fee is $1 per hour. If a certain customer parked his in the mall for 7 hours and 30 minutes, how much is he going to pay?  Select:
A) $11.5.  B) $12.  C) $13.  D) $14.5  E) $15.

Solution: $13.harges for 7 Hours = ( First hour @ $ 0.50 ) + ( 3 hours @ $ 3 ) + ( 3.5 hours @ $ 1 )   $13.harges for 7 Hours = ( 1 @ $ 0.50 ) + ( 3 hours @ $ 3 ) + ( 3.5 hours @ $ 1 )   $13.harges for 7 Hours = ( $ 0.50 ) + ( $ 9) + ( $ 3.5 )   $13.harges for 7 Hours = ( $ 0.50 ) + ( $ 9) + ( $ 3.50 )   $13.harges for 7 Hours = $ 13   Hence correct answer must be ($13.)
Answer: C
A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 80 percent of books that were loaned out are returned and there are 66 books in the special collection at that time, how many books of the special collection were loaned out during that month? Choose the correct option: A) 20 B) 30 C) 35 D) 45 E) 55

Solution: there are 9 books less(75-66) which represents 20% of the loaned books (100-80)   So total loaned out books = 45   Answer 45
Answer: D
Find a 6-digit integer abcdef with the following properties:
Take the rightmost digit and place it in front of the integer to form a new number (abcdef --> fabcde).
The new one is the product of the old one and the shifted digit (fabcde = f*abcdef).
What was the original integer?  Choose the correct choice from the following answers
A) 122564	B) 102564	C) 142564	D) 102574	E) 102566

Solution: a=1 b=0 c=2 d=5 e=6 f=4   fabcde = f x abcdef   410256 = 4 x 102564   ANSWER:102564
Answer: B
A sum of money at simple interest amounts to Rs. 825 in 3 years and to Rs. 840 in 4 years. The sum is?
Pick.
A) s. 780  B) s. 638  C) s. 650  D) s. 730  E) s. 735

Solution: S.I. for 1 year = (840 - 825) = Rs. 2915   S.I. for 3 years = 15 * 3 = Rs. 45   Principal = (825 - 45) = Rs. 780.   s. 780NSWER:s. 780
Answer: A
In how many different number of ways 3 boys and 2 girls can sit on a bench?	Answers.
A) 700	B) 710	C) 120	D) 300	E) 720

Solution: npn = n!   5p5 = 5 × 4 × 3 × 2 × 1 = 120   120)
Answer: C
A committee has 4 men and 7 women. What are the number of ways of selecting 2 men and 4 women from the given committee? Select
A) 125
B) 150
C) 180
D) 210
E) 225

Solution: The number of ways to select two men and four women = 4C2 * 7C4 = 6 * 35= 
6 * 35 = 210
210   The answer is 210.
Answer: D
A train is moving at a speed of 132 km/hr. If the length of the train is 110m, how long will it take to cross a railway platform 165m long?  Choose the correct choice: A) 8 sec B) 9 sec C) 7 1/2 sec D) 10 sec E) None

Solution: Speed of the train=(132*5/18)m/sec=(110/3)m/sec   Distance covered in passing the platform= (110+65)m=275m   Therefore, Time taken=(275*3/110)sec =7 1/2 Sec   Answer: Option 7 1/2 sec
Answer: C
What percent is 70 of 280?
Choose the most appropriate option:  A) 12 %  B) 25 %  C) 26 %  D) 27 %  E) 28 %

Solution: 70/280 = 1/4   1/4 × 100 = 25 %   25 %
Answer: B
An air conditioner can coo the hall in 25 minutes while another takes 30 minutes to cool under similar conditions. if both air conditioners are switched on at same instance then how long will it take to cool the room?
Choose one.
A) about 16 minutes B) about 24 minutes C) about 14 minutes D) about 34 minutes E) about 4 minutes

Solution: Take LCM of 25 and 30 = 150   25*6= 
25*6 = 150
150/ 30*5=150.   So if both are switched on together , room cooled in 150/(6+5)=150/11=13.64 minutes   13.64 can be round to 14 minutes , so about 14 minutes   ANSWER: about 14 minutes
Answer: C
A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 8 more days. How many days would it have taken the second carpenter to do the complete job working alone?  Choose the correct option: A) 4 2/3 B) 7 C) 9 D) 14 E) 28

Solution: A carpenter worked only 1 day on something that takes him 6 MORE days.   Means;   Carpenter finishes his work in 7 days.   Let his buddy finish the same task in x days.   Respective rates per day:   1/7 AND 1/x   To complete 1 work:   First guy worked for 5 days @ rate=1/7 per day.   Second one worked for 8 days @ rate=1/x per day   Expression:   Days*Rate=Work   5*1/7+8*1/x=1   5x+56=7x   2x=56   x=28 days.   Ans:28
Answer: E
A man can row 8 kmph in still water. When the river is running at 2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?	Select the correct option
A) 5.75
B) 5.7
C) 7.5
D) 5.74
E) 5.71

Solution: M = 8   S = 2   DS = 10   US = 6   x/10 + x/6 = 1   x = 3.75   D = 3.75 * 2= 
3.75 * 2 = 7.5
7.5 Answer: 7.5
Answer: C
For her customer feedback score, Jess wants to average at or above an 8.0 rating. For the month of June, she received the following scores: 5, 8, 8, 7, 9, 10, 6, 6, 8 and 7. By what percent did she fall short of her goal?	Select.
A) 4% B) 7.5% C) 8% D) 10% E) 12%

Solution: Expected minimum rating = 8   Deviation from the expected minimum rating = (-3 + 0 + 0 - 1 + 1 + 2 - 2 - 2 + 0 - 1)/10 = -6/10 = -0.6   Current rating is 0.6 less than 8.   Percentage = (0.6/8)*100= 
(0.6/8)*100 = 7.5
7.5%   Answer: 7.5%
Answer: B
The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?  Choose the correct choice from the following.
A) 8 ml B) 5 ml C) 4 ml D) 6 ml E) 1 ml

Solution: 4.5 4.5   30% 70%   30% ----- 4.5   70% ------? => 10.5 - 4.5= 
10.5 - 4.5 = 6
6 ml   Answer:6 ml
Answer: D
The sale price sarees listed for Rs.280 after successive discount is 12% and 8% is?  Answers:
A) 288	B) 226	C) 250	D) 230	E) 262

Solution: 280*(88/100)*(92/100)   = 226   Answer: 226
Answer: B
A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 24m/h. what is the speed of the person while he was going to his office?
Choose the correct choice from the following answers.
A) 8km/h B) 9km/h C) 10km/h D) 11km/h E) 16km/h

Solution: u = k , v= 3k   \inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=24   \inline \Rightarrow 1.5k = 24   \inline \Rightarrow k=16km/h   16km/h
Answer: E
A train 250 m long running at 72 kmph crosses a platform in 15 sec. What is the length of the platform?
Choose the correct choice from the following:	A) 50m	B) 200m	C) 250m	D) 270m	E) 300 m

Solution: D = 72 * 5/18 = 15 = 300 â€“ 250 = 50m   50mNSWER:50m
Answer: A
A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. She mixes peanuts worth $3.50 a pound with cashews worth $4.00 a pound. How many pounds of cashews must she use?  Answers
A) 40
B) 45
C) 50
D) 55
E) 60

Solution: From the question stem we know that we need a mixture of 100 pounds of peanuts and cashews. If we represent peanuts as x and cashews as y, we get x + y = 100. Since the wholesaler wants to sell the mixture of 100 pounds @ $2.50, we can write this as: $2.5 * (x + y) = $1.5x + $4y   From the equation x + y = 100, we can rewrite y as y = 100 - x and substitute this into our equation to get:   $2.5 * (x + 100 - x) = $1.5x + $4(100 - x)   If you solve for x, you will get x = 60, and therefore y = 40. So the wholesaler must use 40 pounds of cashews.   You can substitute into the original equation to see that: $250 = $1.5(60) + $4(40)   Answer is 60
Answer: E
Tough and Tricky questions: Exponents.
If 3^m3^m3^m = 8^n, then m/n =  Select:
A) 1/3  B) 2/3  C) 1  D) 3/2  E) 2

Solution: I also soved it, but a bit differently. Thank you for reminding me of this much easier and logical way!   What I did was to test powers of 3 that would lead to 9.   So, we have 3 raised to the same power 3 times and 9 raised to another power one time: 3^m3^m3^m = 9^n   What I did was test 3 raised to the power of 2 like this:   3^2*3^2*3^2 = 9*9*9 = 9^3. This means that m=2 and n=3. So, m/n=2.2
Answer: E
The value of Underrot 17pi/6 + Underrot 1 is most nearly equal to which of the following integers? (Please refer to the picture below for the exact version of the question) Choices
A) 10  B) 12  C) 8  D) 3  E) 21

Solution: Under root (17pi/6) ~ 9   Under root (1) = 1   Hence, 9+1 = 10 is the approx answer. 10 is the correct answer.
Answer: A
A group of 15 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If n of the people decide not to participate at the last minute, by how many dollars will each remaining person's share of the total cost increase?  Choose one.
A) (D) nE / [15(15-n)]	B) (12 - n)/E	C) E/[12(12-n)]	D) (A) E/(12 - n)	E) (12-n)E/(12n)

Solution: total cost =E   no of people willing to participate initially =15   initial cost for each =E/15   when n people decided not to participate   Cost for each =E/15-n   (D) nE / [15(15-n)]
Answer: A
Two tains of equal lengths take 10 seconds and 16 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?	Select the correct option.
A) 12	B) 14	C) 16	D) 12.3	E) 18

Solution: Sol.   Speed of the first train = [120 / 10] m/sec = 12 m/sec.   Speed of the second train = [120 / 16] m/sec = 7.5 m/sec.   Relative speed = (12 + 7.5) = m/sec = 19.5 m/sec.   ∴ Required time = (120 + 120) / 19.5 secc = 12.3 sec.   Answer 12.3
Answer: D
The price of a cycle is reduced by 25 % The new price is reduced by a further 20 %. The 2 reductions together are equal to a single reduction of
Answers.
A) 25%  B) 38%  C) 40%  D) 52%  E) 28%

Solution: Let the original price of the cycle be 100. After the first reduction the price will be 75.   This new price is then reduced by 20% = 0.8 x 75 = 60   60 represents a reduction of 40 percent on the original.   40%
Answer: C
A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at? Choose the correct choice from the following answers
A) 12 minutes	B) 17 min	C) 19 min	D) 11 min	E) 16 min

Solution: Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.   Relative speed of A and B   = 6 - 1= 
6 - 1 = 5
5 rounds per hour.   Time taken to complete one round at this speed= 1/5 hr   = 12 min.   12 minutesnswer: 12 minutes
Answer: A
A palindrome is a number that reads the same forward and backward, such as 171. How many even, 6-digit numbers are palindromes?
Choose one:
A) 405
B) 450
C) 400
D) 900
E) 2500

Solution: First recognize you only need to consider the first three digits (because the second three are just the first three flipped)   There are 900 possibilities for the first three digits of a 6 digit number, 100-999 inclusive. Everything starting with a 2,4,6,8 will be even, which is 4/9ths of the combinations.   4/9*900= 
4/9*900 = 400
400   ANSWER:400
Answer: C
Two trains one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is
Choose the correct answer.
A) 2 : 3
B) 4 : 3
C) 6 : 7
D) 9 : 16
E) None

Solution: Sol.   Let us name the trains as A and B. Then,   (A's speed) : (B's speed) = √b : √a   = √16 : √9   = 4 : 3.   Answer 4 : 3
Answer: B
Two stations AA and BB are 110 km apart on a straight line. One train starts from AA at 7 am and travel towards BB at 20 km/hr speed. Another train starts from BB at 8 am and travel towards AA at 25 km/hr speed. At what time will they meet? Choose the correct choice from the following
A) 9 am B) 10 am C) 11 am D) 12 am E) None of these

Solution: In 1 hour (7 am to 8 am) train from station A travels 20 km distance and reaches to C, (say).   A ----------------- C ---------------10 am   7 am --------------------------------- 8 am   AC = 20 km, C10 am = 90 km   Distance travelled in 1 hour = 20 km   Remaining distance =110âˆ’20 = 90 km   Time=Distance/Speed   90/20+25=2 hours   So, time = 8 am + 2 am = 10 am   Answer : 10 am
Answer: B
Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for his new house. Each TV costs $200 more than the size below it. Alan spends a total of $3,600. How much would he have spent if he had bought only the 28 inch and 30 inch TVs?	Choose the correct choice:
A) 850 B) 1,100 C) 1,800 D) 2,550 E) 3,400

Solution: Assume the cost of the least sized (26 Inch) TV = x   1,800ost of 28 inches TV = x + 200   1,800ost of 30 inches TV = x + 400   1,800ost of 32 inches TV = x + 600   Total cost = 4x + 1200 = 3600   Therefore x = 2400/4= 
2400/4 = 600
600   Price of 28inch + 30 inch= 800 + 1000= 
800 + 1000 = 1_800
1800   Option 1,800
Answer: C
The seating chart of an airplane shows 30 rows of seats. Each row has 3 seats on each side of the center aisle, and one of the seats on each side is a window saet. The view from the window seats in 10 of the rows is obscured by the wings of the airplane. If the first person to be assigned a seat is assigned a window seat and thw window seat is assigned randomly, what is the probability that the person will get a seat with an unobscured view?  Choose the correct choice from the following
A) 1/6	B) 1/3	C) 2/3	D) 5/6	E) 17/18

Solution: priyalr   6 seats per row, think of a boeing 737. We have 30 rows, therefore window 30 seats one one side and 30 window seats on the other, totaling 60 window seats on the whole plane.   the view of the window of 10 rows is blocked. two wings, therefore 20 window seats are blocked.   Total window seats = 60   Total blocked window seats = 20   Total unblocked seats = 40   We know that a window seat was given, therefore probability for not window seat is 40/60 =2/3   ANS 2/3
Answer: C
what is the smallest integer that is multiple of 6,7 and 20 Choices
A) 141  B) 180  C) 130  D) 122  E) 420

Solution: Correct Answer :420   It is the lcm of 6,7 and 20 which is 420
Answer: E
The owner of a furniture shop charges his customer 25% more than the cost price. If a customer paid Rs. 1000 for a computer table, then what was the cost price of the computer table?  Choose the correct choice from the following options:
A) 620	B) 400	C) 45	D) 500	E) 800

Solution: CP = SP * (100/(100 + profit%))   = 1000(100/125) = Rs. 800.   Answer: 800
Answer: E
The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas? Choices: A) 81 : 121 B) 9 : 11 C) 729 : 1331 D) 27 : 121 E) None of these

Solution: Ratio of the sides = ³√729 : ³√1331 = 9 : 11   Ratio of surface areas = 92 : 112 = 81 : 121   81 : 121NSWER:81 : 121
Answer: A
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is?
Choose the correct choice from the following options
A) 153600	B) 155600	C) 156600	D) 157000	E) 158000

Solution: Perimeter = Distance covered in 8 min. = 12000	x 8	m = 1600 m.   60   Let length = 3x metres and breadth = 2x metres.   Then, 2(3x + 2x) = 1600 or x = 160.   Length = 480 m and Breadth = 320 m.   Area = (480 x 320) m2 = 153600 m^2.   153600)
Answer: A
The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 216° of the circle, what percentage of MegaTek employees are in manufacturing?	Choose the correct choice from the following choices:
A) 20%  B) 25%  C) 30%  D) 35%  E) 60%

Solution: ANSW60%R: 60%   216° divided by 360° equals 0.6, therefore the sector is equal to 60% of the total
Answer: E
A car traveled 300 meters from point A to point B at a speed of 6 meter per second. Then it took the same route and came back to point A at a speed of 2 meter per second. What is its average speed?
Select the correct option:
A) 2m/s
B) 3m/s
C) 4m/s
D) 5m/s
E) 6m/s

Solution: Since the distance traveled is same, we can apply direct formula= 2XS1XS2/(S1+S2)   2X6X2/8= 3. '3m/s' is the answer.
Answer: B
The U.S. Defense Department has decided that the Pentagon is an obsolete building and that it must be replaced with an upgraded version: the Hexagon. The Secretary of Defense wants a building that is exactly 70 feet high and 200 feet on a side, and that has a hexagonal bull's-eye cutout in the center (somewhat like the current one) that is 25 feet on a side. What will be the volume of the new building in cubic feet?
Select:
A) 3,937,500 cubic feet
B) 15,750 cubic feet
C) 11550√3 cubic feet
D) 7,160,947 cubic feet
E) 3,937,500√3 cubic feet

Solution: Volume of the Hexagon with side 200 and height 70 = Area * height   = 6*(sqrt(3)/4)(200^2)(70)   Volume of the center bull's eye that is similar in shape of a hexagon but side 25   = 6 * (sqrt(3)/4)(25^2)*70   Volume of the building = 6*(sqrt(3)/4)(200^2)(70) - 6 * (sqrt(3)/4)(25^2)*70=7,160,947   Answer is 7,160,947 cubic feet
Answer: D
An outlet pipe empties a tank which is full in 10 hours. If the inlet pipe is kept open, which lets water in at the rate of 16 litres/min then outlet pipe would take 8 hours longer. Find the capacity of the tank.	Choose the correct choice from the following choices
A) 8600 litres	B) 200 litres	C) 21600 litres	D) 11200 litres	E) 13200 litres

Solution: Let the rate of outlet pipe be x liters/hour;   Rate of inlet pipe is 16 litres/min, or  16*60= 
 16*60 = 960
960 liters/hour;   Net outflow rate when both pipes operate would be x-960 liters/hour.   Capacity of the tank= x*10 hours = (x-960)*(10+8) hours   10x=(x-960)*18 --> x=2160 --> capacity = 10x = 21600 liters.   Answer: 21600 litres.
Answer: C
In a question on division with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. The correct quotient is? Choose one
A) 15
B) 18
C) 20
D) 25
E) 26

Solution: Number = (35 * 12)= 
(35 * 12) = 420
420   20orrect quotient= 420/21= 
420/21 = 20
20   20)
Answer: C
Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, Annie is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week Annie worked a total of 56 hours. If Harry and Annie were paid the same amount last week, how many hours did Harry work last week? Choices
A) 52	B) 54	C) 56	D) 58	E) 60

Solution: Annie earned 40x + 16(2x) = 72x   Let H be the number of hours that Harry worked.   Harry earned 30x + 1.5x(H-30) = 72x   (1.5x)(H) = 87x   H = 58 hours   The answer is 58.
Answer: D
Two members of a club are to be selected to represent the club at a national meeting. if there are 153 different possible selections of the 2 members, how many members does the club have?
Choose the correct choice from the following answers.
A) 20  B) 27  C) 40  D) 18  E) 95

Solution: I have done this problem by substituting numbers   We have n!/2!(n-2)! =153   or n(n-1)/2 = 153 or n^2 -n =306 or (n-18) (n+17)=0   n=18 satisfies the equation   18
Answer: D
Working at constant rate, pump X pumped out half of the water in a flooded basement in 3 hours. The pump Y was started and the two pumps, working independently at their respective constant rates, pumped out rest of the water in 3 hours. How many hours would it have taken pump Y , operating alone at its own constant rate, to pump out all of the water that was pumped out of the basement?  Pick:
A) a. 20
B) b. 12
C) c. 14
D) d. 18
E) e. 24

Solution: rate of x=1/8   rate of x+y=1/6   rate of y=1/6-1/8=1/24   20 hours   a. 20
Answer: A
An article was sold after a discount of 20% and there was a gain of 20%. If the profit made on it was Rs. 6 less than the discount offered on it, find its selling price?
Pick:  A) 72  B) 88  C) 266  D) 16  E) 19

Solution: Let CP = Rs. 100x   SP = Rs. 120x   MP = 120x/80 * 100 = Rs. 150x   D = Rs. 150x - Rs. 120x = Rs. 30x   D - P = 30x - 20x = Rs. 6, 10x = Rs. 6   120x = 120/10 * 6 = Rs. 72   72nswer: 72
Answer: A
If a copier makes 6 copies every 3 seconds, then continues at this rate, how many minutes will it take to make 6,000 copies? Select: A) 55 B) 60 C) 50 D) 65 E) 70

Solution: 6 copies 3 seconds   6000 copies = (6000*3)/6= 
(6000*3)/6 = 3_000
3000/60= 
3000/60 = 50
50 minutes   Answer : 50
Answer: C
Firm A's revenues are described by the equation Ra = 17.12x and its costs by Ca = 12.87x + 2400.
Firm B's revenues are described by the equation Rb = 13.27x and its costs by Cb = 8.77x + 1500.
(x denotes the quantity of sales).
If A's volume of sales increases from 1000 to 2000 over the same period that B's volume increases from 2000 to 3000, the percent increase in profits for the firm with the biggest dollar increase in profits is  Choose one:
A) 20%  B) 30%  C) 60%  D) 50%  E) 33%

Solution: Because you need the % increase in profit.   The increase in profit = 4.5 * 1000 (increase in the units from 2000 to 3000)   The original profit = 4.5*2000 - 1500 (initially 2000 units were sold)   % increase = (4.5 * 1000)/(4.5*2000 - 1500) * 100= 
(4.5 * 1000)/(4.5*2000 - 1500) * 100 = 60
60%   ANSWER:60%
Answer: C
A man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways is
Choose the correct choice.
A) 11 hrs B) 8 hrs 45 min C) 7 hrs 45 min D) 9 hrs 20 min E) 10 hrs 25 min

Solution: Explanation:   Solution 1Given that time taken for riding both ways will be 2 hours lesser than the time needed for waking one way and riding back.   Therefore,   time needed for riding one way = time needed for waking one way - 2 hours   Given that time taken in walking one way and riding back =5 hours 45 min   Hence, the time he would take to walk both ways   =5 hours 45 min + 2 hours   =7 hours 45 min   ANSWER IS 7 hrs 45 min
Answer: C
The average of six numbers is 3.95. The average of two of them is 3.5, while the average of the other two is 3.85. What is the average of the remaining two numbers? Choose the correct choice from the following options
A) 4.5	B) 4.6	C) 4.7	D) 4.8	E) 4.9

Solution: Sum of the remaining two numbers   = (3.95 × 6) – [(3.5 × 2) + (3.85 × 2)]   = 23.70 – (7.0 + 7.7)   = 23.70 – 14.7 = 9.00   ∴ Required average = (9.0⁄2) = 4.5   4.5nswer 4.5
Answer: A
In a certain sequence the term an is given by the formula:
an=an−1+2n−1 for all integer n>1. If a7=49, what is a1?	Choose the most appropriate option.
A) −1	B) 0	C) 1	D) 2	E) 3

Solution: an=an−1+2n−1an=an−1+2n−1....   as we can see that each subsequent term is 2n-1 greater than previous..   so we can straightway find a7a7=(2*1-1)+(2*2-1)+(2*3-1)+(2*4-1)+(2*5-1)+(2*6-1)+(2*7-1)+a1a1=3+5+7+9+11+13+a1a1   a7a7=49=48+a1a1..   or a1a1=1   ans 1
Answer: C
50% of the apartments in a certain building have windows and hardwood floors. 25% of the apartments without windows have hardwood floors. If 40% of the apartments do not have hardwood floors, what percent of the apartments with windows have hardwood floors?  Pick:  A) 10  B) 16 2/3  C) 40  D) 50  E) 83 1/3

Solution: total apartments = 100   with windows and hardwoods = 50   without windows = 50   without windows but having hardwoods = 0.25 *50 = 12.25   12.25 + with windows and hardwoods = 60   with windows and hardwoods = 47.75   % = 47.75 / 50 > 50%   ANSWER:50
Answer: D
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?
Choose the correct choice from the following.
A) 3/43
B) 5/23
C) 6/21
D) 7/21
E) 8/21

Solution: Explanation:   Total number of balls = (8 + 7 + 6)= 
(8 + 7 + 6) = 21
21   Let E= event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.   Therefore, n(E) = 8.   P(E) = 8/21.   8/21)
Answer: E