MU-NLPC/Calc-aqua_rat huggingface dataset:
Find the area of circle whose radius is 35m?  Choose the correct choice from the following answers
A) 2883	B) 1543	C) 7673	D) 3850	E) 1788

Solution: 22/7 * 35 * 35= 
22/7 * 35 * 35 = 3_850
3850   Answer: 3850
Answer: D
Rectangle ABCD is constructed in the coordinate plane parallel to the x- and y-axes. If the x- and y-coordinates of each of the points are integers which satisfy 7 ≤ x ≤ 11 and -5 ≤ y ≤ 5, how many possible ways are there to construct rectangle ABCD?
Choose the correct choice from the following choices
A) 396  B) 1260  C) 550  D) 7920  E) 15840

Solution: As the rectangle is parallel to coordinate axes, the coordinates of the points of the rectangle would be   (X1, Y1), (X2, Y1), (X2, Y2), (X1,Y2)   given that X1, X2 lie between 7 and 11..ie., 5 possible numbers   Possible combinations for X1,X2 would be 5C2 = 10   Similarly, Possible combinations for Y1, Y2 would be 11C2 = 55   Possible ways of constructing rectangle is by selecting any of the combination of X1,X2 and Y1,Y2   = 10 * 55= 
10 * 55 = 550
550   Ans. 550
Answer: C
The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 17, how many more dollars, in terms of x, will it cost per person? Pick
A) x/6	B) x/16	C) x/40	D) 3x/40	E) 3x/80

Solution: Choose x as a multiple of 17, I chose 64:   So for 10 people, that's 6.4 each and for 16 people it's 4 USD each... Pick one of the options that gives you 6.4 - 4 = 2.4... The answer is 3x/40.
Answer: D
Bottle R contains 250 capsules and costs $6.25. Bottle T contains 100 capsules and costs $3.0. What is the difference between the cost per capsule for bottle R and the cost per capsule for bottle T?  Choose the correct choice from the following options
A) $0.25	B) $0.12	C) $0.05	D) $0.003	E) $0.005

Solution: Cost per capsule in R is 6.25/250=0.625/25= 
0.625/25 = 0.025
0.025   Cost per capsule in T is  3.00/100= 
 3.00/100 = 0.03
0.03   The difference is 0.005   The answer is $0.005
Answer: E
On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?  Select:
A) 33 1/3 %
B) 40%
C) 50%
D) 60%
E) 66 2/3%

Solution: Let the total # of passengers be 100.   Now, 20 passengers held round-trip tickets AND cars.   As 60% of the passengers with round-trip tickets did not take their cars then 40% of the passengers with round-trip tickets did take their cars, so # of passengers with round-trip tickets AND cars is 40% of the passengers with round-trip tickets.   If we take # of the passengers with round trip tickets to be xx then we'll have 0.4x=200.4x=20 --> x=50x=50.   Answer: 50%.
Answer: C
If k is a non-negative integer and 18^k is a divisor of 624,938 then 6^k - k^6 =	Pick.
A) 0  B) 1  C) 36  D) 118  E) 420

Solution: 6+2+4+9+3+8= 
6+2+4+9+3+8 = 32
32, so this number is not divisible by 3 and thus not divisible by 18.   Therefore, k=0   6^k - k^6 =1-0= 
1-0 = 1
1   The answer is 1.
Answer: B
20 men do a work in 20days. How many men are needed to finish the work in 4days?  Choices
A) 50	B) 20	C) 30	D) 100	E) 15

Solution: men required to finish the work in 4days = 20*20/4= 
20*20/4 = 100
100   Answer is 100
Answer: D
A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is  Choose the correct choice from the following answers
A) 8/17  B) 7/15  C) 3/15  D) 8/15  E) 1/4

Solution: Person ( A ) ( B ) ( A+B )   Time - ( 15 ) ( 20 ) (-)   Rate - ( 20 ) ( 15 ) ( 35 )   Work -(300) (300) (300)   therefore A+B requires (300/35) days to complete entire work   For 1st 4 days they work  35 * 4= 
 35 * 4 = 140
140   Remaining work is 300 - 140= 
300 - 140 = 160
160   Remaining fraction of work is= 160/300 = 8/15   Answer 8/15
Answer: D
Working alone, Tom finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Tom alone cleans the entire house in 6 hours. How many hours will it take Nick and Tom to clean the entire house if they work together?
Choose the correct choice from the following:
A) 1.5 B) 2 C) 2.4 D) 3 E) 3.6

Solution: Answer is 3.6 hours.   Tom does the complete house in 6 hours while Nick does it in 9 hours. 1/ (1/6+1/9)= 3.6   answer is 3.6
Answer: E
The length of the rectangular field is double its width. Inside the field there is square shaped pond 4m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
Choose the correct answer:
A) 54
B) 32
C) 75
D) 28
E) 16

Solution: A/8 = 4 * 4 => A = 4 * 4 * 8   x * 2x = 4 * 4 * 8   x = 8 => 2x = 16   Answer:16
Answer: E
When a=4+(2/4) and b=4-(2/4), (2^a^2)/(2^b^2)=?	Choices:
A) 260
B) 256
C) 240
D) 210
E) 225

Solution: --> (2^a^2)/(2^b^2) ={(2)^(a^2-b^2)}=2^(a-b)(a+b). Since a-b=4/4 and a+b=8, 2^(a-b)(a+b)=2^(4/4)(8)=2^8=256   Therefore, the answer is 256
Answer: B
Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 41 pages per hour. If Tom starts reading a novel at 3:20, and Jan begins reading an identical copy of the same book at 4:26, at what time will they be reading the same page?  Pick one
A) 6:26
B) 6:56
C) 7:26
D) 7:56
E) 8:26

Solution: Since Tom reads an average of 1 page every 2 minutes, Tom will read 33 pages in the first 66 minutes. Jan can catch Tom at a rate of 11 pages per hour, so it will take 3 hours to catch Tom.   The answer is 7:26.
Answer: C
Jason can row his boat with the stream at 50 km/h and against the stream in 2 km/h. Jason's rate is? Options
A) 18 kmph B) 24 kmph C) 35 kmph D) 15 kmph E) 12 kmph

Solution: DS = 50   US = 2   S = ?   S = (50 - 2)/2= 
(50 - 2)/2 = 24
24 kmph   Answer:24 kmph
Answer: B
A rectangular field is to be fenced on three sides leaving a side of 8 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required?  Choose the correct choice from the following answers:
A) 244ft	B) 88ft	C) 122ft	D) 178ft	E) 66ft

Solution: Given that length and area, so we can find the breadth.   Length x Breadth = Area   8 x Breadth = 680   Breadth = 85 feet   Area to be fenced = 2B + L = 2 (85) + 8 = 178 feet   Answer: 178ft) 178ft
Answer: D
20 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?  Choose the correct choice from the following answers: A) 380 B) 470 C) 560 D) 650 E) 740

Solution: 2*20C2 = 2*190= 
2*190 = 380
380   The answer is 380.
Answer: A
Find the number which when added to itself 13 times, gives 112.  Choose one:  A) 7  B) 8  C) 9  D) 10  E) 11

Solution: Let the number be x. Then, x + 13x = 112 14x = 112 x = 8.   ANSWER:8
Answer: B
Kuber borrowed rs 169 due in 2 years at 4%per annum compound interest.Find the Present worth?	Pick one.
A) 160.15  B) 225  C) 156.25  D) 180.25  E) 150.5

Solution: 156.25ompound interest=[169*(1+(4/100))^2]   =[169*((104/100)^2)]   =(169*((26/25)^2))   =(169*25*25)/(26*26)   =Rs.156.25   Option 156.25
Answer: C
In three annual examinations, of which the aggregate marks of each was 500, a student secured
average marks 45% and 55% in the first and the second yearly examinations respectively. To secure 40% average total marks, it is necessary for him in third yearly examination to secure marks :	Choose the correct choice from the following answers:
A) 100
B) 350
C) 400
D) 450
E) 500

Solution: total marks:1500 for three exams   40% of 1500=600   first exam marks=45% of 500=225   second exam marks=55% of 500=275   let X be the third exam marks   225 + 275 + X =600   X=100   100NSWER:100
Answer: A
The average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth days was 59 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ? Choose the correct choice from the following choices:
A) 62 degrees	B) 32 degrees	C) 65 degrees	D) 66 degrees	E) 67 degrees

Solution: Explanation:   Sum of temperatures on 1st, 2nd, 3rd and 4th days = (58 * 4)= 
(58 * 4) = 232
232 degrees ... (1)   Sum of temperatures on 2nd, 3rd, 4th and 5th days - (59 * 4)= 236 degrees ....(2)   Subtracting (1) From (2), we get :   Temp, on 5th day - Temp on 1st day = 4 degrees.   Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively.   Then, 8x - 7x = 4 or x = 4. Answer: 32 degrees   Temperature on the 5th day = 8x = 32 degrees.
Answer: B
Sixty men can stitch 200 shirts in 30 days working 8 hours a day. In how many days can 45 men stitch 300 shirts working 6 hours a day?  Choose one:
A) 33
B) 88
C) 27
D) 80
E) 12

Solution: We have M1 D1 H1 / W1 = M2 D2 H2 / W2 (Variation rule)   (60 * 30 * 8)/ 200 = (45 * D2 * 6) / 300   D2 = (60 * 30 * 8 * 300) / (200 * 45 * 6) => D2 = 80.   Answer:80
Answer: D
Divide Rs. 800 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?  Choose the correct choice from the following answers.
A) s.800	B) s.200	C) s.600	D) s.500	E) s.900

Solution: A+s.200+C = 800   A = 1/3(s.200+C); s.200 = 2/3(A+C)   A/(s.200+C) = 1/3   A = 1/4 * 800= 
1/4 * 800 = 200
> 200   ANSWER:s.200
Answer: B
In N is a positive integer less than 200, and 10N/60 is an integer, then N has how many different positive prime factors?  Choose the correct option:
A) 2	B) 3	C) 5	D) 6	E) 8

Solution: (A).   10n/60 must be an integer. => 1n/6 must be an integer. Hence n must be a multiple of 2*3.   => n has 2 different prime integers.
Answer: A
On a certain number line, conditions are a<b<c<d<e and ab>0. Which of the following must be true?
I ab>0 II cd>0 III de>0
Choose the correct choice from the following:
A) I&II only
B) II only
C) III only
D) I only
E) II and III only

Solution: Givena<b<c<d<e abcde="" and="">0.   Suppose, for the product to be greater than 0, we can two variables as -ve or four variables can be -ve.   We are given : I ab>0 II cd>0 III de>0   case 1: a and b can be negative/positive and if they are... we get greater than 0.   case 2: we have cd , then c and d both can be negative/positive and if they are... we get greater than 0.   case 2: we have de , then c and d both can be negative/positive and if they are... we get greater than 0.   if cd both negative , then de both have to negative in order to get greater than 0. In order to abcde>0 , cde can't be negative else we get -ve value, then we need to have either a or b as negative then ab can't be greater than 0.   so cde have to be positive.   I only</b<c<d<e>
Answer: D
If A got 80 marks and B got 60 marks, then what percent of A's mark is B's mark?  Pick one:
A) 60%  B) 80%  C) 65%  D) 75%  E) None of these

Solution: A's marks = 80 ; B's marks = 60.   Let x% of A = B => x/100 * 80 = 60   => x = (60 * 100)/80= 
(60 * 100)/80 = 75
75   B's marks is 75% of A's marks.   ANSWER:75%
Answer: D
An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 7 businessmen, how many possible team submissions are possible? Select:
A) 76 B) 130 C) 162 D) 198 E) 202

Solution: We have 3 scenarios here:   1) 1 tech2 businessmen: 4C1 x 7C2 = 84   2) 2 tech1 businessman: 4C2 x 7C1 =42   3) 3 tech0 businessmen: 4C3 = 4   Total:  84+42+4= 
 84+42+4 = 130
130   Answer: 130
Answer: B
2.09 can be expressed in terms of percentage as	Choose the correct choice from the following answers: A) 2.09% B) 20.9% C) 209% D) 0.209% E) None of these

Solution: Explanation:   While calculation in terms of percentage we need to multiply by 100, so   2.09 * 100= 
2.09 * 100 = 209
209   Answer: Option 209%
Answer: C
A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price? Choose the correct choice from the following choices:
A) 256	B) 375	C) 287	D) 255	E) 123

Solution: CP1 = 100 SP1 = 120   CP2 = 80 SP2 = 80 * (125/100)= 
80 * (125/100) = 100
100   20 ----- 100   75 ----- ?=> 375   Answer: 375
Answer: B
If the time is currently 1:30 pm, what time will it be in exactly 642 hours?
Choose the correct choice from the following answers
A) 3:30 am
B) 4:30 am
C) 5:30 am
D) 6:30 am
E) 7:30 am

Solution: 642 = 26(24) + 18/24   The time will be 18 hours later than 1:30 pm which is 7:30 am.   The answer is 7:30 am.
Answer: E
Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/4 of capacity in 9 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity? Pick one:
A) 3.25
B) 3.6
C) 4.2
D) 4.4
E) 7.2

Solution: Time taken by First tank Fill 1/4 the tank = 9 hours   i.e. Time taken by First tank to Fill 1 complete the tank = 36 hours   Time taken by Second tank Fill 2/3 the tank = 6 hours   i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6= 
(3/2)*6 = 9
9 hours   in 1 Hour, Both tanks together Fill the tank= (1/36)+(1/9) = 5/36 tank   i.e. Time taken by Both tank to Fill 1 complete the tank = 36/5= 
36/5 = 36/5 = around 7.2
7.2 hours   Answer: option 7.2
Answer: E
If the function f(x) is defined for all real numbers x as the maximum value of 2x + 4 and 12 + 4x, then for which one of the following values of x will f(x) actually equal 2x + 4 ?  Choose the correct choice from the following choices
A) –3
B) –5
C) –6
D) –7
E) –9

Solution: Since f(x) defines maximum of 2x + 4 and 12 + 4x,   to find those x when 2x+4 has greater value,   2x + 4 > 12 + 4x   or x < -4   Only value that satisfy this is -5.   Answer is (–5),
Answer: B
A truck driver drove for 2 days. On the second day, he drove 3 hours longer and at an average speed of 15 miles per hour faster than he drove on the first day. If he drove a total of 1,020 miles and spent 22 hours driving during the 2 days, what was his average speed on the first day, in miles per hour?	Choose the correct answer:
A) 25.0 B) 30.6 C) 37.8 D) 40.2 E) 45.1

Solution: Day 1   2t+3=22   t=9.5   Day 2   t+3   9.5+3= 
9.5+3 = 12.5
12.5   9.5r+12.5(r+15)=1020   r=37.8   Answer:37.8
Answer: C
The speeds of three asteroids were compared. Asteroids X-13 and Y-14 were observed for identical durations, while asteroid Z-15 was observed for 2 seconds longer. During its period of observation, asteroid Y-14 traveled three times the distance X-13 traveled, and therefore Y-14 was found to be faster than X-13 by 6000 kilometers per second. Asteroid Z-15 had an identical speed as that of X-13, but because Z-15 was observed for a longer period, it traveled five times the distance X-13 traveled during X-13's inspection. Asteroid X-13 traveled how many kilometers during its observation?	Choose the most appropriate option:
A) 500  B) 1,600/3  C) 1,000  D) 1,500  E) 2,500

Solution: X13: (t, d, s)   Y14: (t, 3d, s+6000mi/hour)   Z15: (t+2 seconds, s, 5d)   d=?   Distance = Speed*Time   x13: d = s*t   x14: 3d = (s+6000)*t ===> 3d = ts+6000t   z15: 5d = s*(t+2t) ===> 5d = st+2st ===> 5d - 2st = st   3d 5  - 2= 
5  - 2 = 3
st   3d= 5d - 2st + 6000t   -2d = -2st + 6000t   2d = 2st - 6000t   d = st - 3000t   x13: d = s*t   st - 3000t = s*t   s - 3000 = s   -1500 = s   I got to this point and couldn't go any further. This seems like a problem where I can set up individual d=r*t formulas and solve but it appears that's not the case. For future reference how would I know not to waste my time setting up this problem in the aforementioned way? Thanks!!!   The distance of Z15 is equal to five times the distance of X13 (we established that x13 is the baseline and thus, it's measurements are d, s, t)   S(T+2) = 5(S*T)What clues would I have to know to set up the equation in this fashion? Is it because I am better off setting two identical distances together?   ST+2S = 5ST   T+2 = 5T   2=4T   t= 1/2   We are looking for distance (d=s*t) so we need to solve for speed now that we have time.   Speed y14 - speed x13   Speed = d/t   3d/t - d/t = 6000 (remember, t is the same because both asteroids were observed for the same amount of time)   2d = 6000   2 = 3000   d=s*t   d=3000*(1/2)= 
3000*(1/2) = 1_500
1500   ANSWER:1,500
Answer: D
A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.400, find the original price per kg?	Choose the most appropriate option:
A) s.7	B) s.9	C) s.10	D) s.11	E) s.19

Solution: 100*(20/100)= 
100*(20/100) = 20
20 --- 10   ? --- 1=> Rs.2   400 --- 80   ? --- 2 => Rs.10   Answer:s.10
Answer: C
The true discount on a bill of Rs. 2560 is Rs. 360. What is the banker's discount?  Answers:  A) Rs. 432  B) Rs. 422  C) Rs. 419  D) Rs. 442  E) None of these

Solution: Explanation :   F = Rs. 2560   TD = Rs. 360   PW = F - TD = 2560 - 360 = Rs. 2200   True Discount is the Simple Interest on the present value for unexpired time   =>Simple Interest on Rs. 2200 for unexpired time = Rs. 360   Banker's Discount is the Simple Interest on the face value of the bill for unexpired time   = Simple Interest on Rs. 2160 for unexpired time   =360/2200 × 2560 = 0.16 × 2560 = Rs. 419 Answer : Option Rs. 419
Answer: C
Statements: Population increase coupled with depleting resources is going to be the scenario of many developing countries in days to come. Conclusions: 1) The population of developing countries will not continue to increase in future. 2) It will be very difficult for the governments of developing countries to provide its people decent quality of life.  Choose the correct choice from the following choices:
A) Only conclusion I follows
B) Only conclusion II follows
C) Either I or II follows
D) Neither I nor II follows
E) Both I and II follow

Solution: The fact given in I is quite contrary to the given statement. So, I does not follow. II mentions the direct implications of the state discussed in the statement. Thus, II follows.   Only conclusion II follows
Answer: B
Which number need to add to 172835 to get a number exactly divisible by 136?
Choose the correct choice from the following choices
A) 27  B) 25  C) 26  D) 21  E) 24

Solution: 172835 / 136 = 1270 and reminder = 115.   136-115= 
136-115 = 21
21   So, the next number divisible by 115 is 21 places in front of 172835   Which means 21 + 172835= 
21 + 172835 = 172_856
172856   21 should be added to 172835   21
Answer: D
The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?  Choose one:
A) 17 kmph
B) 40 kmph
C) 16 kmph
D) 18 kmph
E) 20 kmph

Solution: Speed downstream   = 60 + 20= 
60 + 20 = 80
80 kmph   Speed upstream= 60 - 20= 
60 - 20 = 40
40 kmph   Answer:40 kmph
Answer: B
The market value of a certain machine decreased by 30 percent of its purchase price each year. If the machine was purchased in 1982 for its market value of $10,000, what was its market value two years later?	Choose the correct choice from the following choices:
A) $8,000
B) $4,000
C) $3,200
D) $2,400
E) $800

Solution: B.   Market value in 1982= $ 10000   Market value in 1983 = $ 10000- ($ 10000 x 30/100) = 10000-3000= 
10000-3000 = 7_000
$ 7000   Market value in 1984= Market value in 1983 - (30 % of $10000)= 7000-3000= 
7000-3000 = 4_000
$4000
Answer: B
Ayesha's father was 40 years of age when she was born while her mother was 32 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? Choose the most appropriate option:
A) 12 years
B) 14 years
C) 16 years
D) 7 years
E) 6 years

Solution: Explanation:   Mother's age when Ayesha's brother was born = 32 years.   Father's age when Ayesha's brother was born = (40 + 4)= 
(40 + 4) = 44
44 years.   Required difference= (44 - 32)= 
(44 - 32) = 12
12 years.   12 yearsnswer: Option 12 years
Answer: A
12 men take 18 days to complete a job whereas 12 women in 18 days can complete 5/6 of the same job. How many days will 10 men and 8 women together take to complete the same job?  Choose the correct choice from the following answers
A) 6 B) 13 1â„2 C) 13 D) Data inadequate E) None of these

Solution: 12 M Ã— 18 = 12 W Ã— 18 Ã— 6/5   \ w = 5/6 M   10M + 8W = 10M + 8 Ã— 5/6M = 16 2/3 M   \16 2/3men can complete the same work   in 12Ã—18/16 2/3=13 days   Answer 13
Answer: C
Rectangular tile each of size 25cm by 65cm must be laid horizontally on a rectangular floor of size 150cm by 390cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:  Choose the correct choice from the following answers.
A) 50
B) 40
C) 25
D) 36
E) 45

Solution: Area of tile = 25*65= 
25*65 = 1_625
1625   Area of floor= 150*390= 
150*390 = 58_500
58500   No of tiles= 58500/1625= 
58500/1625 = 36
36   So, the no of tile= 36   ANSWER:36
Answer: D
A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:  Choose the correct choice from the following answers:
A) 250	B) 276	C) 280	D) 285	E) None

Solution: Since the month begins with sunday,to there will be five sundays in the month   Average required = (510x5 + 240x25 /30) = 8550/30= 
8550/30 = 285
285   Answer: Option 285
Answer: D
Find a sum for 1st 6 prime number's?  Choose one
A) 41 B) 28 C) 30 D) 34 E) 36

Solution: Required sum = (2 + 3 + 5 + 7 + 11 + 13)= 
(2 + 3 + 5 + 7 + 11 + 13) = 41
41   Note: 1 is not a prime number   Option 41
Answer: A
The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8500. If his salary for the month of May is Rs.6500, find his salary for the month of January?
Choose one:
A) 4500 B) 5000 C) 6000 D) 6500 E) 7000

Solution: Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000= 
4 * 8000 = 32_000
32000 ----(1)   Sum of the salaries of the person for the months of February, March, April and May= 4 * 8500= 
4 * 8500 = 34_000
34000 ----(2)   (2)-(1) i.e. May - Jan= 2000   Salary of May is Rs.6500   Salary of January = Rs.4500   4500NSWER 4500
Answer: A
The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ?
Choices
A) 170  B) 185  C) 190  D) 196  E) 200

Solution: 185   Answer is 185
Answer: B
Set S consists of integers {6, 7, 10, 12, 15}. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 40%. What is the value of integer n? Choose the correct choice from the following answers:
A) 26  B) 30  C) 34  D) 38  E) 42

Solution: The average of the numbers in set S is 10.   If we increase the mean by 40%, the new mean is 14.   Thus, on average, 5 numbers increase by 4.   Therefore n = 14+20= 
14+20 = 34
34   The answer is 34.
Answer: C
A local bank that has 9 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 9 codes? Choose the most appropriate option:	A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Pick any two integer.   Integers: 12   Code: 11, 12, 21, 22 = 4 Codes   Add one more integer: 3   13, 31, 33, 23, 32 = 5 Codes   Total = 9 Codes. Enough. 3nswer: 3
Answer: A
The area of square ABCD above is 12. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region?
Choose the correct choice from the following answers:
A) 18−9∗π
B) 12−3∗π
C) 9+9/4∗π
D) 9+9/2∗π
E) 9/2−9/4∗π

Solution: =Square - Quarter circle   =12- pi*12/4   =12- pi*3   ANSWER:12−3∗π
Answer: B