MU-NLPC/Calc-aqua_rat huggingface dataset:
If 100!/x is not an integer, which of the following could be the value of x?
Choose the correct choice from the following choices
A) 5^24	B) 7^16	C) 11^9	D) 13^6	E) 17^6

Solution: he answer will be a number which doesn't completely divide 100!   No of 5's in 100! = 24   No of 7's in 100! = 16   No of 11's in 100! = 9   No of 13's in 100! = 7   No of 17's in 100! = 5   There are 5 seventeens in 100! , however we are dividing by 17^6 , so this can not divide 100!   Hence our answer will be 17^6
Answer: E
P is two years older than Q who is twice as old as R. The total of the ages of P, Q and R is 25. How old is Q?  Choices:
A) 7.2 years  B) 8.2 years  C) 9.8 years  D) 9.2 years  E) 9.4 years

Solution: Let age of R =x. Then,   Age of Q =2x   Age of P =2+2x   Total age of P,Q and R =25   ⇒(2+2x)+2x+x=25   ⇒5x=23   ⇒x=23/5= 
23/5 = 23/5 = around 4.6
4.6 years   B's age=2x=2×4.6=9.2 years   ANSWER:9.2 years
Answer: D
A man can row with a speed of 20 kmph in still water. If the stream flows at 7 kmph, then the speed in downstream is?	Choose the correct option
A) 27 B) 23 C) 20 D) 27 E) 12

Solution: M = 20   S = 7   27S = 20 + 7= 
20 + 7 = 27
27   Answer: 27
Answer: D
A theater box office sold an average (arithmetic mean) of 65 tickets per staff member to a particular movie. Among the daytime staff, the average number sold per member was 75, and among the evening staff, the average number sold was 60. If there are no other employees, what was the ratio of the number of daytime staff members to the number of evening staff members?  Options:
A) 1:2
B) 1:4
C) 5:11
D) 1:3
E) 13:15

Solution: Deviation from the mean for the daytime staff = 75 - 65= 
75 - 65 = 10
10.   Deviation from the mean for the evening staff= 65 - 60= 
65 - 60 = 5
5.   Thus, the ratio of the number of daytime staff members to the number of evening staff members is 5:10= 1:2.   The answer is 1:2.
Answer: A
Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Four years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?	Options.
A) A)24  B) B)89  C) C)67  D) D)32  E) E)45

Solution: Let the present ages of Sameer and Anand be 5x years and 4x years respectively.   Then,	(5x + 4/4x + 4)=11/9   9(5x + 4) = 11(4x + 4)   45x + 36 = 44x + 44   45x - 44x = 44 - 36= 
44 - 36 = 8
8.   Anand's present age= 4x = 32 years.   Answer:32
Answer: D
If a man can cover 18 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?	Pick one.
A) 288  B) 162  C) 878  D) 168  E) 243

Solution: 18 m/s = 12 * 18/5 kmph   3 hours 45 minutes = 3 3/4 hours = 15/4 hours   Distance = speed * time = 18 * 18/5 * 15/4= 
18 * 18/5 * 15/4 = 243
243 km.   Answer: 243
Answer: E
How many meaningful English words can be formed with the letters ESRO using each letter only once in each word?
Choose the correct choice from the following answers:
A) 1	B) 3	C) 4	D) 8	E) 9

Solution: Explanation:   Meaningful words are ROSE, SORE and EROS.   Note the meaning of the words SORE and EROS with the help of dictionary.   Answer: 3) Three
Answer: B
If S is the product of all positive integers less than 31, than what is the greatest integer k for which S/18^k is an integer?	Choose the correct choice from the following answers:	A) 3	B) 6	C) 7	D) 14	E) 26

Solution: 30! S must be divisible by (3*3*2)^k.   As I will find a lot of 2's among 30!'s factors I will focus on the 3's (that also occurs twice instead of only once as a factor in 18).   Every multiple of 3 will provide me with atleast one factor of 3. There aren't that many so I list them quickly.   3 6 9*   12 15 18*   21 24 27**   30   The stars are marked as they are multiples of 9* or 27** and thus provides two or three 3's respectively.   3=3 (occurs 10 times) +10   3*3= 
3*3 = 9
9 (occurs 3 times) +3(adding just one additional three each as they were not counted for in the multiples of 3)   3*3*3= 
3*3*3 = 27
27 (occurs 1 time) +1 (again, adding just one as they were previously not counted)   Total: 14.   For every k we add two 3's. So we must divide 14 by 2 to get the highest integer K before we receive a non-integer result.   Answer: 7 -> Answer choice: 7.
Answer: C
What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?	Select the correct option:  A) 3: 8  B) 3: 6  C) 3: 7  D) 3: 1  E) 3: 3

Solution: d = 3d d = d   a√2 = 3d a√2 = d   a = 3d/√2 a = d/√2 => 3: 1   Answer:3: 1
Answer: D
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
Choose one
A) 22
B) 72
C) 37
D) 16
E) 88

Solution: Explanation:   L.C.M. of 2, 4, 6, 8, 10, 12 is 120.   So, the bells will toll together after every 120 seconds(2 minutes).   In 30 minutes,they will together  (30/2)+1= 
 (30/2)+1 = 16
16 times   Answer: 16) 16
Answer: D
A train of length 150 metres takes 40.5 seconds to cross a tunnel of length 300 metres. What is the speed of the train in km/hr ?
Choose the correct choice from the following choices.
A) 13.33
B) 26.67
C) 40
D) 66.67
E) 50

Solution: Explanation:   Speed = 150+300/40.5m/sec   =450/40.5=18/5km/hr = 40 km/hr.   ANSWER IS 40
Answer: C
The ratio of the number of boys and girls in a college is 7:8.If the percentage increase in the number of boys and girls be 20% and 10% respectively.What will be the new ratio?	Choose the correct option:	A) 22:21	B) 19:22	C) 23:22	D) 22:19	E) 21:22

Solution: Let the number of boys and girls in the college be 7x and 8x respectively.   Their increased number=(120% of 7x) and (110% of 8x)   ==[(120/100)*7x] and [(110/100)*8x]   =(42x/5) and (44x/5)   The required ratio =(42x/5):(44x/5)   =21:22   Answer is option 21:22
Answer: E
Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 3. The numbers are
Choose the correct choice from the following answers:
A) 12, 24, 30	B) 12, 24, 38	C) 12, 24, 362	D) 3, 6, 9	E) 12, 24, 321

Solution: Explanation:   Let the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 3   \inline \fn_jvn \therefore The numbers are 3, 6, 9   Answer: 3, 6, 9) 3, 6, 9
Answer: D
A miniature roulette wheel is divided into 10 equal sectors, each bearing a distinct integer from 1 to 10, inclusive. Each time the wheel is spun, a ball randomly determines the winning sector by settling in that sector. If the wheel is spun two times, approximately what is the probability that the product of the two winning sectors’ integers will be even?
Choose the correct choice from the following answers:  A) 88%  B) 75%  C) 67%  D) 63%  E) 50%

Solution: The only way to have an odd product is if both integers are odd.   P(odd product) = 1/2*1/2 = 1/4   P(even product) = 1 - 1/4 = 3/4 = 75%   The answer is 75%.
Answer: B
What is the lowest positive integer that is divisible by each of the integers 1 through 8, inclusive?  Choose the correct choice from the following
A) 420 B) 560 C) 840 D) 960 E) 1080

Solution: The integers are 1 , 2 , 3 , 4 , 5 , 6 , 7 and 8   Lowest positive integer that is is divisible by each of the integers 1 through 8   = 2^3 * 3 * 5 * 7   =8*3 *5 *7   =24 * 35= 
24 * 35 = 840
840   Answer 840
Answer: C
How many different subsets of the set {0, 1, 2, 3, 4, 5,6,} do not contain 0?	Choose the correct answer
A) A.66	B) B.57	C) C.31	D) D.32	E) E.58

Solution: Number of subset   Since we have 6 digits other than 0, we can take any numbers from the set of 6 to make a subset. Also it is a matter of selection and not arrangement.So we will consider combinations.   6c1+6c2+6c3+6c4+6c5+6c6=57   And one set is the NULL set having no elements in it so    57+1= 
 57+1 = 58
58.   ANSWE.58R E.58.
Answer: E
There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one liter every hour in A, it gets filled up like 10, 20, 40, 80, 160 in tank B. (At the end of first hour, B has 10 liters, second hour it has 20, third hour it has 40 and so on). If tank B is 1/32 filled after 21 hours, what is the total duration required to fill it completely?	Select the correct option.
A) 22  B) 28  C) 269  D) 26  E) 82

Solution: The data related to the first tank A is not necessary. As you can see, the capacity that gets filled in the tank B after each hour is doubled. So If the tank is 1/32nd part is full after 21 hours, it is 1/16th part full after 22 hours, 1/8th part full after 23 hours, 1/4th part full after 24 hours, 1/2 full after 25 hours, completely full after 26 hours.   Answer:26
Answer: D
Find the sum of first 30 natural numbers
Choose the correct choice from the following choices.
A) 470	B) 468	C) 465	D) 463	E) 487

Solution: Explanation:   Sum of n natural numbers   =n(n+1) / 2   =30(30+1) / 2=30(31) / 2=465   Option 465
Answer: C
A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?	Pick one.
A) 298  B) 608  C) 279  D) 280  E) 269

Solution: 80* 7: x* 3 = 1:1 1/2   560: 3x = 2: 3   x = 280   Answer:280
Answer: D
If K is the sum of reciprocals of the consecutive integers from 53 to 58, inclusive, then K is closest in value to which of the following?  Choose the correct choice from the following options.
A) 1/12	B) 1/10	C) 1/8	D) 1/6	E) 1/10

Solution: 1/53 , 1/54 , 1/55 , 1/56 , 1/57 , 1/58   Hypothetically , assume all 6 Numbers to be 1/53   Hence sum of it would result in = 6/53 ( almost equals 1/7 , or slightly less than 1/7 - )   If all 6 nos were to be 1/58 ... Sum of which would result in 6/58 = 1/10 .   Hence answer should lie between 1/7 and 1/10   1/10 i.e 1/10
Answer: E
John takes a trip and drives 9 hours from Town X to Town Z at a rate of 60 miles per hour. On his way back, John drives 85 miles per hour and stops in Town Y which is midway between Town X and Town Z. How many hours does it take Scott to drive from Town Z to Town Y?
Choose the most appropriate option
A) 1.75 B) 1.25 C) 1.45 D) 4.15 E) 3.14

Solution: distance from X to Z =9 hr* 60 mph= 540 miles   hence distance from Y to Z= 1/2*540= 
1/2*540 = 270
270   time=270/85=4.15 hrs   IMO: 4.15
Answer: D
A company has 100 employees, 40% of whom are employed part time. If it hires 25 new employees, 40% of whom are employed part time, what will be the percent increase in part time employees?	Choose the correct answer:
A) 1 2/3 %	B) 2 2/3 %	C) 4 %	D) 25 %	E) 9 %

Solution: Total employee = 100   Part time Empl = 40   New part time empl = 25 * (40/100)= 
25 * (40/100) = 10
10   Total new part time Emp= 10+40= 
10+40 = 50
50   Old part time Emp= 40   % increase = (new - old)*100/old   =10*100/40= 
10*100/40 = 25
25%   Ans-25 %
Answer: D
In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively. The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports. If the number of boys participating in the sports is 15, then how many girls are there in the class ? Choices:
A) 22
B) 32
C) 30
D) 28
E) 11

Solution: Let the number of boys and girls participating in sports be 3x and 2x respectively.   Then, 3x = 15 or x = 5.   So, number of girls participating in sports = 2x = 10.   Number of students not participating in sports = 60 - (15 + 10)= 
60 - (15 + 10) = 35
35.   Let number of boys not participating in sports be y.   Then, number of girls not participating in sports= (35 -y).   Therefore (35 - y) = y + 5 2y 30 y = 15.   So, number of girls not participating in sports = (35 - 15)= 
(35 - 15) = 20
20.   Hence, total number of girls in the class= (10 + 20)= 
(10 + 20) = 30
30.   Answer:30
Answer: C
To furnish a room in a model home an interior decorator is to select 4 chairs and 4 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 75 different combinations are possible, how many tables are there in the warehouse? Answers
A) A)6 B) B)8 C) C)10 D) D)15 E) E)30

Solution: Total number of ways to choose 4 chairs from 5= 5C4=5   Total number of combination=75   That means we need get 15 combinations from the selection of tables....   Screening through the answers.... 6C4=15..... 15*5=75   Answer is 6... 6
Answer: A
A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?	Pick one:
A) 66 km/hr
B) 72 km/hr
C) 78 km/hr
D) 81 km/hr
E) 85 km/hr

Solution: Explanation:   4.5 km/hr =(4.5 x	5/18)m/sec =	5/4m/sec = 1.25 m/sec, and   5.4 km/hr =(5.4 x5/18)m/sec =3/2m/sec = 1.5 m/sec.   Let the speed of the train be x m/sec.   Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5   => 8.4x - 10.5 = 8.5x - 12.75   => 0.1x = 2.25   => x = 22.5   Speed of the train =(22.5 x	18/5)km/hr = 81 km/hr.   ANSWER IS 81 km/hr
Answer: D
160 is what percent of 50 ? Options:
A) 5% B) 20% C) 320% D) 200% E) 500%

Solution: 50*x=160 --> x=3.2 --> 3.2 expressed as percent is 320%.   Answer: 320%.
Answer: C
What will come in place of the x in the following Number series? 46080, 3840, ?, 48, 8, 2, 1
Choose the correct option:
A) 1	B) 384	C) 5	D) 7	E) 9

Solution: 46080 /12= 
46080 /12 = 3_840
3840   3840 /10= 
3840 /10 = 384
384   384 /8= 
384 /8 = 48
48   48 /6= 
48 /6 = 8
8   8/4= 
8/4 = 2
2   2 /2= 
2 /2 = 1
1   384
Answer: B
The length of a rectangle is reduced by 20%. By what % would the width have to be increased to maintainthe original area?  Select the correct option
A) 10%  B) 20%  C) 25%  D) 30%  E) 45%

Solution: Sol. Required change = (20*100)/(100-20)= 
(20*100)/(100-20) = 25
25%   25%
Answer: C
Find the average of first 20 natural numbers?  Select.
A) 5.5	B) 7.2	C) 10.5	D) 12.3	E) 15.5

Solution: Sum of first n natural numbers = n(n+1)/2   sum of first 20 natural numbers = 20*21/2= 
20*21/2 = 210
210   average= 210/20= 
210/20 = 21/2 = around 10.5
10.5   Answer is 10.5
Answer: C
The inverse ratio of 4: 2: 1 is?	Answers:  A) 2:4:8  B) 2:3:9  C) 2:3:2  D) 2:3:6  E) 2:3:1

Solution: 1/4: 1/2: 1/1 = 2:4:8   2:4:8nswer:2:4:8
Answer: A
If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
Choose the correct choice from the following answers
A) 3
B) 8
C) 9
D) 6
E) 4

Solution: 96% ---- 12   144% ---- ?     96/144 * 12= 
  96/144 * 12 = 8
8   Answer: 8
Answer: B
A password of a computer used two digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?	Options:
A) 1/32  B) 1/16  C) 1/8  D) 2/5  E) 1/4

Solution: We have two digits can be used for password -0,2,3,5,7.   Assuming that the numbers can be repeated any number of times in the password, probability of selecting any one of them is 5/10 (out of 10 digits from 0-9)   So, 5/10 * 5/10=1/4(1/4)
Answer: E
Three times the first of three consecutive odd integers is 8 more than twice the third. The third integer is:	Choose one:
A) 9
B) 11
C) 13
D) 15
E) 20

Solution: Let the three integers be x, x + 2 and x+ 4.   Then,   3x = 2(x + 4) + 8   x = 16   Third integer = x + 4 = 20.   ANSW20R:20
Answer: E
NHAI employs 100 men to build a highway of 2km in 50 days working 8 hours a day. If in 25 days they completed 1/3 part of work .than how many more employees should NHAI hire to finish it in time working 10 hours a day?
Choose the correct choice from the following options
A) 22
B) 60
C) 28
D) 11
E) 218

Solution: Here 2km is immaterial. The given problem can be written in a tabular form like below.   We can apply chain rule now.   Total men required to complete the remaining work = 100×2525×810×2313100×2525×810×2313 = 160   So additional men required = 160 - 100= 
160 - 100 = 60
60   Answer:60
Answer: B
Two trains 111 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 60 km and the other at the rate of 90 kmph. In what time will they be completely clear of each other from the moment they meet?	Pick
A) 4.85 B) 7.85 C) 6.85 D) 5.85 E) 6.62

Solution: T = (111 + 165)/ (60 + 90) * 18/5   T = 6.62   ANSW6.62R:6.62
Answer: E
A train 500 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?	Answers:
A) 277 m
B) 700 m
C) 800 m
D) 187 m
E) 1678 m

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (500 + x)/60 = 65/3   x = 800 m.   Answer:800 m
Answer: C
The price of a radio was increased by 25 percent. The new price was then increased by 40 percent. A single increase of what percent is equivalent to these two successive increases? Choose the correct option
A) 80%
B) 75%
C) 65%
D) 50%
E) 45%

Solution: consider base price - $100   25% increase = 1.25*100= 
1.25*100 = 125
$125   another 40% increase on new price= 1.4* 125= 
1.4* 125 = 175
$175   so final price of radio - $175   therefore a 75% increase   correct option - 75%
Answer: B
Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has travelled 100 km more than the second. The distance between P and Q is : Options
A) 500 km
B) 630 km
C) 900 km
D) 660 km
E) None

Solution: Sol.   At the time of meeting, let the distane travelled byb the second train be x km. Then,   distance covered by the first train is (x + 100) km   ∴ x/40 = (x+100)/50 ⇔ 50x = 40x 4000 ⇔ x = 400.   So, distance between P and Q = (x+x+100) km = 900 km.   Answer 900 km
Answer: C
What is the investment made if one invests in 15% stock at 50 and earns Rs.2000?
Answers:  A) 5000  B) 2767  C) 2697  D) 126967  E) 19771

Solution: Explanation:   To earn Rs.15, investment = Rs.50.   Hence, to earn Rs.1500, investment = (1500*50)/15   = Rs.5000   5000NSWER: 5000
Answer: A
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 25 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 most appropriate option.
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 25 rows is blocked. two wings, therefore 50 window seats are blocked.   Total window seats = 60   Total blocked window seats = 50   Total unblocked seats = 10   We know that a window seat was given, therefore probability for not window seat is 10/60 =1/6   1/6NS 1/6
Answer: A
Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. If the gain is proportional to the money invested and the time for which the money is invested and the total gain was Rs. 28000, find the earning of Nandan.	Choose the correct option.
A) Rs.7000
B) Rs.5000
C) Rs.6000
D) Rs.Rs.4000
E) Rs.6500

Solution: 3:1   2:1   ------   6:1   7 ----- Rs.28000   1 ----- ? => Rs.28,000/7=Rs. 4000   Answer: Rs.Rs.4000
Answer: D
A certain bakery sells six different-sized wedding cakes. Each cake costs x dollars more than the next one below it in size, and the price of the largest cake is $24.50. If the sum of the prices of the six different cakes is $109.50, what is the value of x? Select the correct option:
A) 1.50
B) 1.75
C) 2.00
D) 2.50
E) 3.00

Solution: Since the price of the largest cake (6th) is $24.50, then the price of the smallest cake (1st) is $(24.50-5x). Now, the prices of the cakes are evenly spaced so the sum of the prices is (average price)*(# of cakes)=(first+last)/2*(# of cakes). So, (24.50-5x+24.50)/2*6= 109.50 --> x=2.5.   Answer: 2.50.
Answer: D
Three bells chime at intervals of 18 min., 24 min. and 32 min. respectively. At a certain time they begin together. What length Z of time will elapse before they chime together again?  Choose the correct choice from the following options:  A) 2 hr. and 24 min.  B) 4 hr. and 48 min.  C) 1 hr. and 36 min.  D) 5 hr.  E) 2 hr.

Solution: It should be simple. All the three bells will chime again together whenver their time intervals intersect eachother.   So the LCM of the three time intervals (18, 24,32) would be the answer.   LCM (18, 24, 32) Z= 288 => 4 hours 48 mins.4 hr. and 48 min.
Answer: B
A man can row downstream at 25 kmph and upstream at 15 kmph. Find the time to reach a destination point at a distance of 50km along the downstream.
Choose the correct choice:
A) 4 hrs.
B) 1 hrs.
C) 3 hrs.
D) 2 hrs.
E) 2 1/2 hrs.

Solution: Let the speed of the man in downstream=25 kmph. distance to be covered along the stream=50kmph   =>time taken =D/S =50/25= 
50/25 = 2
2 Hrs.   Answer:2 hrs.
Answer: D
Find the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters
Look at this series: C19, E21, __, I25, K27, ... What number should fill the blank?
Choose the correct choice from the following answers:
A) D20 B) E21 C) F22 D) G23 E) H24

Solution: E21   G23   In this series, the letters progress by 2, and the numbers increase by 2.
Answer: B
A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train? Choose the correct choice from the following answers:  A) 276m  B) 180m  C) 286m  D) 288m  E) 277m

Solution: Length of the train be ‘X’   X + 120/15 = X + 180/18   6X + 720 = 5X + 900   X = 180m   Answer:180m
Answer: B
The ratio of three numbers is 2:3:5 and their sum is 150. The second number of the three numbers is?
Choose the correct choice from the following.
A) 24	B) 26	C) 27	D) 29	E) 45

Solution: 2:3:5   Total parts = 10   10 parts --> 150   1 part ---->15   The second number of the three numbers is = 3*15= 
3*15 = 45
45   Answer : 45
Answer: E
For any real number x, the operatoris defined as:
(x) = x(2 − x)
If p + 2 =(p + 2), then p =
Options.
A) 1	B) 0	C) 1	D) -2	E) 3

Solution: (x) = x(2 − x)   (p + 2) = (p + 2)(2 - p - 2) = -p(p+1)   We are given that p + 2 =(p + 2)   Therefore -p(p+2) = (p + 2)   Or (p + 2) + p(p+2) = 0   (p + 2)(p+1) = 0   p = -1,p=-2   Option -2
Answer: D
Calculate the circumference of a circular field whose radius is 5 centimeters.
Choose the correct choice
A) 2
B) 4
C) 6
D) 8
E) 10

Solution: Circumference C is given by   C = 2πr = 2π*5 = 10 π cm   correct answer 102 *5= 
2 *5 = 10
10 π cm   correct answer 10
Answer: E
The average age of five persons is 40 years while the average age of some other 10 persons is 25 years. The average age of all the 15 persons is:  Pick one
A) 27 Years B) 32 Years C) 37 Years D) 30 Years E) 35 Years

Solution: x/5==40   x==200   after 10 person   x/10==25   x==250   so avg btwn 15 person is,,   (250+200) / 15==30 ans   ANSWER:30 Years
Answer: D
A slot machine in a Las Vegas casino has an average profit of $600 for each 8-hour shift for the five days Sunday through Thursday, inclusive. If the average per-shift profit on Friday and Saturday is 25% greater than on the other days of the week and the slot machine is in operation every hour of every day, what is the total weekly profit that the casino makes from the slot machine?  Choose the correct answer.
A) a - 4500	B) b - 9000	C) c - 13,500	D) d - 15,500	E) e - 27,000

Solution: Correct answer is C - 13500.   Total profit per weekday = $600 X 3 (shifts)= $1800   Total profit per week (apart from SaturdaySunday) = $1800 X 5 = $9000   Total profit per shift on weekends = $600 X 125/100 = $750   Total profit on weekends = $750 X 3 (shifts) X 2 (Saturday, Sunday) = $4500.   Hence the answer is - $4500 + $9000 = $13,500. (c - 13,500)
Answer: C
What is the greatest prime factor of 2^10 - 1?	Choose the correct option.
A) 17  B) 19  C) 23  D) 29  E) 31

Solution: 2^10-1 = (2^5-1)(2^5+1) = 31*33   The answer is 31.
Answer: E