MU-NLPC/Calc-aqua_rat huggingface dataset:
Find the largest 7 digit number which is exactly divisible by 88?  Choices.
A) 9998765	B) 9998907	C) 9999944	D) 9999954	E) 9999968

Solution: Largest 7 digit number is 9999999   After doing 9999999 ÷ 88 we get remainder 31   Hence largest 7 digit number exactly divisible by 88 = 9999999 - 31= 
9999999 - 31 = 9_999_968
9999968   9999968
Answer: E
How many ways are there to award a gold, silver and bronze medal to 10 contending teams?  Options:
A) 10 × 9 × 8  B) 10!/(3!7!)  C) 10!/3!  D) 360  E) 300

Solution: we clearly know that there can be only one winning team which deserves the gold medal. we can do the selection in 10 ways   if gold medal is given to 1 of the teams then only possible 9 teams can be considered for silver medal. we can do selection in 9 ways   similarly if gold and silver medals are awarded then only remaining 8 teams can be considered for a bronze medal. we can do the selection in 8 ways   Total number of ways to select the 3 possible medal winners = 10 * 9 * 8   Correct answer - 10 × 9 × 8
Answer: A
Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $2000 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years? Choose the correct choice from the following answers: A) $3,750 B) $5,600 C) $8,100 D) $18,000 E) $22,500

Solution: x=8%   112/x years=112/8= 
112/8 = 14
14 years   Now, money triples every 14 years   Therefore, in 14 yrs , if $2000 triples to $6000, in 28 years, it will again triple to $6000*3=$18,000   Answer $18,000
Answer: D
A train speeds past a pole in 15 sec and a platform 130 m long in 25 sec, its length is?  Choose one.
A) 50 m
B) 150 m
C) 195 m
D) 300 m
E) None of these

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y = x/15   (x + 130)/25 = x/15 => x = 195 m.   ANSWER:195 m
Answer: C
If E is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of E? Choose the correct choice from the following options:
A) 10  B) 12  C) 14  D) 16  E) 18

Solution: E = 30!   8   E = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1   Out of these 30 , 27 , 24 , 21 , 18, 15 , 12 , 09 , 06 , 3 are factors of 3   3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2, 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3   So we have a total of 14 three's ...   Therefore the maximum value of K can be 14 (14)
Answer: C
Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is :  Choose the correct choice from the following options:
A) 8400	B) 2288	C) 7767	D) 2998	E) 2771

Solution: Explanation:   Ratio of their shares = 22500 : 35000 = 9 : 14.   Deepak's share = Rs. (13800 * 14/23) = Rs. 8400.   8400nswer: 8400) 8400
Answer: A
A can do a work in 25days and B can do the same work in 20days. They work together for 5days and then A goes away. In how many days will B finish the work?  Choose the correct choice from the following answers
A) 9/15days
B) 11/20days
C) 13/17days
D) 7/15days
E) 1/5days

Solution: A+11/20days can do the work in 5days = 5( 1/25 + 1/20) = 5*45 / 25*20 = 9/20   Rest of the work = 1 - 9/20 = 11/20   11/20days will do the rest of the work in = 1 - 9/20 = 11/20days   Answer is 11/20days
Answer: B
If 6 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
Pick:
A) 6 × 5 × 4 × 3 × 2 × 1	B) 6 × 5 × 4 × 3 × 2 × 1	C) 6 x 5	D) 15	E) 45

Solution: 1st person will have 5 handshakes, 2nd will have 4, ....5th will have 1 and 6th will have 0   = 5+4+3+2+1= 
5+4+3+2+1 = 15
15   if we generalize this: if there are n people then there will be n(n-1)/2 handshakes.   Ans.15)
Answer: D
What could be the range of a set consisting of odd multiples of 7?  Select the correct option.
A) 21	B) 24	C) 35	D) 62	E) 70

Solution: A set of odd multiples of 7 would be something like 7, 21, 35, 49....   The range would always be an even number multiple of 7.   ANSW70R:70
Answer: E
Cara picked a number of pears, each of which she sold, canned, or poached. If she canned 40 percent more than she poached, and she poached 80 percent less than she sold. If there were a total of 111 pears, then how many pears did she sell?  Options
A) 69	B) 72	C) 75	D) 78	E) 81

Solution: Let x be the amount of pears that she sold.   Then she poached 0.2x.   Then she canned  1.4*0.2= 
 1.4*0.2 = 0.28
0.28x.   The total amount of pears is x+0.2x+0.28x=1.48x   The fraction of pears that she sold is 1/1.48=100/148=25/37.   The number of pears she sold is   (25/37)*111= 
  (25/37)*111 = 75
75.   The answer is 75.
Answer: C
A Harsco's train rails across an open track at 250 kilometers per hour. A regular passenger train travels at 68% of the Harsco's train speed. If the two trains start moving from the same station at the same time, how much time longer will it take the passenger train than the Harsco's to travel 850 kilometers? Choose the correct choice from the following options
A) 1 hour and 24 minutes.
B) 1 hour and 36 minutes.
C) 2 hours and 24 minutes.
D) 2 hours and 36 minutes.
E) 5 hours.

Solution: Difference in time = time taken by passenger train- time taken by Harsco's train   850/(250*68) *100 - 850/250   850 (100/ 250*68 - 1/250)   850*32/ (250*68)   1.6 hrs or 1 hr and 36 mins   1 hour and 36 minutes. is the answer
Answer: B
A multiple choice question has 5 options. Choosing the correct option earns the student 1 marks. However choosing the wrong option incurs negative marks so that if a student chooses an option randomly, his expected score is 0. Suppose a student has successfully eliminated 2 incorrect options. His expected score if he chooses randomly among the remaining options is.
Answers:  A) 1/2  B) 1/3  C) 1/4  D) 2/3  E) 4/3

Solution: for right ans 1 no is given and for wrong -.25   so 1(1)+4(-.25)=0   now   1(1)+2(-.25)=.5=1/2.   1/2NSWER:1/2
Answer: A
The tax on a commodity is diminished by 32% but its consumption is increased by 12%. Find the decrease percent in the revenue derived from it? Choose the correct choice from the following answers: A) 20% B) 18% C) 15% D) 12% E) 24%

Solution: 100 * 100= 
100 * 100 = 10_000
10000   68 * 112= 
68 * 112 = 7_616
7616   10000------- 2384   100 ------- ?= 24%   ANSW24%R:24%
Answer: E
The number of female students in a college in the previous year was 400. If in the current year the number of male students in the college doubled over that of the previous year but the proportion of male students halved, then what is the number of female students in the college in the current year?	Select the correct option.
A) 200  B) 600  C) 900  D) 1600  E) 2000

Solution: Let x be the number of male students last year. The number of male students this year is 2x.   Let y be the number of female students this year.   x/400 = 2(2x/y)   y = 1600   The answer is 1600.
Answer: D
Bradley owns b video game cartridges. If Bradley’s total is one-fourth the total owned by Andrew and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
Choose the most appropriate option.
A) (16/3)b  B) (17/4)b  C) (13/4)b  D) (19/12)b  E) (21/4)b

Solution: Step 1: Categorize the problem   This problem is testing basic algebra and equations, with an extra layer of complexity by having variables in the answer choices.   Step 2: Think like the test maker   What is the key detail or key details in the problem? The key detail to immediately recognize is that the problem gives you Andrew and Charlie’s totals in relation to Bradley’s total rather than giving you Bradley’s total in relation to the other two; and then the problem asks you to solve the problem in terms of b. This means that you have to relate Andrew and Charlie’s values in relation to Bradley’s total. The test maker is attempting to force you to structure the problem in the opposite way that most people are used to structuring information. By gaining this insight, it makes it easier to solve the problem.   Step 3: Solve the problem   b = Bradley’s total   4b = Andrew’s total   (1/4)b = Charlie’s total   Add each total   b + 4b+ (1/4)b = 5b + (1/4)b = (21/4)b   Therefore,choose (21/4)b.
Answer: E
If in coded language
2+6+7=24
8+2+8=73
3+4+4=40
Then
7+3+9=??	Choices.
A) 29	B) 30	C) 31	D) 32	E) 33

Solution: As we have   (2+6+7)+9= 
(2+6+7)+9 = 24
24   (3+4+4)+29= 
(3+4+4)+29 = 40
40   (8+2+8)+55= 
(8+2+8)+55 = 73
73   similarly   (7+3+9)+87= 
(7+3+9)+87 = 106
106   Now Consider no.   9 then 29 then 55 then 87   Its series of difference 29 and 9 as 5×4+0=20   Then 55 and 29 as 5×5+1=26   Then 87 and 55 as 5×6+2=32   ANSWER:32
Answer: D
When positive integer N is divided by positive integer J, the remainder is 16. If N/J = 204.04, what is value of J? Pick one
A) 100
B) 120
C) 400
D) 260
E) 380

Solution: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder   So, Dividend/Divisor = Quotient + Remainder/Divisor   Given that N/J = 204.04   Here 204 is the quotient.   Given that Remainder = 16   So, 204.04= 204 + 16/J   So, J = 400   Answer: 400
Answer: C
A cylinder with 6 meter radius and 12 meter height is filled to capacity with water. If the content of the cylinder is used to fill several smaller cylinders of 4 meter diameter and 8 meter height, how many smaller cylinders will be filled to capacity?
Choose one
A) 13
B) 12
C) 4
D) 16
E) 18

Solution: Calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder.   volume of cylinder =πr2h   larger cylinder volume=1357.17   smaller cylinder volume=100.53   therefore the number of cylinders B that can be filled to capacity=1357.17/100.53=13.5   13nswer is 13 only 13 smaller cylinders can be filled to capacity.
Answer: A
If a car went the first third of the distance at 80 kmh, the second third at 15 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?  Options
A) 30 kmh  B) 40 kmh  C) 42 kmh  D) 44 kmh  E) 50 kmh

Solution: 30 kmhssume D/3 = 240 (this number is convenient because it is divisible by 80, 15 and 48)   So:   240 = 80*T1 = 3 hrs   240 = 15*T2 = 16 hrs   240 = 48*T3 = 5 hrs   T = T1 + T2 + T3 = 24 hrs   D = RT   (240*3) = R*24   R = 30   30 kmhNSWER: 30 kmh
Answer: A
Last year 26 members of a certain club traveled to England, 26 members traveled to France, and 32 members traveled to Italy. Last year 6 members of the club traveled to both England and France, no members traveled to both England and Italy, and 11 members traveled to both France and Italy. How many members of the club traveled to at least one of these three countries last year?	Choose the correct choice from the following choices
A) 52 B) 71 C) 67 D) 73 E) 79

Solution: n(E or F or I) = n(E) + n(F) + n(I) - n(E and F) - n(F and I) - n(I and E) +n(E and F and I)   n(E or F or I) = 26 + 26 + 32 - 6 - 11 - 0 + 0   Why is the number of people who traveled to E and F and I 0? Because no one traveled to both England and France. So obviously, no one would have traveled to England, France and Italy.   n(E or F or I) = 67   Answer (67)
Answer: C
How many seconds will a train 120 meters long take to cross a bridge 200 meters long if the speed of the train is 36 kmph?
Choose the correct answer
A) 22 sec  B) 32 sec  C) 25 sec  D) 24 sec  E) 31 sec

Solution: Explanation:   D = 120 + 200= 
120 + 200 = 320
320   S= 36 * 5/18= 
36 * 5/18 = 10
10 mps   T= 250/10 = 32 sec   Answer: Option 32 sec
Answer: B
If a man buys 100 biscuits for $900 and sold them for $10 dollars determine his gain.	Choose the correct choice from the following answers: A) $ 100 B) $ 90 C) $ 80 D) $110 E) $ 115

Solution: Cost of 100 biscuits = $90   Sold each biscuits for $10   So he sold 100 biscuits for $(100 × 10) = $1000   Loss = $(1000 – 900) = $100   Therefore, gain = $ 100.   $ 100nswer:$ 100
Answer: A
Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 2 minutes the first is turned off. How many more minutes will it take for the cistern to fill after the first pipe is turned off?
Choose the correct choice.
A) 8.5	B) 9.5	C) 10.5	D) 11.5	E) 12.5

Solution: Let x be the total time it takes for the cistern to fill.   2/12 + x/15 = 1   x/15 = 5/6   x = 12.5   After the first pipe is turned off, it takes 10.5 more minutes to fill the cistern.   The answer is 10.5.
Answer: C
Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 6 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps? Options:
A) 5 : 1	B) 30 : 2	C) 15 : 2	D) 20 : 2	E) 25 : 2

Solution: U/I = 6/2   I/B = 5/1   Since I is multiple of both 2 (as per first ratio) and 5 (as per second ratio) so let's assume that I = 10   i.e. Multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator   then, U : I : B = 30 : 18 : 2   i.e. U : 30 : 2 =30 : 2   Answer: Option 30 : 2
Answer: B
There are 10person among whom 2are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1person sit between the brothers, is equal to?
Answers:  A) 7!  B) 7!*2!  C) 7!*3!  D) 8!*1!  E) 8!*4!

Solution: Total number of ways = 7!*2!.   7!*2!
Answer: B
At a certain high school, the senior class is three times the size of the junior class. If 1/6 of the seniors and 1/4 of the juniors study Japanese, what fraction of the students in both classes study Japanese? Select
A) 1/4	B) 3/16	C) 1/2	D) 5/16	E) 2/3

Solution: Start by deciding on a number of students to represent the number of students in the senior class. For this example I will choose 300 students. That would make the number of students in the junior class 100. Then we can find out how many students are taking Japanese in each grade and add them together. (1/6)*300=50 and   (1/4)*100= 
  (1/4)*100 = 25
25. 50+25=75. There are a total of 400 students in the junior class and senior class combined (100+300=300), and there are 75 total students in Japanese, so 75 students in Japanese / 400 total students equals 3/16 of the students in both classes that study Japanese.   Answer: 3/16
Answer: B
While visiting a small town in the United States, I lost my overcoat in a bus. When I reported the matter to the bus company I was asked the number of the bus. Though I did not remember the exact number I did remember that the bus number bad a certain peculiarity about it. The number plate showed the bus number as a perfect square and also if the plate was turned upside down.? the number would still be a perfect square—of course it was not?
I came to know from the bus company they had only five hundred buses numbered from 1 to 500.
From this I was able to deduce the bus number. Can you tell what was the other number.	Answers.
A) 127	B) 196	C) 116	D) 140	E) 234

Solution: B   196   The only numbers that can be turned upside down and still read as a number are 0, 1, 6, 8 and 9.   The numbers 0, 1 and 8 remain 0, 1 and 8 when turned over, but 6 becomes 9 and 9 becomes 6.   Therefore the possible numbers on the bus were 9, 16, 81, 100, 169 or 196. However, the number 196 is the only number which becomes a perfect square when turned over because 961 is the perfect square of 31. Therefore 196 is the correct answer.
Answer: B
A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
. Choose the correct option.
A) Rs. 650	B) Rs. 690	C) Rs. 698	D) Rs. 700	E) Rs. 720

Solution: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.   S.I. for 3 years = Rs.(39 x 3) = Rs. 117.   Principal = Rs. (815 - 117) = Rs. 698. Answer: Option Rs. 698
Answer: C
A bag contains 6 red, 2 yellow and 4 green balls. 3 balls are drawn randomly. What is the probability that the balls drawn contain balls of different colours?
Choose the most appropriate option:
A) 12/55
B) 3/5
C) 3/11
D) 1/4
E) 7/16

Solution: Total number of balls = 6+2+4= 
6+2+4 = 12
12   n(S)= 12C3 = 12*11*10 / 3*2 = 220   n(E) = 6C1 * 2C1 * 4C1 = 48   Probability = 48/220 = 12/55   12/55nswer is 12/55
Answer: A
The ages of two persons differ by 20 years. If 5 years ago, the older one be 5 times as old as the younger one, then their present ages, in years, are
Choose the correct choice from the following.
A) 25, 5  B) 30, 10  C) 35, 15  D) 50, 30  E) None of these

Solution: Let the ages be ’x’ and ’y’ years now.   Then x - y = 20 ...(i)   (x - 5) = 5(y - 5) ...(ii)   From (i) and (ii),   20 + y - 5 = 5y - 25   y = 10 and x = 30.   ANSWER:30, 10
Answer: B
Three people candidates contested an election and they received 1136, 7636 and 11628 votes respectively. What is the percentage of the total votes did the winning candidate get?  Choose one: A) 40% B) 45% C) 57% D) 58% E) 60%

Solution: tot no of votes = (1136+7636+11628)= 
(1136+7636+11628) = 20_400
20400   req= > (11628/20400 * 100)= 
(11628/20400 * 100) = 57
> 57%   ANSWER 57%
Answer: C
The Present worth of Rs. 1404 due in two equal half-yearly instalments at 8% per annum simple interest is :  Select.
A) Rs. 1325  B) Rs. 1300  C) Rs. 1350  D) Rs. 1500  E) None

Solution: Solution   Required sum = P.W. of Rs. 702 due 6 month hence + P.W. of Rs. 702 due 1 year hence   = Rs.[(100x702/100 + 8 x1/2 )+ ( 100x702/100 + (8x1) )] = Rs. (675+650) = Rs. 1325.   Rs. 1325nswer Rs. 1325
Answer: A
The moon revolves around the earth at a speed of approximately 0.9 kilometers per second. This approximate speed is how many kilometers per hour?  Options:
A) 60 B) 61.2 C) 3240 D) 3,600 E) 3,672

Solution: moon revolves around the earth at a speed of 1.02kilometers per second.   one hour equal to 60 minutes.   one minute equals to 60 seconds. so one hour equals to 3600seconds.   so one hour, speed= 0.9*3600= 
0.9*3600 = 3_240
3240kilometers per hour.   Option 3240 is correct
Answer: C
What is the 9th term in this sequence?
2,4,6,13,22,35,60 Pick:
A) 138
B) 148
C) 158
D) 168
E) 178

Solution: 2+4= 
2+4 = 6
6 +0= 
6 +0 = 6
6   6+4= 
6+4 = 10
10+3= 
10+3 = 13
13   13+6= 
13+6 = 19
19+3= 
19+3 = 22
22   22+13= 
22+13 = 35
35+0= 
35+0 = 35
35   35+22= 
35+22 = 57
57+3= 
57+3 = 60
60   60+35= 
60+35 = 95
95+3= 
95+3 = 98
98   98+60= 
98+60 = 158
158+0= 
158+0 = 158
158   so 9th term is 158   ANSWER:158
Answer: C
a man owns 2/3 of market reserch beauro buzness,and sells 3/4 of his shares for 6500rs,what is the value of buzness?
Choose the correct choice from the following choices.
A) 150000
B) 16000
C) 15000
D) 190000
E) 13000

Solution: If value of business=x   Total sell (2x/3)(3/4)=6500   ->x=13000   ANSW13000R:13000
Answer: E
One fourth of a solution that was 8% sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight? Choose the correct choice from the following choices:	A) 74%	B) 52%	C) 40%	D) 18%	E) 8.5%

Solution: Say the second solution (which was 1/4 th of total) was x% sugar, then 3/4*0.08+1/4*x=1*0.16 --> x=0.4. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.08+25*x=100*0.16 --> x=0.4.   Answer: 40%.
Answer: C
5 pumps, working 9 hours a day, can empty a tank in 3 days. How many hours a day should 6 pumps work in order to empty the tank in 1 day? Choose the correct choice.
A) 20 hours
B) 22.5 hours
C) 23 hours
D) 23.5 hours
E) 24 hours

Solution: Let the required hours needed be x   More pumps, less hours (Indirect proportion)   More Days, less hours (Indirect proportion)   Hence we can write as   (pumps)5:6   }::x:9   (days)3:1   =>5*3*9=6*1*x   =>x=45/2= 
45/2 = 45/2 = around 22.5
>22.5   ANSWER:22.5 hours
Answer: B
A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 6 rows or 4 rows or 8 rows, then no tree will be left. Find the least number of trees required Choose the correct choice from the following answers
A) 24
B) 60
C) 28
D) 76
E) 21

Solution: Explanation:   The least number of trees that are required = LCM(6,4,8) = 24   24nswer: 24
Answer: A
David has $1,500 at the beginning of his trip, after spending money, he still has exactly $500 less than he spent on the trip. How much money does John still have?
Choose the correct choice:
A) $200 B) $400 C) $500 D) $800 E) $1,200

Solution: Suppose total money spent = x   Not spend (Money he still has)= x-500   x+x-500 = 1500   x= 1000   Money not spend= 1000-500= 
1000-500 = 500
500   Answer : $500
Answer: C
At a meeting, 4 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?	Select:
A) 6 B) 7 C) 12 D) 14 E) 20

Solution: The number of arrangements of n distinct objects in a row is given by n!   The number of arrangements of n distinct objects in a circle is given by (n−1)!   "The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:   R=n!-n=(n−1)!   (n−1)!=(4−1)!=6   6nswer: 6
Answer: A
In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 60 per square m? Choose the correct choice from the following answers:
A) Rs. 50000
B) Rs. 51000
C) Rs. 57000
D) Rs. 60000
E) Rs. 65000

Solution: Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m   Total area of the hall to be covered with mat = 2(lb + bh + hl)   = 2(20 * 15 + 15 * 5 + 5 * 20)   =2(300 + 75 + 100)   = 2 * 475= 
2 * 475 = 950
950 sq. m   Total expenditure= 60 * 950   = Rs. 57000   Rs. 57000
Answer: C
Of the diplomats attending a summit conference, 17 speak French, 32 do not speak Russian, and 20% of the diplomats speak neither French nor Russian. If 10% of the diplomats speak both languages, then how many diplomats attended the conference? Choose the correct choice from the following answers.
A) 72	B) 96	C) 108	D) 120	E) 150

Solution: {Total} = {French} + {Russian} - {Both} + {Neither}   {Total} = 17 + ({Total} - 32) - (0.1*{Total}) + 0.2*{Total}   Solving gives {Total} = 150.   Answer: 150.
Answer: E
If a fair 6-sided die is rolled three times, what is the probability that exactly one 4 is rolled?
Choose one:
A) 25/216	B) 50/216	C) 25/72	D) 25/36	E) 5/6

Solution: Total ways in which a 6-sided die can be rolled three times = 6*6*6= 
6*6*6 = 216
216   To get exactly one 4 , there are three ways:   A 4 on the first roll and non 4 on other two rolls. This can be done in 1*5*5= 
1*5*5 = 25
25 ways.   The 4 could be on the second or third roll too. So total favorable cases= 25*3= 
25*3 = 75
75   Required Probability= 75/216 = 25/72   Answer (25/72)
Answer: C
15 people entered a theater before Sujit. 7 people entered the theater between Sujit and Suraj and 20 people entered the theater after Suraj.
How many people are there in the theater?
Choose the correct choice from the following answers.
A) 28 B) 36 C) 44 D) 40 E) Cannot be determined.

Solution: Explanation:   If Sujit entered before Suraj then the number of people will be 15 + 1(Sujit) + 7 + 1(Suraj) + 20 = 44.   If Suraj entered before Sujit then number of people will be 7 + 1(Suraj) + 7 + 1(Sujit) + 12 = 28.   So, the number of people in the theater cannot be determined.   ANSWCannot be determined.R IS Cannot be determined.
Answer: E
If three eighth of a number is 141. What will be the approximately value of 32.08% of this number?  Choose the correct option.
A) 119	B) 187	C) 181	D) 120	E) 891

Solution: Explanation:   x * 3/8 = 141 => x= 376   376 * 32.08/100 = 120   Answer: 120
Answer: D