MU-NLPC/Calc-aqua_rat huggingface dataset:
The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 25 years and the average age of the last three persons is 32 years, then find the age of the person sitting in the middle of the row?  Choose one:
A) 9 years B) 29 years C) 25 years D) 19 years E) 17 years

Solution: Total age seven persons = (28 * 7)years   Total age of the first three persons and the last three persons are (25 * 3) years and (32 * 3) years respectively.   Age of the person sitting in the middle of the row = 28 * 7 - 25 * 3 - 32 * 3 = 196 - 75 - 96= 
196 - 75 - 96 = 25
25 years.   ANSWER:25 years
Answer: C
Consider a right circular cone of base radius 4 and height 10 cm. A cylinder is to be placed inside the cone with one of the flat surface resting on the base of the cone. Find the largest possible total surface area (in sq cm) of the cylinder.	Pick
A) 100π/3 B) 80π/3 C) 120π/7 D) 130π/9 E) 110π/7

Solution: Explanation :   Let the radius of cylinder be r and its height is h.   So, the height remained above cylinder is 10-h   Also, triangles ABC and ADE are similar. so ratio of corresponding sides must be equal   i.e AB/AD = BC/DE.   i.e. (10-h)/10 = r/4.   so 40 - 4h = 10r (by cross multiply)   h = (40-10r)/4 = 10-2.5r   Now we have total surface area of cyl = 2*π*r*h + 2*π*r2.   Putting value of h = 10 - 2.5r here, we get S = 2*π*r*(10-2.5r) + 2*π*r2.   S = 20*π*r- 5 * π * r2 + 2 * π * r2 .   S = 20 *π*r- 3*π*r .   Now, we have to maximize S, so differentiate it w.r.t r, we get   S = 20*π - 6 * π * r setting it to zero, we get   => 20*π - 6 * π * r= 0   => r = 20/6 = 10/3.   So, h = 10 - 2.5r = 10 - 2.5*10/3 = 5/3   So,   => S = 2 * π * r * h + 2 * π * r2.   => S = 2 * π * 10/3 * 5/3 + 2 * π* 100/9.   => S = 2 * π * 50/9 + 2 * π* 100/9.   => S = 2π150/9.   => S = 100π/3.   100π/3nswer : 100π/3
Answer: A
A two digit no is 18 less than square of the sum of its digit.how many such no are there?
Choose the correct option
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: 63=(6+3)^2-18=81-18   82=(8+2)^2-18=100-18   2NSWER:2
Answer: A
If a/b = 5/2, b/c = 1/2, c/d = 1, d/e = 3/2 and e/f = 4/3, then what is the value of abc/def ?
Select:
A) 15/8 B) 14/3 C) 41/7 D) 3/18 E) 18/4

Solution: Say a = 2. Then:   a/b = 5/2 --> b = 2/5;   b/c = 1/2 --> c = 4/5;   c/d = 1 --> d = 4/5;   d/e = 3/2 --> e = 8/15;   e/f = 4/3 --> f = 2/5.   abc/def = (1*2/5*4/5)/(4/5*8/15*2/5) = 15/8.   15/8nswer: 15/8.
Answer: A
If 3x < 2y < 0, which of the following must be the greatest? Choose the most appropriate option:
A) 2y - 3x  B) 3x - 2y  C) -(3x - 2y)  D) -(3x + 2y)  E) 0

Solution: Plugging in -1 for both x and y we get   A. 2y - 3x = 2   B. 3x - 2y = -1   C. -(3x - 2y) = 3   D. -(3x + 2y) = 15   E. 0   Answer: -(3x + 2y)
Answer: D
TOM traveled the entire 60 miles trip. If he did the first 15 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 45 miles per hour, what is the his average speed, in miles per hour?
Answers:	A) 35.62mph	B) 25.45mph	C) 34.52mph	D) 36.92mph	E) 36.29mph

Solution: avg speed = total distance/ total time = (d1+d2)/(t1+t2) = (15+45) / ((15/24)+(45/45)) = 60*2/3 = 36.92mph   36.92mph
Answer: D
There are X persons and Y chocolates. If each person is given 1 chocolate then 1 chocolate is left, if each person is given 2 chocolates then 1 person will be left. So how many persons and chocolates are there??  Choose the correct answer
A) 3,2
B) 3,3
C) 3,4
D) 4,5
E) 4,4

Solution: X person, Y chocolates   1st equation ==> (Y-1)/x = 1   2nd equation ==> Y/(X-1) = 2   Solving we get x = 3 , Y =4   ANSWER:3,4
Answer: C
23 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus? Choose the correct choice.
A) None of these B) 506 C) 512 D) 524 E) 542

Solution: Explanation :   He can go in any bus out of the 23 buses.   Hence He can go in 23 ways.   Since he can not come back in the same bus that he used for travelling,   He can return in 22 ways.   Total number of ways = 23 x 22 = 506. Answer : Option 506
Answer: B
(x-2) men can do a piece of work in x days and (x+7) men can do 75% of the same work in (x-10)days. Then in how many days can (x+10) men finish the work? Select the correct option: A) 27 days B) 12 days C) 25 days D) 18 days E) None of these

Solution: Explanation:   (3/4) × (x - 2)x = (x + 7)(x - 10)   => x2 - 6x - 280 = 0   => x= 20 and x=-14   so, the acceptable values is x=20   Total work = (x - 2) × x = 18 × 20 = 360 unit   Now 360 = 30 × k (30 = 20 + 10)   k = 12 days   Answer: 12 days
Answer: B
If 20,374 + x is a multiple of 5, which of the following could be the value of x? Pick.
A) 1	B) 2	C) 3	D) 4	E) 6

Solution: Sum of the digits of 20,374 is  2+0+3+7+4= 
 2+0+3+7+4 = 16
16   Now 16 is not a multiple of 5, the next multiple of 5 close to 16 is 20, which is 4 added to 16.   So the least number to be added to 20,374 is 4.   4
Answer: D
There are 3 numbers A, B and C. If A:B = 3/4, B:C = 4/5, C:D = 5/6, then A:D will be? Choose the correct choice from the following.
A) 1 : 2
B) 2 : 3
C) 3 : 5
D) 4 : 7
E) 4 : 9

Solution: Sol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6   ∴A∶B∶C∶D= 3 : 4 : 5 : 6.   Thus, 1 : 2 : D = 3 : 6 or, 1 : 2   1 : 2
Answer: A
Pat, kate and mark charged a total of 198 hours to a certain project . If pat charged twice as much time to the project as kate and 1/3 as much times as mark, how many more hours did mark charge to the project than kate.	Options:	A) 18	B) 36	C) 72	D) 110	E) 108

Solution: Let Kate charge for x hours,   then Pat charged for 2x and Mat - for 6x.   So, 2x+6x+x = 198 -total hours charged for,   x= 22.   Mat charged 6x-x or 5x for more hours than kate, or for 110 hours .   110 is correct
Answer: D
According to the directions on the can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounces cans of the concentrate are required to prepare 240 6 ounces servings of orange juice? Options
A) a) 25
B) b) 34
C) c) 50
D) d) 67
E) e) 30

Solution: Its E.   Total juice rquired = 240*6= 
240*6 = 1_440
1440 ounce   12 ounce concentate makes= 12 * 4= 
12 * 4 = 48
48 ounce juice   Total cans required= 1440/48= 
1440/48 = 30
30.   Answer e) 30
Answer: E
is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 47, then how old is B?
Choose the correct choice from the following: A) 7 B) 8 C) 9 D) 18 E) 11

Solution: Let C's age be x years.   Then, B's age = 2x years.   A's age = (2x + 2) years.   (2x + 2) + 2x + x = 47   5x = 45 => x = 9   Hence, B's age = 2x = 18 years.   ANSWER:18
Answer: D
Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1215 as rent for parking his cars, what is the total rent paid by all the four agencies?	Choose the correct answer
A) 6642	B) 2778	C) 1279	D) 6150	E) 2771

Solution: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15   = 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60   Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.   The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k   It is given that A paid Rs. 1215   45k 45  + 60  + 81  + 60= 
45  + 60  + 81  + 60 = 246
246k   It is given that A paid Rs. 1215   45k= 1215 => k = 27   246k = 246(27) = Rs. 6642   Thus the total rent paid by all the four agencies is Rs. 6642.   6642nswer: 6642
Answer: A
Last year the range of the annual bonus of the 100 employees at Company X was $20,000. If the annual bonus of each of the 100 employees this year is 10 percent greater than it was last year, what is the range of the annual bonus of the 100 employees this year?
Options:
A) $27,000
B) $22,000
C) $33,000
D) $16,000
E) $43,000

Solution: let the lowest bonus be x.   Therefore, highest bonus is x +20000.   Now bonus of each employee is increased by 10%.   Therefore the bonus will remain arranged in the same order as before.   or Lowest bonus = 1.1x and Highest = 1.1 * (x+20000)   or Range = highest - lowest = 1.1 * (x+20000) - 1.1x   = 22000, Hence, $22,000
Answer: B
A fruit seller had some apples. He sells 40% and still has 420 apples. Originally, he had ? Choose the correct choice from the following answers.
A) 588 apples
B) 600 apples
C) 672 apples
D) 700 apples
E) None

Solution: Answer   ∵ 60% of N = 420   ∴ N = (420 x 100)/60 = 700   Correct Option: 700 apples
Answer: D
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Choose the most appropriate option.
A) 40 sec B) 11 sec C) 88 sec D) 19 sec E) 10 sec

Solution: Speed = 45 * 5/18 = 25/2 m/sec   Total distance covered = 360 + 140= 
360 + 140 = 500
500 m   Required time= 500 * 2/25= 
500 * 2/25 = 40
40 sec   40 secnswer: 40 sec
Answer: A
After running a series of television advertisements, a leading beverage producer saw its sales increase by 25% to $3 million dollars per month. Prior to the advertising campaign, about how many dollars in sales did the company average per day?
Pick one:
A) $1.25 million B) $80,000 C) $750,000 D) $27,000 E) $10,000

Solution: Let sales in previous month = X   1.25 X=2,000,000   5/4 X= 2,000,000 ..........> X=2,400,000   sales per day= 2,400,000/30= less than 80,000   Answer:$80,000
Answer: B
A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform.	Choices
A) 310 meter  B) 335 meter  C) 345 meter  D) 350 meter  E) None of these

Solution: Explanation:   Speed = 350 meteristance/time = 300/18 = 50/3 m/sec   Let the length of the platform be x meters   then   350 meteristance=Speed∗Time   x+300=50/3∗39   =>3(x+300)=1950   =>x=350 meters   Option 350 meter
Answer: D
By selling 45 lemons for Rs 40, a man loses 20 %. How many should he sell for Rs 24 to gain 20 % in the transaction ?	Choose the correct choice from the following.
A) 33  B) 18  C) 99  D) 27  E) 36

Solution: Explanation:   Let S.P. of 45 lemons be Rs. x.   Then, 80 : 40 = 120 : x or x = = 60   For Rs.60, lemons sold = 45   For Rs.24, lemons sold == 18.   Answer: 18
Answer: B
I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ?	Select:
A) 25	B) 37	C) 54	D) 65	E) 72

Solution: Explanation:   Clearly, the required number would be such that it leaves a remainder of 1 when divided by 2, 3 or 4 and no remainder when divided by 5. Such a number is 25.   25nswer: 25
Answer: A
A work as fast as B. If B can complete a work in 36days independently,the number of days in which A and B can together finish the work in?	Choose the correct answer:
A) 12days B) 3days C) 4days D) 5days E) 6days

Solution: Ratio of rates of working of 12days and B = 2:1   ratio of times taken = 1:2   12days's 1day work = 1/18   B's 1day work = 1/36   12days+B 1day work = 1/18 + 1/36  +  1= 
 +  1 = 1
1/18 + 1/36= 3/36 = 1/12   12days and B can finish the work in 12days   12daysnswer is 12days
Answer: A
If an object travels at six feet per second, how many feet does it travel in one hour?  Choices:	A) 21600	B) 3778	C) 12788	D) 18000	E) 2881

Solution: Explanation:   If an object travels at 6 feet per second it covers 6x60 feet in one minute, and 6x60x60 feet in one hour.   21600nswer = 21600   21600nswer: 21600) 21600
Answer: A
A certain restaurant offers 7 different salads, 4 different main courses, and 6 different desserts. If customers choose one salad, one main course, and two different desserts for their meal, how many different meals are possible?
Select the correct option:
A) 340	B) 380	C) 420	D) 460	E) 500

Solution: The number of possible choices for desserts is 64202 = 15   The number of possible meals is   7*4*15= 
  7*4*15 = 420
420   The answer is 420.
Answer: C
A profit of Rs. 20000 is to be distributed among A, B, C in the proportion 2 : 3 : 5. What will be the difference between B’s and C’s shares
Choose the correct choice.
A) 4000  B) 3000  C) 5500  D) 4500  E) None of these

Solution: Explanation :   B's share = Rs 20000 *(3/10)= 
20000 *(3/10) = 6_000
Rs 6000   C's share= Rs 20000 * (5/10)= 
20000 * (5/10) = 10_000
Rs 10000   Difference in B's and C's shares= Rs 4000   4000nswer : 4000
Answer: A
In a room filled with 8 people, 6 people have exactly 2 siblings in the room and 2 people have exactly one sibling in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings? Choose the correct choice from the following choices:  A) 5/8  B) 3/8  C) 3/5  D) 2/3  E) 3/4

Solution: The 8 people consist of two sets of 3 siblings and 1 set of 2 siblings.   The number of ways to choose 2 people is 8C2 = 28.   The number of ways to choose 2 from the first group of siblings is 3C2 = 3.   The number of ways to choose 2 from the second group of siblings is 3C2 = 3.   The number of ways to choose 2 from the third group of siblings is 2C2 = 1.   The number of ways to choose 2 people who are siblings is  3+3+1= 
 3+3+1 = 7
7.   The number of ways to choose 2 people who are not siblings is   28-7= 
  28-7 = 21
21.   P(the two people are not siblings)= 21/28 = 3/4   The answer is 3/4.
Answer: E
Tom, working alone, can paint a room in 20 hours. Peter and John, working independently, can paint the same room in 10 hours and 5 hours, respectively. Tom starts painting the room and works on his own for two hour. He is then joined by Peter and they work together for two hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?	Choose one:
A) 5/7
B) 7/8
C) 2/5
D) 3/5
E) 1/5

Solution: Let the time when all three were working together be t hours. Then:   Tom worked for t+4 hour and has done 1/20*(t+4) part of the job;   Peter worked for t+2 hour and has done 1/10*(t+2) part of the job;   John worked for t hours and has done 1/5*t part of the job:   1/20*(t+4)+1/10*(t+2)+1/5*t=1 --> multiply by 20 --> (t+4)+(2t+2)+4t=20 --> t=2;   Hence Peter has done 1/10*(2+2)=4/10 =2/5   Answer: 2/5
Answer: C
The probability that a family with 6 children has exactly four boys is:  Choices
A) 1/3  B) 1/64  C) 15/64  D) 3/8  E) none of the above

Solution: Now let's find the # of combinations where there's a BGB combination. Let the sequence of BG=A:   BBAA   BAAB   BABA   ABBA   ABAB   AABB   So there are 6 combinations here. But since BG can also be GB, we have to multiply by 2. We have to multiply by another 2 because there are 2 As. Therefore, there are 6x2x2=24 combinations.   We also have to include the instances where GG occurs at the end or the front, that is:   GGBBBB   BBBBGG   (all the other instances such as BBGGBB have been taken care of in the calculation at the top)   So we have   24+2= 
  24+2 = 26
26 possibilities of 4 boys and 2 girls.   The total number of possibilities is 2^6=64. Therefore, the probability is 26/64, which is 13/32. The answer is none of the above
Answer: E
A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is frozen if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently nine spaces behind player B, what is the probability that player B will be frozen after player A rolls?	Choose the correct choice from the following answers:	A) 1/12	B) 5/36	C) 1/9	D) 1/3	E) 17/36

Solution: no. of possible outcomes = 6*6= 
6*6 = 36
36   no. of outcomes that result a total of 9 (as A is 9 spaces behind B)= 4 ( (3,6), (4,5), (5,4), (6,3) )   So, the probability = 4/36=1/9 (Option 1/9)
Answer: C
9 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 48 cm height. What is the diameter of each sphere?	Choose the correct choice from the following choices
A) 4 cm	B) 6 cm	C) 8 cm	D) 10 cm	E) 12 cm

Solution: Volume of cylinder = pi*r^2*h   Volume of a sphere = 4*pi*R^3 / 3   9*4*pi*R^3 / 3 = pi*r^2*h   R^3 = r^2*h / 12 = 64 cm^3   R = 4 cm   D = 8 cm   The answer is 8 cm.
Answer: C
A can do a work in 7 days. B is 20% more efficient than A. How many days does B alone take to do the same job?  Choose the correct choice from the following choices.
A) 28/6 B) 25/6 C) 35/6 D) 33/6 E) 39/6

Solution: Ratio of times taken by A and B = 120:100 = 6:5   suppose B alone to take x days to do the work   then, 6:5::7:x   6x= 5*7= 
5*7 = 35
35/6 days   correct option is 35/6
Answer: C
The average (arithmetic mean) of the even integers from 0 to 60 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 30 inclusive?	Choose the correct choice from the following choices:
A) 10
B) 15
C) 20
D) 25
E) 30

Solution: The sum of even numbers from 0 to N is 2 + 4 +...+ N   = 2(1 + 2 + ...+ N/2)   = 2(N/2)(N/2+1)/2 = (N/2)(N/2+1)   The average is (N/2)(N/2+1)/(N/2+1) = N/2   The average of the even numbers from 0 to 60 is  60/2= 
 60/2 = 30
30   The average of the even numbers from 0 to 30 is  30/2= 
 30/2 = 15
15   The answer is 15.
Answer: B
What is the are of an equilateral triangle of side 8 cm? Answers.
A) 64√5 B) 64√9 C) 16√3 D) 64√3 E) 64√2

Solution: Area of an equilateral triangle = √3/4 S2   If S = 8, Area of triangle = √3/4 * 8 * 8 = 16√3 cm2;   Answer: 16√3
Answer: C
Soymilk are sold in packages of two or three only. If Hannah bought 17 Soymilk exactly, what could be the number of large packs Hannah bought?	Choices:
A) 1	B) 4	C) 3	D) 5	E) 8

Solution: Let number of packs of three = t   let number of packs of two = w   3t + 2w = 17   Now , we need to test for values of w .   Since sum 17 is odd and 2w will always be even, therefore w can't be even .   Now , we can test for values w = 1 , 3 and 5   2*4 + 3*3 = 8 + 9= 
8 + 9 = 17
17   Answer 3
Answer: C
Robert ate 10 chocolates, Nickel ate 5 chocolates. How many more chocolates did Robert ate than nickel?
Select:
A) A)4  B) B)7  C) C)9  D) D)5  E) E)2

Solution: 10-5= 
10-5 = 5
5. Answer is 5
Answer: D
In the fifth grade at Parkway elementary school there are 500 students. 350 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer? Choose the correct answer
A) 69. B) 73. C) 81. D) 91. E) 115.

Solution: Total students = 500   Boys = 350, Girls = 150   Total playing soccer = 250   86%of 250 = 215 are boys who play soccer.   Girls who play soccer = 35.   Total girls who do not play soccer = 150 - 35= 
150 - 35 = 115
115.   Correct option: 115.
Answer: E
The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Choose the most appropriate option.
A) 776 B) 298 C) 245 D) 266 E) 256

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time   = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X)   = 750 ==> X   = 245 m.   Answer: 245
Answer: C
Virginia, Adrienne, and Dennis have taught history for a combined total of 87 years. If Virginia has taught for 9 more years than Adrienne and for 9 fewer years than Dennis, for how many years has Dennis taught?	Select the correct option.
A) 23 B) 32 C) 38 D) 41 E) 44

Solution: Let number of years taught by Virginia = V   number of years taught by Adrienne = A   number of years taught by Dennis = D   V+A+D = 96   V= A+9   =>A = V-9   V= D-9   => A = (D-9)-9 = D-18   D-9 + D-18 + D = 87   => 3D = 87+ 27= 
87+ 27 = 114
114=> D = 38   Answer 38
Answer: C
Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms? Choose the correct choice from the following:
A) 478
B) 476
C) 472
D) 471
E) 445

Solution: 3 1/2 * 8 1/2 = 1/4 * 1/4 * x => x   = 476   Answer:476
Answer: B
In a cricket team, the average of eleven players is 28 years. Out of these, the average ages of three groups of three players each are 25 years, 28 years and 32 years respectively. If in these groups, the captain and the youngest player are not included, and the captain is eleven years older than the youngest player, what is the age of the captain ? Select the correct option.
A) 32 years
B) 34 years
C) 35 years
D) 36 years
E) 37 years

Solution: Explanation :   Let the age of youngest player be x.   Then, age of the captain = (x + 11).   => 3*25 + 3*28 + 3*32 + x + x + 11= 
+ 11 = 11
11*28.=> 75+84+96+2x+11=308   so 2x = 42   so x = 21.   Age of the captain = (x+11)   = 32 years.   32 yearsnswer : 32 years
Answer: A
Two trains are running in opposite directions with the same speed. If the length of each train is 100 m and they cross each other in 12 sec, then the speed of each train is? Choose the correct answer:  A) 30  B) 35  C) 36  D) 37  E) 38

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (100 + 100)/12 => x = 8.33   Speed of each train = 10 m/sec.   = 8.33 * 18/5 = 30 km/hr.   30nswer: Option 30
Answer: A
In a school of 850 boys, 34% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?  Choose the correct choice
A) A)125
B) B)627
C) C)153
D) D)238
E) E)159

Solution: 34 + 28 + 10= 
34 + 28 + 10 = 72
72%   100 – 72= 28%    850 * 28/100= 
 850 * 28/100 = 238
238   Answer:238
Answer: D
If a farmer wants to plough a farm field on time, he must plough 120 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?
Choose the correct choice from the following answers:
A) 334  B) 720  C) 667  D) 261  E) 181

Solution: Let xx be the number of days in the initial plan. Therefore, the whole field is 120⋅x120⋅x hectares. The farmer had to work for x+2x+2 days, and he ploughed 85(x+2)85(x+2) hectares, leaving 4040 hectares unploughed. Then we have the equation:   120x=85(x+2)+40120x=85(x+2)+40   35x=21035x=210   x=6x=6   So the farmer planned to have the work done in 6 days, and the area of the farm field is 120⋅6=720120⋅6=720 hectares   Answer:720
Answer: B
What number should replace the question mark? 11, 15, 16, 12, 21, 9, ---? Choose the correct choice:
A) 21	B) 29	C) 28	D) 27	E) 26

Solution: Answer: 26   11, 15, 16, 12, 21, 9, ---?   There are two alternate sequences: +5 and -3.
Answer: E
David works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 600 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 4,800. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.? Choose the correct choice from the following answers:
A) 2400	B) 3600	C) 3000	D) 2800	E) 2500

Solution: let the rate be x, then population of the bacteria after each hour can be given as 600,600x, 600(x^2), 600(x^3)   now population at 4pm =4800   thus we have 600(x^3) = 4800 =8   thus x=2   therefore population at 3pm = 600(4) = 2400   2400nswer : 2400
Answer: A
What is the sum of the 1st 6 prime numbers greater than 10?	Choose one:	A) 112	B) 111	C) 212	D) 115	E) 113

Solution: Required numbers are= (11 + 13 + 17 + 19 + 23+ 29)= 
(11 + 13 + 17 + 19 + 23+ 29) = 112
112   Note: 1 is not a prime number   112nswer 112
Answer: A