MU-NLPC/Calc-aqua_rat huggingface dataset:
In the first week of the Year, Pancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Pancy saved during the 52 weeks?
Choose the correct choice:  A) $1,326  B) $1,352  C) $1,378  D) $2,652  E) $2,756

Solution: In the first week of the Year, Pancy saved $1.If you don't recall the formula, there is one method:   1 + 2 + 3 + 4 + 5 ........ + 26 + 27 + ............ + 48 + 50 + 51 + 52   Sum of 1stlast digit = 1 + 52= 
1 + 52 = 53
53   Sum of 2nd2nd last digit= 2 + 51= 
2 + 51 = 53
53   Sum of 3rd3rd last digit= 3 + 50= 
3 + 50 = 53
53   .   .   .   .   This is repeated 26 times   So, 26 * 53= 1378   Answer = $1,378
Answer: C
In a games hour 4 different types of players came to the ground? cricket 11, hockey 15, football 21, softball 15. In these 4 people play both cricket and hockey, 3people play both softball and football. 5 people play both cricket and football. How many people play only cricket? Choose the correct choice from the following answers:	A) 11	B) 2	C) 5	D) 3	E) 9

Solution: people play only cricket = total players in cricket- both cricket and football- both cricket and hockey.   people play only cricket = 11-4-5= 
11-4-5 = 2
2   Answer is 2
Answer: B
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 14 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?	Choose the correct choice from the following answers: A) 477 B) 420 C) 279 D) 276 E) 291

Solution: 1h ----- 5   ? ------ 60   12 h   RS = 14 + 21= 
14 + 21 = 35
35   T= 12   D = 35 * 12= 
35 * 12 = 420
420.Answer: 420
Answer: B
A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride. The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. If the water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloride stays the same, what will be the concentration of water in the mixture in 2 hours?	Pick:
A) 43% B) 50% C) 52% D) 54% E) 56%

Solution: The tank of 24 gallons is filled to a quarter so it had 6 gallons of water with 40% sodium chloride. In 2 hrs, .5*2 = 1 gallon of pure water (0% sodium chloride) will evaporate.   In essence, the initial mix of 6 gallons (40% sodium chloride) was a mix of 5 gallons of x% sodium chloride and 1 gallon of pure water.   Working with sodium chloride concentrations:   w1/w2 = (A2 - Avg)/(Avg - A1)   5/1 = (0 - 40)/(40 - x)   x = 48   So concentration of water is   100 - 48= 
  100 - 48 = 52
52%   ANSWER:52%
Answer: C
Find the roots of the quadratic equation: x2 + 2x - 15 = 0?	Answers: A) -5,3 B) 6,5 C) 8,9 D) 7,6 E) 3,5

Solution: Explanation:   x2 + 5x - 3x - 15 = 0   x(x + 5) - 3(x + 5) = 0   (x - 3)(x + 5) = 0   => x = 3 or x = -5.   -5,3nswer -5,3
Answer: A
Pipe A can fill a tank in 24 minutes. Pipe B can fill the same tank 6 times faster than pipe A. If both the pipes are connected to the tank so that they fill the tank simultaneously, how long will it take for the empty tank to overflow?	Choose the correct choice from the following options
A) 4 minutes
B) 32/7 minutes
C) 192/7 minutes
D) 3 minutes
E) 28 minutes

Solution: Pipe A can fill a tank in 24 minutes --> the rate of A = 1/24 tank/minute;   Pipe B can fill the same tank6 times fasterthan pipe A --> the rate of B = 1/24 + 6/24 = 7/24 tank/minute.   Their combined rate = 1/24 + 7/24 = 1/3tank/minute;   Therefore, A and B can fill the tank in 3 minutes.   Answer: 3 minutes
Answer: D
A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
Select: A) 12899 B) 12800 C) 27891 D) 18992 E) 78812

Solution: 16*8: x*4 = 5:2   x = 12.8   => Rs.12800   Answer: 12800
Answer: B
A and B started a business investing Rs. 75,000 and Rs 20,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?
Choose the correct choice from the following choices.
A) 9:2	B) 3:2	C) 18:20	D) 18:4	E) 13:4

Solution: A: B = 75000 : 20000   = 75 : 20   = 13 : 4   ANSW13:4R:13:4
Answer: E
A boatman can row 3 km against the stream in 30 minutes and return in 18 minutes. Find the rate of current ?	Options.
A) 2 kmph	B) 8/2 kmph	C) 5/2 kmph	D) 1/2 kmph	E) 2/2 kmph

Solution: Explanation:   Speed in upstream = Distance / Time = 3 x 60/30 = 6 km/hr.   Speed in downstream = 3 x 60/18 = 10 km/hr   Rate of current = (10-6)/2= 
(10-6)/2 = 2
2 km/hr.   2 kmphnswer: 2 kmph
Answer: A
If a(a + 4) = 21 and b(b + 4) = 21, where a ≠ b, then a + b =
Select
A) −4
B) −5
C) 2
D) 46
E) 48

Solution: i.e. if a = 3 then b = -7   or if a = -7 then b = 3   But in each case a+b = -7+3 = -4   −4nswer: option −4
Answer: A
Two representatives must be selected from each of two groups of students. One group consists of two men and one woman, and the other group consists of two women and one man. What is the probability that 2 men and 2 women will be selected ?  Answers:
A) 1/6
B) 1/4
C) 5/9
D) 1/3
E) 1/2

Solution: Group 1: 2 Men and 1 Woman   Group 2: 1 Men and 2 Woman   Need: 2 Men and 2 women   5/9ase 1: 2 Men from Group 1 and 2 women from group 2 - 25/92*25/92 = 1 ways   5/9ase 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 2*1*1*2 = 4 ways   Total Favorable cases = 1+4= 
1+4 = 5
5   Total Possible ways of selecting students 2 from each group= 35/92*35/92 = 3*3= 
3*3 = 9
9   Probability= 5/9   Answer : Option 5/9
Answer: C
Two stations A and B are 110 km apart on a straight line. One train starts from A at 5 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?  Choose the correct choice from the following options: A) 11 B) 10 C) 8 D) 12 E) 15

Solution: Suppose they meet x hours after 5 a.m.   Distance covered by A in x hours = 20x km.   Distance covered by B in (x - 1) hours = 25(x - 1) km.   Therefore 20x + 25(x - 1) = 110   45x = 135   x = 3.   So, they meet at 8 a.m.   Answer: 8
Answer: C
At a company, the average wage of male employees is $4 per hour, and the average wage of female employees is $8 per hour. If the average wage of all employees is $7.5 per hour, what is the ratio of the number of male employees to the number of female employees?
Choose the correct choice from the following answers:	A) 1 to 7	B) 2 to 3	C) 3 to 2	D) 5 to 3	E) 2 to 1

Solution: 1 to 7verage hourly wage of male employees = 4 $   1 to 7verage hourly wage of female employees = 8 $   1 to 7verage hourly wage of all employees = 7.5 $   Let number of male employees = m   number of female employees = f   7.5 = (4m + 8f ) / m+f   =>7.5m + 7.5f = 4m + 8f   => 3.5m = .5f   => m/f = .5/.15 = 1/7   1 to 7nswer 1 to 7
Answer: A
A sum of Rs. 12500 amounts to Rs. 16500 in 4 years at the rate of simple interest. What is the rate of interest?	Select.
A) 4% B) 5% C) 6% D) 8% E) 14%

Solution: S.I. = (16500 - 12500) = Rs. 4000/-   Rate = (100 * 4000) / (12500 * 4)= 
(100 * 4000) / (12500 * 4) = 8
8%   ANSWER:8%
Answer: D
what is the probability of getting 53 mondays in a leap year?  Choose the correct answer
A) 1/7	B) 2/7	C) 3/7	D) 4/7	E) 5/7

Solution: in a leap year contains 52 monday's since 52 weeks are present and 2 days extra   it may be sunday and monday   2.monday and tuesday   3.tuesday and thursday   4.thursday and friday   similary 7 alternatives are possible .among this only 2 are possible cases so 2/7   ANSWER:2/7
Answer: B
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 18 kmph and 72 kmph. After how much time will the trains meet? Choose the correct choice from the following answers:
A) 20/8 sec  B) 20/4 sec  C) 20/7 sec  D) 4 sec  E) 60/7 sec

Solution: They are moving in opposite directions, relative speed is equal to the sum of their speeds.   Relative speed = (18 + 72)*5/18 = 5*5= 
5*5 = 25
25 mps.   The time required= d/s = 100/25= 
100/25 = 4
4 sec.Answer:4 sec
Answer: D
The volume of the largest right circular cone that can be cut out of a cube of edge 7 cm is :
Choose the correct option.
A) 89.8 cm³	B) 92.5 cm³	C) 132.8 cm³	D) 144.5 cm³	E) none

Solution: Sol.   Volume of the block = (10 * 5 * 2) cm³.   Volume of the cone carved out = [1/3 * 22/7 * 3 * 3 * 7= 
1/3 * 22/7 * 3 * 3 * 7 = 66
66 cm³   ∴ Wood wasted= (100 - 66)= 
(100 - 66) = 34
34%.   89.8 cm³nswer 89.8 cm³
Answer: A
A factory produces 6400 toys per week. If the workers at this factory work 3 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?  Pick:  A) 1375 toys  B) 2133 toys  C) 3375 toys  D) 4375 toys  E) 5375 toys

Solution: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 3 days) by 3.   6400 / 3= 2133 toys   correct answer 2133 toys
Answer: B
There are three different hoses used to fill a pool: hose x, hose y, and hose W. Hose x can fill the pool in a days, hose y in b days, and hose W in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true?
I. d<c
II. d>b
III. c/3<d<a/3
Choose the correct choice from the following choices.
A) I
B) III
C) II&III
D) II
E) I&II

Solution: Name T = full pool   X fills a pool in a days ==> 1 day X fills: T/a   Y fills a pool in b days ==> 1 day Y fills: T/b   W fills a pool in c days ==> 1 day W fills: T/c   1 day (X+Y+W) together fill: T(1/a + 1/b + 1/c)   d days (X+Y+W) together fill: T   ==> d = Tx1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca)   ==>d = abc/(ab+bc+ca)   d cannot be greater than c ; d is greater than b ; d is greater than c/3 but not less than a/3   II
Answer: D
A basketball team composed of 12 players scored 100 points in a particular contest. If none of the individual players scored fewer than 7 points, what is the greatest number of points Q that an individual player might have scored?  Choose the correct answer:	A) 7	B) 13	C) 16	D) 21	E) 23

Solution: General rule for such kind of problems:   to maximize one quantity, minimize the others;   to minimize one quantity, maximize the others.   Thus to maximize the number of points of one particular player minimize the number of points of all other 11 players.   Minimum number of points for a player is 7, so the minimum number of points of 11 players is 7*11= 
7*11 = 77
77.   Therefore, the maximum number of points Q for 12th player is  100-77= 
 100-77 = 23
23.   Answer: 23.
Answer: E
A family consists of two grandparents, two parents, and four grandchildren. The average age of the grandparents is 66 years, the average age of the parents is 40 years, and the average age of the grandchildren is 9 years. What is the average age (in years) of the family?
Choose the most appropriate option.
A) 27	B) 29	C) 31	D) 33	E) 35

Solution: Total age of the grandparents = 66 Ã— 2 = 132   Total age of the parents = 40 Ã— 2 = 80   Total age of the grandchildren = 9 Ã— 4 = 36   Average age of the family = (132+80+36)/8 = 248/8= 
248/8 = 31
31 years   The answer is 31.
Answer: C
The amount of principal Rs.8000 at compound interest at the ratio of 5% p.a. for 2 years is Choose the correct choice from the following:	A) s.9621	B) s.6921	C) s.8820	D) s.6261	E) s.6361

Solution: c.i=p(1+r/100)^n   =8000(1+5/100)^2   =Rs8820   ANSWER:s.8820
Answer: C
A baseball game is played at Wickley Field. The Blues vs. The Grays. 25% of all players hit a home-run (hit the ball out of the park). Some players on The Grays team were injured, so they didn't play. If the ratio of players of the teams is 5:4, respectively, and the percentage of players who hit a home-run for The Blues is 15%, what percentage of players for The Grays hit a home-run?
Choices.
A) 40% B) 45% C) 35% D) 45.5% E) 35.5%

Solution: Let B and G be number players Blues and Grays, respectively, and h represent hit a home-run.   B + G = total players.   45%:G = 5:4   45%h/45% = 15%   Gh/G = ?   [(5)(45%h/45%) + (4)(Gh/G)]/(5 + 4) = 25%   [(5)(15%) + (4)(Gh/G)]/9 = 25%   Gh/G = 45%   Answer: 45%
Answer: B
John can eat a quarter of a pizza in one minute. How long does it take John to eat one pizza and a half?
Options
A) 1 min
B) 3 min
C) 7 min
D) 6 min
E) 9 min

Solution: The above problem could also be solved by dividing the mixed number 1 and 1/2 by 1/4   1 (1/2) * 1 / 4 = 3 / 2 * 4 / 1= 
3 / 2 * 4 / 1 = 6
6 minutes.   correct answer 6 min
Answer: D
If 5% more is gained by selling an article for Rs. 360 than by selling it for Rs. 340, the cost of the article is	Choose the correct answer.
A) 289  B) 400  C) 200  D) 288  E) 111

Solution: Explanation:   Let C.P. be Rs. x.   Then, 5% of x = 360 - 340= 
360 - 340 = 20
20   x/20= 20 => x = 400   Answer: 400
Answer: B
At golds gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class?
Choose one.
A) 20 B) 24 C) 36 D) 48 E) 96

Solution: We are given that golds gym class can be divided into 8 teams or 12 teams, with an equal number of players on each team. Translating this into two mathematical expressions we can say, where G is the total number of students in the gym class, that:   G/8 = integer and G/12 = integer   This means that G is a multiple of both 8 and 12.   We are asked to determine the lowest number of students in the class, or the lowest value for variable “G”. Because we know that G is a multiple of 8 and of 12, we need to find the least common multiple of 8 and 12. Although there are technical ways for determining the least common multiple, the easiest method is to analyze the multiples of 8 and 12 until we find one in common.   Starting with 8, we have: 8, 16, 24, 32   For 12, we have: 12, 24   For the multiples of 12, we stopped at 24, because we see that 24 is also a multiple of 8. Thus, 24 is the least common multiple of 8 and 12, and therefore we know that the lowest possible number of students in the gym class is 24.   Answer 24.
Answer: B
Reena and Shaloo are partners in a business. Reena invests Rs. 35,000 for 8 months and Shaloo invests Rs. 42,000 for 10 months. Out of a profit of Rs. 31,570, Reena's share is : Pick:  A) Rs. 9471  B) Rs. 12,628  C) Rs. 18,040  D) Rs. 18,942  E) Rs. 18,000

Solution: Explanation:   Ratio of their shares = (35000 * 8) : (42000 * 10) = 2 : 3.   Reena's share = Rs.   (31570âˆ—2/5)   = Rs. 12628.   ANSWER IS Rs. 12,628
Answer: B
What will be the LCM of 8, 24, 36 and 54	Choose the correct choice from the following answers:
A) 54	B) 108	C) 216	D) 432	E) None of these

Solution: Explanation:   L216M of 8-24-36-54 will be     2*2*2*3*3*3= 
  2*2*2*3*3*3 = 216
216   Answer: Option 216
Answer: C
6x − 24 = 6y
5y + 5x = 15
Which of the following is the number of solutions to the system of equations shown above? Choose the correct choice from the following answers.
A) Exactly one
B) Exactly three
C) Exactly two
D) More than three
E) None

Solution: 6x − 24 = 6y   => 6x - 6y = 24   => x- y =4 -- 1   5y + 5x = 15   =>x + y = 3 -- 2   From equation 1 and 2 , we get   2x = 7   => x=3.5   y=.5   Therefore , the given system will have Exactly one solution   Exactly onenswer : Exactly one
Answer: A
Each of 435 bags contains at least one of the following three items: coconut, almonds, and peanuts. The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. The number of bags that contain only almonds is 20 times the number of bags that contain only coconut and peanuts. The number of bags that contain only peanuts is one-fifth the number of bags that contain only almonds. 210 bags contain almonds. How many bags contain only one kind of item?	Choose one.
A) 256
B) 260
C) 316
D) 320
E) 350

Solution: Fill the diagram step by step:   coconut, almonds, and peanuts.PNGAlso given that there are total of 435 bags and 210 bags contain almonds.   From the diagram 20y=5x --> y=x/4. Now, Total=435={Almonds}+10x+y+x --> 435=210+10x+x/4+x --> x=20 --> # of bags that contain only one kind of item is the sum of yellow segments: 10x+x+5x=16x=320.   Answer: 320.
Answer: D
A train running at the speed of 70 km/hr crosses a pole in 9 sec. What is the length of the train?	Choose the correct choice from the following:	A) 227 m	B) 150 m	C) 167 m	D) 175 m	E) 187 m

Solution: Speed = 70 * 5/18 = 175/9 m/sec   Length of the train = speed * time = 175/9 * 9= 
175/9 * 9 = 175
175 m   Answer: 175 m
Answer: D
A train 108 m long is moving at a speed of 50 km/hr . It crosses a train 112 m long coming from opposite direction in 6 seconds. What is the speed of the second train? Choose the correct choice from the following options:
A) 82 kmph	B) 76 kmph	C) 44 kmph	D) 58 kmph	E) 56 kmph

Solution: Explanation:   Total distance = 108+112= 
108+112 = 220
220 m   Time= 6s   Relative speed = distance/time = 220/6 m/s = 110/3 m/s   = (110/3) × (18/5) km/hr = 132 km/hr   => 50 + speed of second train = 132 km/hr   => Speed of second train = 132-50= 
132-50 = 82
82 km/hr   82 kmphnswer: Option 82 kmph
Answer: A
The average of 35 students in a class is 15 years. The average age of 25 students is 13. What is the average age of remaining 10 students? Choose the correct option: A) 17 years B) 18 years C) 19 years D) 20 years E) 21 years

Solution: Sum of the ages of 14 students   = (15 * 35) - (13 * 25) = 525 - 325= 
525 - 325 = 200
200   Required average= (200/10)= 
(200/10) = 20
20 years.   Answer:20 years
Answer: D
A train 400 m long can cross an electric pole in 40 sec and then find the speed of the train?	Choose the correct option:  A) 36 Kmph  B) 40 Kmph  C) 42 Kmph  D) 45 Kmph  E) 38 Kmph

Solution: Length = Speed * time   Speed = L/T   S = 400/40= 
400/40 = 10
10 M/Sec   Speed= 10*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 36 Kmph   36 KmphNSWER:36 Kmph
Answer: A
A person crosses a 600 meter long street in 5 minutes. What is the speed in Km/hr  Choose the correct option
A) 6.2 km/hr  B) 7.2 km/hr  C) 8.2 km/hr  D) 9.2 km/hr  E) None of these

Solution: ExplanaƟon:   Two things to give aƩenƟon on this quesƟon.   First Ɵme is in minutes, we need to change it to seconds to get speed in m/sec, then we need to get the   final answer in km/hr.   So lets solve this.   Speed=DistanceTimeDistance=650meterTime=5   minutes=300secSpeed=600300=2m/sec=>2   ∗   185km/hr=7.2km/hr   Answer:7.2 km/hr
Answer: B
A 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 27, then how old is B?
Choose the correct choice
A) 11 years B) 10 years C) 18 years D) 189 years E) 28 years

Solution: Let C's age be x years.   Then, B's age = 2x years.   A's age = (2x + 2) years.   (2x + 2) + 2x + x = 27   5x = 25 => x = 5   Hence, B's age = 2x = 10 years.   Answer: 10 years
Answer: B
Two persons start running simultaneously around a circular track of length 440 m from the same point at speeds of 14 kmph and 24 kmph. When will they meet for the first time any where on the track if they
are moving in the opposite direction ?	Choose the correct choice from the following:
A) 144  B) 36  C) 124  D) 42  E) 38

Solution: Time taken to meet the first time = length of track/relative speed   = 440/ (14 +24) (5/18)   = 400/38 *(18/5) = 42 sec.   Answer : 42
Answer: D
Pipe A can fill a tank in 10 hours, pipe B in 5 hours and pipe C in 5 hours. If all the pipes are open, in how many hours will the tank be filled?	Select
A) 2 hours B) 3 hours C) 4 hours D) 5 hours E) 6 hours

Solution: Part filled by A + B + C in 1 hour = 1/10 + 1/5 + 1/5= 1/2   All the three pipes together will fill the tank in 2 hours.   2 hoursnswer:2 hours
Answer: A
In a hockey team of 11 members, the captain's age is 26 years old and the goalkeeper is 3 years older If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?	Choose the correct choice from the following
A) 23 years  B) 24 years  C) 25 years  D) 27 years  E) 29 years

Solution: Explanation :   Let the average age of the whole team be x years.   11x - (26 + 29) = 9(x - 1)   11x - 9x = 46   2x = 46   x = 23   So, average age of the team is 23 years.   23 yearsnswer : 23 years
Answer: A
Let y = 2m + x^2 and m = 5x + 3. If m^2 =64, then which of the following can be a value of 2y + 3m?	Select the correct option
A) 68	B) 58	C) 78	D) 88	E) 98

Solution: m^2 = 64 => m=8   8= 5x+3 => x=1   y= 2*8+1^2 = 17   2y+3m = 2*17+3*8= 
2*17+3*8 = 58
58   Answer : 58
Answer: B
Pat's watch gains an extra 10 seconds every 4 hours. Kim's watch loses 5 seconds every 4 hours. If both watches are set to correct time at 8 o'clock in the morning and run without interruption, after 24 hours, what will be the difference in time between Pat's watch and Kim's watch?	Options: A) 5 min 30 sec B) 4 min 30 sec C) 3 min 30 sec D) 2 min 30 sec E) 1 min 30 sec

Solution: In 24 hours Pat's watch will gain an extra   24/4*10= 
  24/4*10 = 60
60 seconds.   In 24 hours Kim's watch will lose   24/4*5= 
  24/4*5 = 30
30 seconds.   Hence the difference will be   60 + 30= 
  60 + 30 = 90
90 seconds.   Answer: 1 min 30 sec.
Answer: E
Four packages have an average weight of 12.5 pounds. What is the minimum possible weight of the heaviest package in pounds if the median is 10 pounds? Choose the correct choice from the following answers
A) 20	B) 19	C) 18	D) 17	E) 16

Solution: Let us denote the weights of the packages in pounds by a, b, c, d naming from the lightest one to the heaviest one. The median is 10 pounds. Therefore (b + c) / 2 = 10.   b + c = 20   The average is 12.5 pounds. Therefore (a + b + c + d) / 4 = 12.5.   a + (b + c) + d = 50   a + 20 + d = 50   a + d = 30   The weight a must be no greater than 10, since 10 is the median. Therefore the minimum possible weight of the heaviest package is 30 – 10 = 20 pounds (all the other packages would weigh 10 pounds in this case).   20nswer: 20
Answer: A
If xerox paper costs 5 cents a sheet and a buyer gets 10% discount on all xerox paper one buys after the first 2000 papers and 20% discount after first 10000 papers, how much will it cost to buy 20000 sheets of xerox paper?	Answers.
A) $1250  B) $1060  C) $1350  D) $900  E) $1000

Solution: 30 sec approach - solve it using approximation   20000 sheet at full price, 5 cent = 1000   20000 sheet at max discount price, 4 cent = 800   Your ans got to be between these two.   Ans $900 it is.
Answer: D
A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in - days if they work together.
Pick
A) 5 6/2 B) 3/15 C) 8/7 D) 22 1/2 E) 1/9

Solution: Explanation :   If A completes a work in 1 day, B completes the same work in 3 days   Hence, if the difference is 2 days, B can complete the work in 3 days   => if the difference is 60 days, B can complete the work in 90 days   => Amount of work B can do in 1 day= 1/90   Amount of work A can do in 1 day = 3 × (1/90) = 1/30   Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45   => A and B together can do the work in 45/2 days = 22 ½ days   ANSWER:22 1/2
Answer: D
The sum of first 45 natural numbers is
Pick: A) 1035 B) 1280 C) 2070 D) 2140 E) None

Solution: Solution   We know that(1+2+3+.....+45)	= n(n+1)/2   Therefore (1+2+3+....+45)	=(45×46 / 2)   = 1035.   1035nswer 1035
Answer: A
The ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 5292 sq cm. What is the ratio of the width and the area of the rectangle?  Choose the correct option
A) 1:72
B) 1:76
C) 1:80
D) 1:84
E) 1:88

Solution: Let the length and the width be 4x and 3x respectively.   Area = (4x)(3x) = 5292   12x^2 = 5292   x^2 = 441   x = 21   The ratio of the width and the area is 3x : 12x^2 = 1 : 4x = 1 : 84   The answer is 1:84.
Answer: D