MU-NLPC/Calc-aqua_rat huggingface dataset:
Samantha's investment portfolio consists of three stocks: an airline, a bank, and a computer company. In the month of February, the price of the airline's stock rose by 10%, that of the bank decreased by 15% and that of the computer company also decreased by 12%, but the overall value of her portfolio increased. If Samantha owns equal amounts of all three stocks, which of the following could be the initial prices of the three stocks in the order airline, bank, and computer company respectively?  Options: A) $75, $25, $20 B) $65, $60, $60 C) $65, $55, $90 D) $55, $85, $40 E) $25, $60, $70

Solution: Since Samantha owns equal amounts of stocks, the 10% increase alone should set off the 15% decrease in each of the other two stocks. i.e The stock which increased should have a substantially higher value than the two stocks which decreased. Between B and A, A is obviously the safer bet and is the right answer.   $75, $25, $20nswer is $75, $25, $20.
Answer: A
A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1.5 cm when a man gets on it. The mass of man is Pick one:
A) 12 kg B) 90 kg C) 72 kg D) 96 kg E) None

Solution: Solution   Volume of water displaced	= (3 x 2 x 0.015)m3   = 0.09m3.   Mass of man	=Volume of water displaced ×Density of water   = (0.09×1000) kg   = 90 kg.   Answer 90 kg
Answer: B
Tough and Tricky questions: Ratios
4/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip?
Select the correct option:
A) 1/2
B) 2/3
C) 13/15
D) 23/30
E) 4/5

Solution: let total no. of students be 30   students left on a field trip = 4/5(30) =24   thus 6 students left behind   1/3(6)=2 students did not want to go. thus 4 students want to go on the trip   1/2(4)=2 were able to join the other students on the field trip.   thus total number of students that went on a field trip =24+2= 
24+2 = 26
26   thus required fraction= 26/30 =13/15   13/15
Answer: C
A group of people were given 2 puzzles. 70% people solved puzzle X and 89% people solved puzzle Y. What is the maximum and minimum percentage of people who could have solved both the puzzles?	Choose one:
A) 11%, 0% B) 49%, 33% C) 70%, 57% D) 79%, 68% E) 89%, 79%

Solution: To solve this question, we don't need any formulas. Just read the question carefully. If 70% of the people solved puzzle X and 89% solved puzzle Y, then maximum % that can solve both correctly can only be 70%. From the given options, only D looks good   Answer 70%, 57%
Answer: C
A tradesman by means of his false balance defrauds to the extent of 30%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?	Options
A) 17% B) 77% C) 44% D) 16% E) 69%

Solution: g% = 30 + 30 + (30*30)/100= 
30 + 30 + (30*30)/100 = 69
69%   Answer: 69%
Answer: E
If a train, travelling at a speed of 180 kmph, crosses a pole in 6 sec, then the length of train is?
Answers:
A) 300 B) 125 C) 288 D) 266 E) 121

Solution: D = 180 * 5/18 * 6= 
180 * 5/18 * 6 = 300
300 m   300nswer: 300
Answer: A
Let A be the positive integer satisfying the following equation.
9/10
+
99/102th +
999/103rd + · · · +
9999999999/1010th =
A/1010th
How many 8’s appear in the decimal representation of A ? Select
A) 0	B) 1	C) 5	D) 8	E) 9

Solution: The sum equals (1- 0.1) + (1- .01) +...+ (1 - .0000000001) = 10 .1111111111 =   9:8888888889. Thus A = 98888888889   correct answer 9
Answer: E
A man was asked to state his age in years. His reply was , "Take my age 6 years hence, multiply it by 6 and subtract 6 times my age 6 years ago and you will know how old I am." What was the age of the person ?	Choose the correct answer
A) 18
B) 92
C) 72
D) 26
E) 19

Solution: Explanation:   Let the present age of person be x years.   Then, 6(x + 6) - 6(x - 6 ) = x <=> (6x + 36) - (6x - 36) = x <=> x = 72..   Answer: 72
Answer: C
In what time will a railway train 120 m long moving at the rate of 36 kmph pass a telegraph post on its way? Choose the correct choice from the following answers:
A) 12 sec
B) 7 sec
C) 8 sec
D) 9 sec
E) 10 sec

Solution: T = 120/36 * 18/5= 
120/36 * 18/5 = 12
12 sec   12 secnswer:12 sec
Answer: A
Given that there are 8 cricket players per team, how many ways can you select 10 cricket players from 2 teams if no more than 3 players can be selected from each team?  Choose the correct choice from the following answers.
A) 2456  B) 3136  C) 1452  D) 3565  E) 2134

Solution: Now from each group we have to select 5 persons only: 8C3 * 8C3 = 56 * 56= 
56 * 56 = 3_136
3136   Total ways=3136 ways.   Answer 3136
Answer: B
The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?	Choose the correct choice from the following answers.
A) 76 Kmph B) 68 Kmph C) 79 Kmph D) 25 Kmph E) 28 Kmph

Solution: Length of the two trains = 600m + 400m   Speed of the first train = X   Speed of the second train= 48 Kmph   1000/X - 48 = 180   1000/x - 48 * 5/18 = 180   50 = 9X - 120   X = 68 Kmph   Answer: 68 Kmph
Answer: B
In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?  Choices.
A) 30%	B) 40%	C) 70%	D) 80%	E) 90%

Solution: C   70%   Let C.P. = $ 100. Then, profit = $ 320, S.P. = $ 420   New C.P. = 125% of $ 100 = $ 125.   New S.P. = $ 420   Profit = 420 - 125= 
420 - 125 = 295
$ 295   Required percentage= 295/420 * 100 = 1475/21 = 70%
Answer: C
Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm?  Choose the correct answer:
A) 827 cm2 B) 216 cm2 C) 285 cm2 D) 178 cm2 E) 176 cm2

Solution: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)   = 1/2 (20 + 18) * (15)   = 285 cm2   Answer:285 cm2
Answer: C
P has $35 more than what Q and R together would have had if both B and C had 1/7 of what P has. How much does P have? Pick one:
A) $45
B) $47
C) $49
D) $51
E) $53

Solution: P = (2/7)*P+35   (5/7)*P=35   P=49   The answer is $49.
Answer: C
The total expense of a boarding house is partly fixed and partly variable with the number of boarders. When the number of boarders is 25, then the charge is Rs 70 per head and the same is Rs 60 when the number of boarders is 50. What would be the charge per head if there are 100 boarders?
Select the correct option:  A) 51  B) 52  C) 53  D) 54  E) 55

Solution: consider x as partly fixed and y as partly variable.   as number of boarders has been changing consider it as y.   sum(total expense including fixed n change)=x+25y=1750(25*70)   x+60y=3000(60*50)   by solving those equations v get x as 500 and y as 50   now do for 100 boarders 100y=100*50=5500   per head consists of 5500/100= 
5500/100 = 55
55.   ANSW55R:55
Answer: E
If YWVSQ is 25 - 23 - 21 - 19 - 17, Then MKIGF  Choose the correct choice:	A) 13 - 11 - 9 - 7 - 9	B) 13 - 11 - 9 - 7 - 6	C) 13 - 11 - 9 - 7 - 7	D) 13 - 11 - 9 - 7 - 3	E) 13 - 11 - 9 - 7 - 1

Solution: MKIGF = 13 - 11 - 9 - 7 - 6   Note: this is a dummy question. Dont answer these questions   Answer:13 - 11 - 9 - 7 - 6
Answer: B
The salary of a person was reduced by 25%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?	Pick.
A) 10%	B) 33.33%	C) 20%	D) 25%	E) 50%

Solution: Let the original salary be $100   new salary = $75   increase on 75 = 25   increase on 100 = [(25/75)100]% = 33.33%   Answer is 33.33%
Answer: B
Find the numbers which are in the ratio 5:2:4 such that the sum of the first and the second added to the difference of the third and the second is 18?
Select.
A) 4,3,22
B) 4,4,22
C) 10,4,8
D) 9,6,12
E) 9,2,23

Solution: Let the numbers be a, b and c.   a:b:c = 5:2:4   Given, (a + b) + (c - b) = 21   => a + c = 21   => 5x + 4x = 18 => x = 2   a, b, c are 5x, 2x, 4x   a, b, c are 10, 4, 8.   Answer:10,4,8
Answer: C
If m and n are even integers, which of the following is an odd integer?  Pick one:
A) mn + 2
B) m(n − 1)
C) m(m + 5)
D) 3m + 4n
E) (m + 3)(n − 1)

Solution: If m and n are even integers, then:   A. mn + 2: even + even = even   B. m(n − 1): even(odd) = even   C. m(m + 5): even(odd) = even   D. 3m + 4n: even + even = even   E. (m + 3)(n − 1): (odd)(odd) = odd.   Answer is (m + 3)(n − 1).
Answer: E
By how much does the larger root of the equation 2a^2+5a = 12 exceed the smaller root?	Choose the correct choice from the following choices.
A) 5/2 B) 10/3 C) 7/2 D) 14/3 E) 11/2

Solution: For 2a^2+5a = 12 Roots are [-5 + sqrt(25 + 96)]/4 OR [-5 - sqrt(25 + 96)]/4   = 1.5 OR -4   Hence larger root 1.5 is  1.5 - (-4)= 
 1.5 - (-4) = 5.5
5.5= 11/2 greater than smaller root (-4).   Hence option (11/2).
Answer: E
The cross-section of a water channel is a trapezium in shape. If the channel is 14 meters wide at the top and 8 meters wide at the bottom and the area of cross-section is 880 square meters, what is the depth of the channel (in meters)?	Options:
A) 50
B) 60
C) 70
D) 80
E) 90

Solution: 1/2 * d * (14 + 8) = 880   d = 80   The answer is 80.
Answer: D
At what time between 5 and 6 o' clock are the hands of a 3 minutes apart ?  Choose the correct choice from the following options: A) 24 B) 55 C) 66 D) 88 E) 21

Solution: In this type of problems the formuae is   (5*x+ or - t)*12/11   Here x is replaced by the first interval of given time. Here x is 5.   t is spaces apart   Case 1 : (5*x + t) * 12/11   (5*5 + 3) * 12/11   28 * 12/11 = 336/11= min   therefore the hands will be 3 min apart at 31 5/11 min past 5.   Case 2 : (5*x - t) * 12/11   (5*5 -3 ) * 12/11   22 *12/11= 
22 *12/11 = 24
24 min   therefore the hands will be 3 min apart at 24 min past 5   24nswer: 24) 24min
Answer: A
Benny goes to the market for buying some apples to be distributed between her nine kids equally.She takes 360 dollars with her .The cost of each apple is 3 dollars .How many apples does she buy to share them equally between her six kids? Choose the correct choice from the following answers:
A) 20  B) 9  C) 15  D) 7  E) 10

Solution: cost of each apple = 3 dollars   Apples that Benny can buy with the amount she has=360/3= 
360/3 = 120
120.   Apples that each kid gets evenly= 120/6= 
120/6 = 20
20 Apples.   So the answer is 20=20
Answer: A
A and B complete a work in 4 days. A alone can do it in 6 days. If both together can do the work in how many days?
Options
A) 3.75 days  B) 3.7 days  C) 3.6 days  D) 2.4 days  E) 5.75 days

Solution: 1/4+ 1/6 = 5/12   12/5= 
12/5 = 12/5 = around 2.4
2.4 days   Answer:2.4 days
Answer: D
The ratio of the present age of Viju to that of Aju is 7:2. Four years from now, the ratio of the ages of Viju to Aju will be 5:2. What was Viju age 6 years ago ? (RBI Assistant 2015)  Choose the correct choice:
A) 24 B) 18 C) 12 D) 15 E) 13

Solution: Let the present age of Viju be 7x years and that of Aju be 2x years.   Then, 4 years from now   7x + 4 / 2x + 4 = 5 / 2   or 4x = 12   or x = 3   Viju present age = 7 * 3= 
7 * 3 = 21
21 years   Viju age 6 years ago= 21 - 6= 
21 - 6 = 15
15 years   answer :15
Answer: D
How many prime numbers are between 25/3 and 84/6?	Choices
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: 25/3 = 8.xxx   84/6= 
84/6 = 14
14.xxx   So we need to find Prime numbers between 8 (Exclusive) - 13 (Inclusive)   There are 2 Prime numbers 1113   Hence answer will be (2) 2   2
Answer: B
Two tables are purchased for the total cost of Rs. 5000. First table is sold at 40% profit and second at 40% loss. If selling price is same for both the tables, what is the cost price of the table that was sold at profit?
Select the correct option:
A) Rs. 1500.	B) Rs. 2500.	C) Rs. 3500.	D) Rs. 4500.	E) Rs. 5500.

Solution: Ans: 140% of cost price of first table = 60% of cost price of second table.   Therefore, Cost price of first table : Cost price of second table   = 60 : 140 = 3 : 7   Therefore, Cost price of first table = 3/10× 5000 = Rs. 1500.   Rs. 1500.nswer Rs. 1500.
Answer: A
The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 21. What is the last numbers? Choose the correct answer.
A) 2  B) 4  C) 9  D) 5  E) 7

Solution: A + B + 9 = 48   B + 9 + D = 45   A + D = 21   A – D = 3   A + D = 21   2D = 18   D = 9   ANSWER 9
Answer: C
Broke’s only source of income comes from his job as a question writer. In this capacity, Broke earns a flat salary of $200 per week plus a fee of $9 for every question that he writes. Every year, Broke takes exactly two weeks of unpaid vacation to visit his uncle, a monk in Tibet, and get inspired for the next year. If a regular year consists of 52 weeks and the number of questions that Broke wrote in each of the past 5 years was an odd number greater than 20, which of the following could be Broke’s median annual income over the past 5 years?
Choose the correct choice from the following:  A) $22,474  B) $25,673  C) $27,318  D) $28,477  E) $31,227

Solution: Okay u just need less than one min to answer this question. any odd number greater than 20 means that that last digit must be 1,3,5,7, or 9. 9$ per week for every question. So (odd)(odd) will give odd digit. A and C out. (50 weeks) (200) = 10,000. subtract this amount from option B, $28,477 and E and u will find that only option $28,477 is divisible by 9 (once 10,000 is subtracted from 28477) so its the right choice..$28,477.
Answer: D
From a pack of 52 cards, 1 card is drawn at random. What is the probability that a jack, queen, or king is drawn?  Select the correct option:
A) 1/4 B) 1/12 C) 2/13 D) 3/13 E) 3/26

Solution: The total number of cards is 52.   The number of jacks, queens, or kings is 12.   P(jack, queen, king) = 12/52 = 3/13   The answer is 3/13.
Answer: D
At a dinner party, 5 people are to be seated around a circular table. 2 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?	Choose the correct answer
A) 5  B) 10  C) 24  D) 32  E) 120

Solution: If it were a line/column combination/permutation problem, the solution would be : 5! = 120.   However it is a circular combination/permutation problem, the solution would be: 5!/5 = 24 because you need to keep 1 person static. For that, lets say A cannot move from his place and next to him you can put 4 people. Then 3, then 2 and 1. So the no. of ways 5 people can be seated around a circular table is 4! = 24.   ANS:24
Answer: C
3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 15 pumps work to empty the tank in 1 day?
Answers.
A) 3.5
B) 4.8
C) 5.1
D) 5.2
E) 6.3

Solution: 3 pumps take 16 hrs total (8 Hrs a day)   If 1 pump will be working then, it will need   16*3= 
  16*3 = 48
48 hrs   1 pump need 48 Hrs   If I contribute 15 pumps then   48/15=3.5 hrs.   answer :3.5
Answer: A
Out of four consonants and three vowels, how many words can be made so that each word contains two consonants and three vowels?
Select the correct option:
A) 480
B) 540
C) 600
D) 720
E) 900

Solution: 4C2 x 3C3 x 5! = 720   The answer is 720.
Answer: D
Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?  Pick:
A) 1000
B) 3889
C) 8908
D) 3780
E) 2709

Solution: 1120 = P [1 + (5*12/5)/100]   P= 1000   1000nswer: 1000
Answer: A
The average marks of a class of 40 students is 44 and that of another class of 45 students is 70. Find the average marks of all the students?	Choose the correct choice from the following answers:
A) 52.6
B) 52.4
C) 52.1
D) 69.5
E) 52.9

Solution: Sum of the marks for the class of 40 students = 40 * 44= 
40 * 44 = 1_760
1760   Sum of the marks for the class of 45 students= 45 * 70= 
45 * 70 = 3_150
3150   Sum of the marks for the class of 85 students=   2760 + 3150= 
2760 + 3150 = 5_910
5910   Average marks of all the students= 5910/85 = 69.5.Answer: 69.5
Answer: D
Of the families in City X in 1956, 25 percent owned a personal computer. The number of families in City X owning a computer in 1960 was 15 percent greater than it was in 1956, and the total number of families in City X was 5 percent greater in 1956 than it was in 1960. what percent of the families in City X owned a personal computer in 1960?
Choose the correct choice
A) 50%
B) 51.22%
C) 5.26%
D) 7.20%
E) 27.38%

Solution: Say a 100 families existed in 1956 then the number of families owning a computer in 1956 - 25   Number of families owning computer in 1960 = 25 * 115/100= 
25 * 115/100 = 115/4 = around 28.75
28.75   Number of families in 1960= 105   The percentage = 28.75/105 * 100 = 27.38%.   Option: 27.38%
Answer: E
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 8 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is :	Choose the correct choice: A) 22 B) 21 C) 88 D) 37 E) 24

Solution: 24xplanation:   Lot the total number of workers be v Then,   8OOOv = (12000 * 8) + 6000 (v - 8) <=> 2000v = 48000 <=> v = 24   Answer: 24) 24
Answer: E
The average age of 28 students in a group is 16 years. When teacherâ€™s age is included to it, the average increases by one. What is the teacherâ€™s age in years?  Pick one:  A) 45  B) 36  C) 41  D) 51  E) 48

Solution: Sol.   Age of the teacher = ( 29 Ã— 17 â€“ 28 Ã— 16 ) years = 45 years.   45nswer 45
Answer: A
Find the area of a triangle whose sides measure 13 cm, 14 cm and 15 cm.  Choose the most appropriate option:
A) 72 B) 21 C) 84 D) 53 E) 18

Solution: Sol. Let a = 13, b = 14 and c = 15. Then, S = (1/2)(a + b + c) = 21.   (s- a) = 8, (s - b) = 7 and (s - c) = 6.   Area = (s(s- a) (s - b)(s - c)^(1/2) = (21 *8 * 7*6)^(1/2) = 84 cm^2.   Ans: 84
Answer: C
In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?  Choose the correct choice from the following options:
A) 1/68  B) 62/89  C) 12/68  D) 11/84  E) 5/6

Solution: 5/6xplanation:   Let us say the ratio of the quantities of cheaper and dearer varieties = x : y   By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6   Answer:5/6
Answer: E
The average age of the district level hockey team of eleven is 22 years.The average age gets no change when the coach age is also included.what is the age of the coach ?	Pick.
A) 22 yrs.  B) 23 yrs.  C) 25 yrs.  D) 24 yrs.  E) 21 yrs.

Solution: Explanation:   Total age of players in team = 22 x 11 = 242   When coach is included, total members = 12, Avg age is 22   Total age when coach is included = 22x12 = 264   Age of coach = 264-242= 
264-242 = 22
22 yrs.   22 yrs.nswer: 22 yrs.
Answer: A
Sneh's age is 1/6 th of her father's age. Sneh's father's age will be twice of Vimal's age after 10 years. If Vimal's eighth birthday was celebrated two years before, then what is Sneh's present age?  Answers:
A) 10 years
B) 25 years
C) 35 years
D) None of these
E) Cannot be determined

Solution: Solution   Vimal's age after 10 years	= (8+2+10)= 
(8+2+10) = 20
20 years.   Sneh's father age after 10 years= 40 years   Sneh's father Present age	= 30 years   Therefore Sneh's age	= (1/6 x 30)years   = 5 years.   Answer None of these
Answer: D
The wages earned by Robin is 44% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much % is the wages earned by Charles more than that earned by Robin?
Choose the correct choice from the following answers:
A) 23% B) 18.75% C) 30% D) 30.55% E) 100%

Solution: Explanatory Answer   Let the wages earned by Erica be $100   Then, wages earned by Robin and Charles will be $144 and $160 respectively.   Charles earns $44 more than Robin who earns $144.   Therefore, Charles' wage is 44/144*100 = 30.55%.   The correct choice is (30.55%)
Answer: D
Tom was asked how old he was. He replied "In 2 years I will be twice as old as I was five years ago.' How old is he ?	Pick one
A) 11	B) 13	C) 12	D) 15	E) 17

Solution: 12   12   If Tom's age is X years   X+2= 
+2 = 2
2(X-5)   X +2= 
 +2 = 2
2X-10   X=12
Answer: C
The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively.The Sum is : Choose the most appropriate option
A) Rs. 1800 B) Rs. 1450 C) Rs. 1360 D) Rs. 6800 E) None

Solution: Solution   Sum = S.I xT.D/ ( S.I) - ( T.D)= 85 x80/85 - 80=Rs.1360.   Answer Rs. 1360
Answer: C
Consider two statements
Statement 1 => If T is an integer and T=2p+1 where p is not an integer.
Statement 2 => If Y is an integer and Y=2q where q is not an integer
Which of the following correctly specifies the Even/Odd nature of T and Y respectively  Choose the correct choice from the following answers:
A) 1) Odd,Even	B) 2) Odd,Odd	C) 3) Even,Odd	D) 4) Even,Even	E) 5) Cannot be determined

Solution: answer will be 5) Cannot be determined   T = integer   T = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out   if n were even T would odd   if n odd T would be even   ANSW5) Cannot be determinedR IS 5) Cannot be determined
Answer: E
The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 36. Find their present ages.	Select.
A) 20, 28
B) 21, 27
C) 35, 45
D) 35, 55
E) of these

Solution: Let their present ages be 4x, 7x and 9x years respectively.   Then, (4x - 8) + (7x - 8) + (9x - 8) = 36   20x = 60 => x = 3   Their present ages are 12, 21 and 27 years respectively.   ANSWER:21, 27
Answer: B
In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.42, the number of 25 paisa coins is?
Choose the correct option:
A) 31	B) 42	C) 62	D) 72	E) 71

Solution: 5x 6x 2x   50 25 100   250x + 150x + 200x = 4200   600x = 4200   x = 7 => 6x = 42   Answer:42
Answer: B
A meal cost $ 35.50 adn there was no tax. If the tip was more than 5 pc but less than 8pc of the price, then the total amount paid should be: Options:
A) 40-42
B) 39-41
C) 38-40
D) 37-38
E) 36-37

Solution: 5%(35.5) = 1.775   8%(35.5) = 2.84   total amount could have been 35.5+1.775 and 35.5+2.84   => could have been between 37.275 and 38.34   => approximately between 37 and 38   Answer is B.37-38
Answer: D
A box has exactly 100 balls, and each ball is either red, blue, or white. If the box has 12 more blue balls than white balls, and six times as many red balls as blue balls, how many white balls does The box has ?	Choose the correct choice from the following.
A) 8 B) 10 C) 2 D) 14 E) 16

Solution: x = the number of red balls   y = the number of blue balls   z = the number of white balls   From the first sentence we have   Equation #1: x + y + z = 100   ...the box has 12 more blue balls than white balls...   Equation #2: y = 12 + z   ...thrice as many red balls as blue balls...   Equation #3: x = 6y   Solve equation #2 for z: z = y - 12   Now, we can replace both x and z with y in Equation #1   6y + y + (y - 12) = 100   8y - 12 = 100   5y = 112   y = 14   There are 14 blue balls. This is 12 more than the number of white balls, so z = 2. That's the answer. Just as a check, x = 84, and   84 + 14 + 2= 
  84 + 14 + 2 = 100
100.   Answer= 2,(2)
Answer: C
The dimensions of a field are 16.5 m by 10 m. A pit 10 m long, 5.5 m wide and 4 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of field as a result of this operation ?  Options: A) 2 m B) 3 m C) 1 m D) 2.5 m E) 3.5 m

Solution: The volume of the earth removed is 10*5.5*4= 
10*5.5*4 = 220
220 m^3.   The remaining area of the field is   16.5*10 - 10*5.5= 
  16.5*10 - 10*5.5 = 110
110 m^2.   220 m^3 of the earth evenly spread over the area of 110 m^2 will rise the height by (height)= (volume)/(area) = 220/110= 
220/110 = 2
2 m.   2 mnswer: 2 m
Answer: A