MU-NLPC/Calc-aqua_rat huggingface dataset:
The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 50% profit?	Choose the correct answer.
A) 220
B) 230
C) 960
D) 780
E) 400

Solution: C   C.P. = Rs. x.   Then, 832 - x = x - 448   2x = 1280 => x = 640   Required S.P. = 150% of Rs. 640 = 150/100 * 640 = Rs. 960.
Answer: C
At a certain college there are twice as many history majors as English majors and three times as many history majors as mathematics majors. What is the ratio of the number of english majors to the number of mathematics majors?	Pick one.
A) 6 to 1  B) 2 to 3  C) 3 to 2  D) 1 to 5  E) 1 to 6

Solution: This is how I translated the question:   At a certain college there are twice as many english majors as history majors   H = 2E   and three times as many english majors as mathematics majors.   H = 3M   What is the ratio of the number of history majors to the number of mathematics majors?   What is E:M?   Just set E equal to each other to get the ratio in terms of E and M.   2E = 3M   E/M = 3/2   The answer is 3:2   Answer : 3 to 2
Answer: C
Choose the missing terms out of the given alternatives.
AZ, BY, CX, DW, EV ?  Choose the correct answer:  A) EF  B) GH  C) ED  D) FU  E) KN

Solution: D   FU   The first letter moves one step forward. The second letter moves one step backward.
Answer: D
If 2|2 –a| = 5, what is the sum of all the possible values for a ? Choose the correct choice from the following answers:  A) 1/2  B) 2  C) 5/2  D) 4  E) 5

Solution: if a<2, then 2-a=5/2; a=-1/2   if a>2 , then a-2=5/2; a=9/2   9/2-1/2=8/2= 
8/2 = 4
4=4
Answer: D
Carol and Blake invested 12000 and 24000, respectively in a business. Carol manages the business and for this he receives 9% of the profit while the rest is divided in proportion to their capitals. Find the share of Carol in a profit of 4000.	Answers.
A) 2573.3	B) 1573.3	C) 1565.3	D) 2473.3	E) 6573.3

Solution: The Carol gets for managing   = 9% of Rs. 4000 = 360   Remaining profit = 4000 â€“ 360 = 3640   This is to be divided in the ratio 12000 :24000=12: 24=1:2.   Share of Carol = 1/3 of 3640 = 1213.3   â‡’ Total share of Carol = 360 + 1213.3 = 1573.3.   Answer 1573.3
Answer: B
6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?	Choose the correct choice from the following options:  A) Friday  B) Saturday  C) Wednesday  D) Sunday  E) None of these

Solution: Explanation :   Number of days from 6th March, 2004 to 5th March 2005 = 365 days   (Though Feb 2004 has 29 days as it is a leap year, it will not come in the required period)   365 days = 1 odd day   Given that 6th March, 2005 is Monday   Hence 6th March, 2004 = (Monday - 1 odd day) = Sunday   Answer : Option Sunday
Answer: D
To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took. Select:	A) 375	B) 475	C) 575	D) 675	E) 775

Solution: Let x be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made:   3⋅25+(x−3)⋅30=75+30(x−3)   Therefore: 25x=75+30(x−3)−100   25x=75+30x−90−100   190−75=30x−25   115=5x   x=23   So the company worked 23 days and they made 23⋅25+100=675 pieces.   correct answer 675
Answer: D
Number of ways in which the letters of word PARDENS can be arranged with vowels in alphabetical order, is
Choose the correct choice from the following answers.
A) 360
B) 240
C) 2520
D) 480
E) None of these

Solution: Solution   Order of vowels of fixed   âˆ´ required number of ways are 7!/2!.   Answer 2520
Answer: C
A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day? Choose the correct choice from the following choices:
A) 22
B) 77
C) 26
D) 41
E) 66

Solution: (1 man + 1 woman)'s 1 day work = (1/3 + 1/4) = 7/12 Work done by 1 man and 1 woman in 1/4 day = (7/12 * 1/4) = 7/48   Remaining work = (1 - 7/48) = 41/48   Work done by 1 boy in 1/4 day = ( 1/12 * 1/4) = 1/48   Number of boys required = 41/48 * 41 = 41.   Answer: 41
Answer: D
A shopkeeper sold an article at $1200 and gained a 20% profit. What was the cost price? Choose the correct choice from the following choices.
A) $1000
B) $1020
C) $1040
D) $1060
E) $1080

Solution: Let x be the cost price.   1.2x = 1200   x = 1200/1.2= 
1200/1.2 = 1_000
1000   The answer is $1000.
Answer: A
10 books are placed at random in a shelf. The probability that a pair of books will always be together is ?	Choices:
A) 1/8
B) 1/4
C) 1/5
D) 1/9
E) 1/1

Solution: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!   Required probability = 1/5   Answer:1/5
Answer: C
A and B invests Rs.8000 and Rs.12000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?	Choose the correct answer:  A) 32:99  B) 82:31  C) 8:15  D) 34:89  E) 35:21

Solution: A : B   (8000*4)+(4000*8) : (12000*6)+(9000*6)   64000 : 120000   8 : 15   Answer:8:15
Answer: C
How many different possible arrangements S can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's? Choose the correct choice from the following answers.
A) 360
B) 720
C) 900
D) 1800
E) 5040

Solution: Total ways for arranging without restriction = 7!/ (2!2!) { 2! is becoz of two T's and other 2! for two I's)   Restriction : atleast one character between I's = Possible ways - both I's together i.e.o character between I's   _ _ _ _ _ (I I)   Both I's Together = 6! (Assuming 2 I's as one unit) /2!(for 2 T's) * 2! (No of arrangements of 2 I's)/2! (for 2 I's)   =6!/2!   Therefore ans S= 7!/ (2!2!) -6!/2! = 900   HEN900E 900.
Answer: C
The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 48 years, was replaced by a new person. Find the age of the new person?  Choose the correct choice from the following: A) 18 B) 56 C) 12 D) 17 E) 14

Solution: Initial average age of the 10 persons be P.   Age of the new person Q.   Sum of the ages of the initial 10 persons = 10P   New average   = (P-3) 10(P-3)   = 10P - 48 + Q   => Q = 18   18nswer:18
Answer: A
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
Choose one: A) 33/96 B) 33/91 C) 33/93 D) 13/91 E) 33/99

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91.Answer: 33/91
Answer: B
Find the invalid no.from the following series 15, 16, 33, 105, 424, 2124, 12756	Choose the correct option:  A) 16  B) 33  C) 105  D) 424  E) 2124

Solution: 2nd term = (1st term) * 1 + 1 = 15 *1 + 1= 
15 *1 + 1 = 16
16.   3rd term= (2nd term) * 2 + 2 = 16 * 2 + 2= 
16 * 2 + 2 = 34
34   4th term= (3th term) *3 + 3 = 34 * 3 + 3= 
34 * 3 + 3 = 105
105   5th term= (4th term) * 4 + 4 = 105 * 4 + 4= 
105 * 4 + 4 = 424
424   6th term= (5th term) * 5 + 5 = 424 * 5 + 5= 
424 * 5 + 5 = 2_125
2125   3th term should 34 instead of 33.   33
Answer: B
A shopkeeper sold two radio sets for 792 each, gaining 10% on one, and losing 10% on the other. Then he Choose the correct choice from the following answers
A) neither gains nor loses	B) gains 1%	C) loses 1%	D) gains 5%	E) None of these

Solution: Sol.(c) When selling price of two articles is same and   % gain = % loss   then there will be always loss.   and overall % loss = (10)2⁄100% = 1%. Answer loses 1%
Answer: C
If x and y are numbers such that (x+5)(y-5)=0, what is the smallest possible value of x^2 + y^2 Choices:
A) 0
B) 4
C) 9
D) 25
E) 16

Solution: From (x+5)(y-5)=0 it follows that either x=-5 or y=5. Thus either x^2=25 or y^2=25.   Now, if x^2=8125, then the least value of y^2 is 0, so the least value of x^2 + y^2 = 25 + 0= 
25 + 0 = 25
25.   Similarly if y^2=25, then the least value of x^2 is 0, so the least value of x^2 + y^2 = 0 + 25= 
0 + 25 = 25
25.   Answer: 25.
Answer: D
In how many different ways can the letters of the word ‘GEOMETRY’ be arranged so that the vowels always come together?  Choose the correct choice from the following.
A) 4323
B) 2797
C) 4320
D) 2997
E) 0811

Solution: Explanation:   There are in all 8 letters in the given word of which 3 are vowels. As the vowels should always be together, considering the 3 vowels as one letter, there are in all 6   letters which can be arranged in 6! ways = 720   Also the 3 vowels can be arranged in 3! ways = 6   Total number of arrangements = 720*6= 
720*6 = 4_320
4320   ANSWER:4320
Answer: C
if(x-10)(y-5)(z-2)=1000 then what is the least value of x+y+z? if x,y,z are all integer no.	Choices:
A) 7 B) 8 C) 9 D) 10 E) 11

Solution: (x-10)(y-5)(z-2)=1000   put x=0   y=-5   z=12   then   (0-10)(-5-5)(12-2)=1000   (-10)(-10)(10)=1000   1000=1000   7NSWER:7
Answer: A
In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many S different victory circles are possible? Pick one:	A) 24	B) 52	C) 96	D) 144	E) 648

Solution: Possible scenarios are:   1. Gold/Silver/Bronze/No medal (no ties) - 4!=24;   2. Gold/Gold/Silver/No medal - 4!/2!=12;   3. Gold/Silver/Silver/No medal - 4!/2!=12;   4. Gold/Gold/Gold/No medal - 4!/3!=4.   Total:  24+12+12+4= 
 24+12+12+4 = 52
52   Answer: 52.
Answer: B
Jim and Reneeh will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Reneeh have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win?	Options:
A) 5/6
B) 2/3
C) 1/2
D) 5/12
E) 1/3

Solution: 1/3   probability of jim winning is basically the sum of three probabilities:   probability of jim picking rock and reneeh picking scissors = 1/3*1/3 = 1/9   probability of jim picking scissors and reneeh picking paper = 1/3*1/3=1/9   probability of jim picking paper and reneeh picking rock = 1/3*1/3=1/9   1/9 + 1/9 + 1/9 = 3/9 = 1/3=1/3
Answer: E
In a cinema hall for the matinee show which started at 2.30 pm and ended at 5.30 pm the vehicle parking lot had only three wheelers (auto rickshaws) and four wheelers. Today the wheels of the vehicles parked was counted and found to be 240. What could be the number of three wheelers parked therein ? Choose the correct choice from the following answers.
A) 10 B) 48 C) 37 D) 97 E) 12

Solution: 3X + 4y = 240   by substitute through options 48 is correct   Answer: 48
Answer: B
How many cubes of 3cm edge can be cut out of a cube of 18cm edge  Answers:
A) 36 B) 232 C) 216 D) 455 E) 363

Solution: number of cubes=(18 x 18 x 18) / (3 x 3 x 3) = 216   Answer: 216
Answer: C
A = {2, 3, 5, 7, 11}
B = {2, 4, 6, 13}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?	Choices.
A) 15	B) 16	C) 19	D) 20	E) 36

Solution: This would be the generic strategy:   Step 1: Find out the number of products you get.   5 distinct numbers in set A and 4 distinct in set B so number of products = 5*4= 
5*4 = 20
20   Step 2: Remove the products that appear more than once.   Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B.   2, 3   2, 4, 6   The only product repeated when you take a number from each set is 12. (3*4 and 2*6) Rest all are distinct.   Answer= 20 - 1= 
20 - 1 = 19
19   ANSWER:19
Answer: C
Bruce purchased 7kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?	Choose the correct choice from the following options:  A) A)985  B) B)1050  C) C)1055  D) D)1065  E) E)1075

Solution: Cost of 7 kg grapes = 70 × 7 = 490.   Cost of 9 kg of mangoes = 55 × 9 = 495.   Total cost he has to pay = 490 + 495= 
490 + 495 = 985
985   985
Answer: A
If the reciprocals of two consecutive positive integers are added together, what is the sum in terms of the greater integer p?  Options
A) (2p-1)/(p^3- p) B) (2p-1)/(p^4- p) C) (2p-1)/(p^2- p) D) (2p-1)/(p^2- 2p) E) (2p-4)/(p^2- 3p)

Solution: Let two consecutive positive integers be p and p-1 (Greater integer is p)   So,   (1/p) + [1/(p-1)]   = (2p-1)/p(p-1)   =(2p-1)/(p^2- p)   Answer : (2p-1)/(p^2- p)
Answer: C
Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 20 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?  Select the correct option.
A) 3:5
B) 9:25
C) 5:2
D) 25:9
E) Cannot be determined from the information provided

Solution: Same circumferential rate means that a point on both the gears would take same time to come back to the same position again.   Hence in other words, time taken by the point to cover the circumference of gear A = time take by point to cover the circumference of gear B   Time A = 2*pi*25/Speed A   Time B = 2*pi*10/Speed B   Since the times are same,   50pi/Speed A = 20pi/Speed B   SpeedA/Speed B = 50pi/30pi = 5/2   5:2orrect Option: 5:2
Answer: C
If the price of a certain computer increased 30 percent from d dollars to 351 dollars, then 3d =  Choose the correct choice from the following:
A) 540  B) 570  C) 619  D) 649  E) 710

Solution: Before Price increase Price = d   After 30% Price increase Price = d+(30/100)*D = 1.3d = 351 (Given)   i.e. d = 351/1.3= 
351/1.3 = 270
$270   i.e. 3d= 3*270 = 710   Answer: option 710
Answer: E
The ratio of the ages of Anil and his son at present is 7 : 3. Six years hence, the ratio of the ages of the Anil's wife and the son will be 2 : 1. Find the ratio of the present ages of Anil and his wife?	Answers:
A) 270
B) 266
C) 209
D) 298
E) 277

Solution: 12*8 :16*9 = 18*6   8: 12: 9   9/29 * 870= 
9/29 * 870 = 270
270   270nswer: 270
Answer: A
Income and expenditure of a person are in the ratio 9 : 8. If the income of the person is Rs. 36000, then find his savings?	Answers:
A) 2000
B) 3000
C) 4000
D) 5000
E) 6000

Solution: Let the income and the expenditure of the person be Rs. 9x and Rs. 7x respectively.   Income, 9x = 36000   => x = 4000   Savings = Income - expenditure   = 9x - 8x = x   So, savings =Rs.4000.   Answer: 4000
Answer: C
A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
Choose the correct choice from the following choices
A) Rs. 7500  B) Rs. 9000  C) Rs. 9500  D) Rs. 10,000  E) None

Solution: Solution: A : B : C = (20,000 * 24) : (15,000 * 24) : (20,000 * 18) = 4 : 3 : 3.   So B's share = Rs. (25000 * 3/10) = Rs. 7,500.   Rs. 7500nswer: Option Rs. 7500
Answer: A
If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 650, what is the least possible value of n? Pick
A) 10
B) 11
C) 12
D) 13
E) 14

Solution: 650 = 2 * 5 * 5 * 13   so the least value forNcan be 13.   13
Answer: D
Palindromes are words or phrases that read the same in both directions, e.g. EYE
Now consider the word LEVEL, such a word is known as palindromes.
Find the maximum possible number of five letter palindromes.  Pick one:
A) 17515
B) 17566
C) 17576
D) None
E) Cannot be determined

Solution: Explanation :   The first letter from the right can be chosen in 26 ways because there are 26 alphabets.   Having chosen this, the second letter can be chosen in 26 ways.   => The first two letters can be chosen in 26*26= 
26*26 = 676
676 ways   Having chosen the first two letters, the third letter can be chosen in 26 ways.=> All the three letters can be chosen in 676*26= 
676*26 = 17_576
17576 ways.   It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.   Answer : 17576
Answer: C
what is the next term of this series6,10,9,15,12,20,15,25...?	Pick.
A) 9	B) 10	C) 11	D) 12	E) 18

Solution: 3&2=6;    5*2= 
 5*2 = 10
10;    3*3= 
 3*3 = 9
9   3*5= 
3*5 = 15
15   3*4= 
3*4 = 12
12   5*4= 
5*4 = 20
20   3*5= 
3*5 = 15
15   5*5= 
5*5 = 25
25   3*6= 
3*6 = 18
18   ANSW18R:18
Answer: E
Helen went to the stationers and bought things worth Euro 22, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?	Choose the correct choice: A) uro 19.70 B) uro 15.70 C) uro 13.70 D) uro 18.70 E) uro 16.70

Solution: E   Euro 16.70   Let the amount taxable purchases be Euro x.   Then, 6% of x = 30/100   x = (30/100 x 100/6) = 5.   Cost of tax free items = uro 16.70uro [  22 - (5 + 0.30)= 
  22 - (5 + 0.30) = 16.7
uro 16.70uro 16.70
Answer: E
A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.675 in all. Find the share of B?  Choose the correct choice from the following options
A) 140
B) 120
C) 125
D) 130
E) 190

Solution: 140+B+C = 675   140 = 3B   3B+B+B-25 = 675   5B = 700   B = 140   140NSWER 140
Answer: A
What is the are of an equilateral triangle of side 16 cm?
Options
A) 64√8 cm2
B) 64√1 cm2
C) 68√3 cm2
D) 64√3 cm2
E) 24√3 cm2

Solution: Area of an equilateral triangle   = √3/4 S2   If S = 16, Area of triangle   = √3/4 * 16 * 16   = 64√3 cm2;   Answer: 64√3 cm2
Answer: D
A marketing company devised a methodology of spreading its message through one another. One person can tell it to 3 persons in 4 minutes and these three persons tell the other three persons each in further 4 minutes and the process continues so on. How many minutes will it take to spread the message to 2187 persons.
Choose the correct choice from the following.
A) 48 minutes
B) 24 minutes
C) 32 minutes
D) 28 minutes
E) 29 minutes

Solution: according to the given condition 3^1 + 3^2 + 3^3 + ........ = 2187   or 3(3^x - 1)/(3-1) = 2187   or 3(3^x - 1)/2 = 2187   or 3^x - 1 = 2187*2/3 = 4374/3= 
4374/3 = 1_458
1458   or 3^x= 1459 so x = 6 to 7   so total time taken = (6to7)*4 = 24 to 28 min   but if we take only the last step persons then 3^x = 2187 so x = 7   so time = 7*4= 
7*4 = 28
28 min   ANSWER:28 minutes
Answer: D
Mr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 7000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995? Pick one
A) 100000  B) 100500  C) 147000  D) Data inadequate  E) None of these

Solution: Let the investment of X in 1995 be x.   ∴ Profit = x⁄5   ∴ Income = (x + x⁄5) = 6⁄5x   Investment of company X in 1996 would be (x – 7000) From the question,   (x - 7000) × 126⁄100 = 6⁄5x ⇒ x = 147000   Answer 147000
Answer: C
Which of the following CANNOT be weighed using a balance scale and these unit weights: 1, 4, 7, and 10  Select the correct option:
A) 13
B) 15
C) 17
D) 19
E) 21

Solution: A. 13 (cannot be weighed)   B. 15 (can be weighed by keeping weights of 10,4 and 1 kg)   C. 17 (can be weighed by keeping weights of 10 and 7 kg)   D. 11(can be weighed by keeping weights of 10 and 1 kg)   E. 21 (can be weighed by keeping weights of 10, 7 and 4 kg)   13
Answer: A
The average monthly salary of 10 employees in an organisation is Rs. 1600. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary?
Choose the correct choice from the following options.
A) Rs.3601	B) Rs.3618	C) Rs.2700	D) Rs.3619	E) Rs.3610

Solution: Manager's monthly salary   = Rs. (1700 * 11 - 1600 * 10)   = Rs. 2700 Answer:Rs.2700
Answer: C
The angle between the minute hand and the hour hand of a clock when the time is 10.30, is
Choose the correct choice from the following answers:	A) 35°	B) 65°	C) 45°	D) 135°	E) 95°

Solution: Angle between hands of a clock   When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock   =30(H−M/5)+M/2 degree   When the minute hand is ahead of the hour hand, the angle between the two hands at M minutes past H 'o clock   =30(M/5−H)−M/2 degree   Here H = 10, M = 30 and minute hand is behind the hour hand.   Hence the angle   =30(H−M/5)+M/2   =30(10−30/5)+30/2   =30(10−6)+15   =30×4+15 =135°   Answer is 135°.
Answer: D
When x is multiplied by 3, the result is 26 more than the result of subtracting x from 26. What is the value of x?
Select the correct option:
A) -4 B) -2 C) 11 D) 13 E) 22

Solution: The equation that can be formed is:   3x-26=26-x   or, 4x=52   or, x=13.   13 answer.
Answer: D
All the following EXCEPT one are correct values for a in the equation: a = x/5 + y/5^2 + z/4^3, where x, y, and z are each equal to 1 or 0.  Select:
A) 15/32	B) 7/64	C) 13/32	D) 1/64	E) 5/32

Solution: a = x/5 + y/5^2 + z/4^3   = x/5 + y/25 + z/64   = (25x + 5y + z ) /64   Depending on whether x, y and z take 0 or 1.   Answer 5/32
Answer: E
The ages of two persons differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively Choose the correct choice from the following answers.
A) 20,20
B) 20,10
C) 25,15
D) 30,10
E) None of these

Solution: Explanation:   Let their ages be x and (x + 20) years.   5 (x - 5) = (x + 20 - 5) or 4x = 40 or x = 10.   Their present ages are 30 years and 10 years   Option 30,10
Answer: D
The Brookfield girl scouts sold 90 boxes of cookies on their first day which averaged 30% more than the other local area teams. Increasing their effort, by the end of the second day their sales increased their average to be 50% more than the other teams. How many boxes of cookies must the girls have out sold by to have attained this average? Choose the correct choice from the following answers:
A) 12 B) 50 C) 20 D) 36 E) 15

Solution: Explanation: First, set the information into algebraic phrases, set that information into an equation, then solve.   Number of boxes sold the first day @ 30% more: 30% * 90=27   Increasing their effort on the second day average increased to 50%. (Let x represent the unknown amount of additional cookies sold to solve the equation.) Therefore, the total boxes sold by the girls is 90+x, and the total number of boxes increased in 27+x. This gives the equation as: 50%*(90+x)=27+x   Solve: Let's get rid of the percent sign   50/100*(90+x)=27+x   1/2 *(90+x)=27+x   Get rid of the fraction:   2[1/2 * (90+x)]=2(27+x)   1 * (90+x) =54+2x   90+x =54+2x   (90-54)+x = (54-54)+2x   36+x/x = 2x/x   36 = x   Answer: 36
Answer: D
In a class of 25 students in an examination in maths 5 students scored 95 marks each, 3 get zero each and the average of the rest was 45. What is the average of the whole class?	Pick one:
A) A)47 B) B)45.6 C) C)44 D) D)48 E) E)49.6

Solution: 49.6xplanation:   Total marks obtained by a class of 25 students   = 5*95 + 3*0 + 17 * 45= 
5*95 + 3*0 + 17 * 45 = 1_240
1240   Average marks of whole class= 1240/25= 
1240/25 = 248/5 = around 49.6
49.6   Answer: Option 49.6
Answer: E