MU-NLPC/Calc-aqua_rat huggingface dataset:
A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (Assume that the order of the colors in a pair does not matter.)
Choose the correct option:
A) 4
B) 5
C) 6
D) 12
E) 24

Solution: Let's start with 4 minimum number of colors   So single color code we can make 4 nos.   Now if we need to make 2 color combination out of 4 we can do so in 4!/2!*2! or 4*3/2 or 6   So total we can make 4+6= 
4+6 = 10
10 color combinations but we have 12 boxes   So let's look at 5 we get 5 single color codes   and out 5 color choices, we can choose 2 in 5!/2!*3! ways or 10 ways.   So total we can have 5+10= 
5+10 = 15
15 color combinations.   So, minimum number we need will be 5   Ans is 5.......
Answer: B
Three candidates contested an election and received 600, 7025 and 11620 votes respectively. What percentage of the total votes did the winning candidate get?
Choose the correct option
A) 57%  B) 60.3%  C) 65%  D) 90%  E) 80%

Solution: total votes are 19245 ( sum of votes obtained by 3 candidates)   percentage of the total votes recd by the winning candidate = 100*11620/19245 = 60.3%   ANSWER:60.3%
Answer: B
You collect baseball cards. Suppose you start out with 16. Since you're nice, you give John 6 baseball cards. How many baseball cards do you have at the end?	Choose the correct choice from the following answers:
A) 11
B) 12
C) 13
D) 14
E) 10

Solution: Solution   Start with 16 baseball cards.   John takes 6 baseball cards from you:   16 - 6= 
  16 - 6 = 10
10 baseball cards.   So you have 10 at the end.   Correct answer : 10
Answer: E
In how many different number of ways 6 men and 4 women can sit on a shopa which can accommodate persons?	Choose the correct option
A) 17 B) 90 C) 20 D) 21 E) 23

Solution: 10p2 = 10 Ã— 9 = 90   Answer : 90
Answer: B
the present average age of a couple and their daughter is 35 years. Fifteen years from now, the age of the mother will be equal to the sum of present ages of the father and the daughter. Find the present age of mother?
Choose the correct choice from the following answers.
A) 22 years	B) 77 years	C) 76 years	D) 45 years	E) 56 years

Solution: (f + m + d)/3 = 35   => f + m + d = 105 --- (1)   m + 15 = f + d   Substituting f + d as m + 15 in (1), we get   2m + 15 = 105   2m = 90 => m = 45 years.   Answer: 45 years
Answer: D
Find four consecutive even integers so that the sum of the first two added to twice the sum of the last two is equal to 766.	Choose the correct choice from the following
A) 124 ,126, 128, 130
B) 120 ,122 , 124 ,128
C) 120 ,121 , 122 ,123
D) 123 ,125 , 127 ,129
E) None of these

Solution: Let x, x + 2, x + 4 and x + 6 be the four integers. The sum of the first two   x + (x + 2)   twice the sum of the last two is written as   2 ((x + 4) + (x + 6)) = 4 x + 20   sum of the first two added to twice the sum of the last two is equal to 766 is written as   x + (x + 2) + 4 x + 20 = 766   Solve for x and find all four numbers   x = 124 , x + 2 = 126 , x + 4 = 128 , x + 6 = 130   124 ,126, 128, 130nswer 124 ,126, 128, 130
Answer: A
Select a card from pack of 52 playing cards, 2cards are drawn together at random. Find the probability of both the cards being king ? Select the correct option
A) 1/111 B) 2/121 C) 1 by 221 D) 2/213 E) 3/412

Solution: Two cards can be drawn from a pack of 52 playing cards in 52C2 ways. i,e., 52 x 51 / 2 = 1326 ways. The event that two kings appear in a single drawn of cards is 4C2 ways, i.e 6 ways.   ∴ The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221   1 by 221
Answer: C
If Dev works alone he will take 20 more hours to complete a task than if he worked with Tina to complete the task. If Tina works alone, she will take 5 more hours to complete the complete the task, then if she worked with Dev to complete the task? What is the ratio of the time taken by Dev to that taken by Tina if each of them worked alone to complete the task?	Pick
A) 4 : 1  B) 2 : 1  C) 10 : 1  D) 3 : 1  E) 1 : 2

Solution: Let time taken by Dev to complete the work alone be x days and that by Tina be y days   Work done by Dev in 1 day = 1/x   Work done by Tina in 1 day = 1/y   Work done by DevTina in 1 day = 1/x + 1/y = (x+y)/xy   Thus working together they will complete the work in xy/(x+y) days   Acc. to the ques :   1)If Dev works alone he will take 20 more hours to complete a task than if he worked with Tina'   x - xy/(x+y) = 20   => (x^2)/(x+y) = 20.............(i)   2)If Tina works alone, she will take 5 more hours to complete the complete the task, then if she worked with Dev   y - xy/(x+y) = 5   => (y^2)/(x+y) = 5..............(ii)   Dividing (i) by (ii)   x^2/y^2 = 4   => x/y = 2   Ans : 2 : 1   Hope it helps
Answer: B
6x – 5y + 3z = 27
4x + 8y – 11z = 7
5x – 6y + 2z = 12
Given the equations above, x + y + z = ?	Pick
A) 11 B) 12 C) 13 D) 14 E) 15

Solution: (6x – 5y + 3z) - (5x – 6y + 2z ) = 27-12   or, x+y+z = 15   Option 15 is the ans
Answer: E
In how many different number of ways a combination of 3 persons can be selected from 4 boys and 2 girls.
Select the correct option: A) 152 B) 160 C) 176 D) 180 E) 200

Solution: 6C3 × 5C2   6C3   = 6!/(3! . 3!)   = (6 × 5 × 4)/(3 × 2)   = 5 × 4 = 20.   5C2   = 5!/(3! . 2!)   = 5 × 2 = 10   = 20 × 10 = 200.   200)
Answer: E
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? Select: A) 350m B) 380m C) 350m D) 320m E) 150m

Solution: Speed = [300 / 18] m/sec = 50/3 m/sec.   Let the length of the platform be x meters.   Then, x + 300 / 39 = 50/3   3(x + 300) = 1950 è x = 350m.   Answer: 350m
Answer: C
The average of 10 numbers was calculated as 17. It is discovered later on that while calculating the average, one number, namely 56, was incorrectly read as 26. What is the correct average?	Select:
A) 19
B) 20
C) 21
D) 22
E) 23

Solution: 10*17 - 26 + 56= 
10*17 - 26 + 56 = 200
200   200 / 10= 
200 / 10 = 20
20   The answer is 20.
Answer: B
In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?
Pick one
A) 190	B) 200	C) 205	D) 210	E) 220

Solution: Answer: Option '210'   7p3 = 7 × 6 × 5 = 210
Answer: D
How many kilograms of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per Kg so that there may be a gain of 10% by selling the mixture at Rs.9.24 per Kg? Choose one:	A) 36 Kg	B) 42 Kg	C) 54 Kg	D) 63 Kg	E) None of these

Solution: Solution   Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.   Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind.   Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg   Answer 63 Kg
Answer: D
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is ?  Select:
A) 1:3 B) 3:2 C) 3:5 D) 3:7 E) None of these

Solution: Explanation:   Let the speeds of the two trains be x m/sec and y m/sec respectively.   Then, length of the first train = 27x metres,   Length of the second train = 17y metres.   [because distance = speed*time]   27x+17y /x+y=23   =>27x+17y=23x+23y   =>4x=6y   =>x/y=6/4   So ratio of the speeds of train is 3:2   Option 3:2
Answer: B
If two numbers are in the ratio 5:2. If 10 is added to both of the numbers then the ratio becomes 5:4 then find the largest number?  Pick:
A) 3	B) 7	C) 4	D) 5	E) 6

Solution: 5:2   5x + 10 : 2x + 10 = 5 : 4   5[2x + 10] = 4[5x + 10]   10x + 50 = 20x + 40   20x - 10x = 50 - 40   x = 1   Then the first number is = 5X   5x = 5   Option '5'
Answer: D
The sale price Laptops listed for Rs.30000 after successive discount is 30% and 20% is?
Select the correct option:
A) 18600  B) 17600  C) 18600  D) 16800  E) 16700

Solution: 30000*(70/100)*(80/100)= 
30000*(70/100)*(80/100) = 16_800
16800   Answer: 16800
Answer: D
Find the length of the wire required to go 15 times round a square field containing 69696 m^2.  Choose the correct choice from the following answers:
A) 15840
B) 26480
C) 15642
D) 15640
E) 15849

Solution: a^2 = 69696 => a = 264   4a = 1056   1056 * 15= 
1056 * 15 = 15_840
15840   15840nswer: 15840
Answer: A
Excluding stoppages, the speed of a train is 48 kmph and including stoppages it is 40 kmph. Of how many minutes does the train stop per hour? Options:
A) 16
B) 17
C) 15
D) 10
E) 12

Solution: T = 8/48 * 60= 
8/48 * 60 = 10
10   Answer: 10
Answer: D
A cyclist traveled for two days. On the second day the cyclist traveled 4 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day. If during the two days she traveled a total of 240 miles and spent a total of 12 hours traveling, what was her average speed on the second day? Select the correct option.
A) 5 mph
B) 10 mph
C) 20 mph
D) 30 mph
E) 40 mph

Solution: SOLUTION:   D = 280 Mi   T = 12 hrs   Đây 1 time = T1   Dây 2 time = T2   T2 - T1 = 4 hrs ----- (I)   T1 + T2 = 12 hrs ----- (II)   Adding I and II, T2 = 8 hrs and T1 = 4 hrs   Dày 1 Rate = R1   Dây 2 Rate = R2   R1 - R2 = 10 mph   í.ẹ. R1 = 10 + R2   280 = 8R2 + 4R1   í.ẹ. 280 = 8R2 + 4 (10 + R2)   í.ẹ. R2 = 20 mph   ANSWER: 10 mph
Answer: B
A, B and C, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $ 1170, what will be B's share of the earnings?  Answers.
A) $390 B) $520 C) $1080 D) $1170 E) $630

Solution: Explanatory Answer   A, B and C will share the amount of $1170 in the ratio of the amounts of work done by them.   As A takes 6 days to complete the job, if A works alone, A will be able to complete 1/6 th of the work in a day.   Similarly, B will complete 1/8th and C will complete 1/12th of the work.   So, the ratio of the work done by A : B : C when they work together will be equal to 1/6 : 1/8 : 1/12   Multiplying the numerator of all 3 fractions by 24, the LCM of 6, 8 and 12 will not change the relative values of the three values.   We get 24/6 : 24/8 : 24/12 = 4 : 3 : 2.   i.e., the ratio in which A : B : C will share $1170 will be 4 : 3 : 2.   Hence, B's share will be  3*1170/9= 
 3*1170/9 = 390
390.   correct choice is ($390)
Answer: A
What is the number of different committees of 4 women that can be selected from a group of 7 women? Select:
A) a) 20
B) b) 35
C) c) 80
D) d) 120
E) e) 210

Solution: 7c4 = 35   Answer is b) 35.
Answer: B
If there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if the total number of wheels is 54?	Choose the correct choice from the following answers
A) 11	B) 12	C) 13	D) 14	E) 15

Solution: four wheeler=13*4= 
13*4 = 52
52(max)   2 wheel=1   so no of 4 wheeler=13   ANSWER:13
Answer: C
If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in?  Choose the correct choice from the following answers.
A) 20  B) 21  C) 30  D) 9  E) 7

Solution: C = 1/4 - 1/12 â€“ 1/18 = 1/9 => 9 days   ANSWER 9
Answer: D
Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 2-cent stamps she could have bought ?	Pick one:
A) 5
B) 10
C) 7.5
D) 20
E) 25

Solution: 2.65 = 0.05x + 0.25x + 2 * 0.10x + 0.02y   => 2.65 = 0.30x + 0.20x + 0.02y   => 265 = 50x + 2y   So Max value of 50x < 265 = 250   Hence y = 7.5   Answer - 7.5
Answer: C
A 340-liter solution of Kola is made from 88% water, 5% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 10 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar?  Choices
A) 6%
B) 7.5%.
C) 9.2%
D) 10.5%.
E) 11%.

Solution: Denominator:   340+10+3.2+6.8= 
340+10+3.2+6.8 = 360
360   Numerator:   340(1-.88-.05)+3.2   340(0.07)+3.2   23.8+3.2   27   Ratio:   27/360=3/40   Answer: 7.5%.
Answer: B
A train of length 150 metres takes 40.5 seconds to cross a tunnel of length 300 metres. What is the speed of the train in km/hr ?  Choose one
A) 13 33	B) 26.67	C) 40	D) 66.67	E) None

Solution: Solution   speed	=(150 + 300 / 40.5)m/sec   =(450/40.5x18/ 5) km/hr   = 40 km/hr   Answer 40
Answer: C
48% of respondents to a survey consisted of those who used both M and N and those who used neither M nor N. 38% of respondents did not use M. 32% used N. What percent of respondents used only N? Choose the most appropriate option:
A) 19.5% B) 11% C) 20% D) 18.5% E) 17.5%

Solution: From the question, we can summarize the information as follows:   N Not N   M X   Not M Ans y 38   32 100   Then we can set a system of 3 equations 3 unknowns described below:   X + Y = 48   X + Ans = 32   Y + Ans = 38   Sum up all three equations to get 2X + 2Y + 2Ans = 118   Divide both sides by 2 to get X + Y + Ans = 59   Replace X + Y with 48 to get 48 + Ans = 59   Substract 48 from both sides to get Ans = 59 - 48= 
59 - 48 = 11
11   The answer must be 11%.
Answer: B
A farmer needs to plant seeds on a plot of land. She will plant 300 seeds in a rectangle in the field. The rectangle will have E seeds in a row and F seeds in a column. If the number of seeds in a row is no less than 10 and no more than 30, how many different combinations of rectangular shapes are possible?	Choose the correct choice from the following.
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: firstly factors of 300 = 1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300   the question says each row will have seeds no less than 10 and no more than 30,   therefore, we should be interested in the factors between 10 and 30 (inclusive)   10(in each row) * 30(number of columns) =300, similarly   12 * 25   15 * 20   20 * 15   25 * 12   30 * 10   total possibilities = 6   option 6
Answer: B
How many multiples of 7 are there between 14 and 252 ? Choose the correct answer: A) 33 B) 46 C) 59 D) 66 E) 80

Solution: It should be mentioned whether 14 and 252 are inclusive.   If 14 and 252 are inclusive, then the answer is   (252-14)/7+1= 
  (252-14)/7+1 = 35
35.   If 14 and 252 are NOT inclusive, then the answer is   (245-21)/7+1= 
  (245-21)/7+1 = 33
33.   Since O33 is 33, then we have NOT inclusive case.
Answer: A
If a train, travelling at a speed of 90 kmph, crosses a pole in 5 sec, then the length of train is?
Choose the correct choice from the following choices
A) 167 m
B) 125 m
C) 761 m
D) 143 m
E) 132 m

Solution: D = 90 * 5/18 * 5= 
90 * 5/18 * 5 = 125
125 m   Answer:125 m
Answer: B
If n=4p where p is a prime number greater than 2, how many different positive even divisors does n have, WITHOUT N VALUE?
Answers.
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: We're told that N = 4P and that P is a prime number greater than 2. Let's TEST P = 3; so N = 12   The question now asks how many DIFFERENT positive EVEN divisors does 12 have, including 12?   12:   1,12   2,6   3,4   How many of these divisors are EVEN? 2, 4, 6, …..3 even divisors.   ANSWER:3
Answer: C
Ritesh and Co. generated revenue of Rs. 1,600 in 2006. This was 12.5% of its gross revenue. In 2007, the gross revenue grew by Rs. 2,500. What is the percentage increase in the revenue in 2007?
Choices
A) 12.5%
B) 19.53%
C) 25%
D) 50%
E) None of these

Solution: Explanation :   Given, Ritesh and Co. generated revenue of Rs. 1,600 in 2006 and that this was 12.5% of the gross revenue.   Hence, if 1600 is 12.5% of the revenue, then 100% (gross revenue) is:   =>(100/12.5)×1600.   =>12,800.   Hence, the total revenue by end of 2007 is Rs. 12,800. In 2006, revenue grew by Rs. 2500. This is a growth of:   =>(2500/12800)×100.   =>19.53%.   Answer : 19.53%
Answer: B
A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? Pick one
A) 1.8
B) 1.6
C) 1.3
D) 1.5
E) 1.1

Solution: M = 4.5   S = x   1.5S = 4.5 + x   US = 4.5 + x   4.5 + x = (4.5 - x)2   4.5 + x = 9 -2x   3x = 4.5   x = 1.5   Answer: 1.5
Answer: D
The probability that A speaks truth is 3/5 and that of B speaking truth is 2/7. What is the probability that they agree in stating the same fact?	Select
A) 16/35  B) 16/37  C) 16/39  D) 16/33  E) 16/31

Solution: If both agree stating the same fact, either both of them speak truth of both speak false.   Probability = 3/5 * 2/7 + 2/5 * 5/7   = 16/35   16/35nswer:16/35
Answer: A
p:q = 7:6 , q:r = 4 : 7 , p:q:r = ?
Select the correct option
A) 28 : 24 : 42
B) 28 : 24 : 40
C) 28 : 24 : 52
D) 28 : 24 : 41
E) 28 : 24 : 48

Solution: p:q = 7:6 ,   q:r = 4 : 7   p:q:r =28 : 24 : 42   28 : 24 : 42nswer : 28 : 24 : 42
Answer: A
Two partners (Moses and Norris) invested Rs 5000 and Rs.12000 in a business. Moses runs the business while Norris is a sleeping partner in the business. Moses receives 4% of the profit for managing the business the rest is divided in proportion of their capitals. Out of a total profit of Rs.5500, how much did Moses receive?  Choices:
A) 1772.95
B) 1537.6
C) 1877.6
D) 1937.6
E) 1857.6

Solution: ratio of their investments Rs.5000:12000=5:12   4% of the profit for managing the business =4/100*5500= 
4/100*5500 = 220
220   remaining profit=5500-220= 
5500-220 = 5_280
5280   share profit in ratio of investment 5280/17=310.59   Moses's ratio share=5*310.59= 
5*310.59 = 1_552.95
1552.95   total money Moses collects=1552.95+220= 
1552.95+220 = 1_772.95
1772.95   1772.95nswer: 1772.95
Answer: A
A person buys an article at $500. At what price should he sell the article so as to make a profit of 20%? Answers:  A) 560  B) 449  C) 600  D) 740  E) 460

Solution: 600   600   600ost price = $500   profit = 20% of 500 = $100   Selling price = 600ost price + Profit   = 500 + 100= 
500 + 100 = 600
600
Answer: C
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. What is the present age of the husband?  Choose the correct choice from the following answers:
A) 30
B) 40 years
C) 20
D) 50
E) 25

Solution: Let the present age of the husband = h   Present age of the wife = w   Present age of the child = c   3 years ago, average age of husband, wife and their child = 27   => Sum of age of husband, wife and their child before 3 years = 3 × 27 = 81   => (h-3) + (w-3) + (c-3) = 81   => h + w + c = 81 + 9= 
81 + 9 = 90
90 --- equation(1)   5 years ago, average age of wife and child= 20   => Sum of age of wife and child before 5 years = 2 × 20 = 40   => (w-5) + (c-5) = 40   => w + c = 40 + 10= 
40 + 10 = 50
50 --- equation(2)   Substituting equation(2) in equation(1)=> h + 50 = 90   => h = 90 - 50= 
90 - 50 = 40
40   i.e., Present age of the husband= 40   Answer is 40 years.
Answer: B
A , B , and C started a partnership business by investing $45,000 , $63,000 , and $72,000 respectively. At the end of the year, the profit was distributed among them. If C's share of profit is $16,000, what is the total profit? Answers
A) $28,000
B) $32,000
C) $36,000
D) $40,000
E) $44,000

Solution: A:B:C = 45000:63000:72000 which is a ratio of 5:7:8.   Let the total profit be x.   x * 8/20 = 16000   x = 16000*20/8 = 40,000.   The answer is $40,000.
Answer: D
A and B finish the job in 15 days.while A,B and C can finish it in 11 days . C alone will finish the job in
Select the correct option:
A) 41.25 days	B) 30.25 days	C) 60.25 days	D) 71.25 days	E) 51.25 days

Solution: Explanation:   11= (15 * x)/(15 + x)   165+11x=15x   4x=165   X=41.25   41.25 daysnswer: Option 41.25 days
Answer: A
Kim purchased n items from a catalog for $8 each. Postage and handling charges consisted of $2 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?	Choose the correct choice from the following answers:  A) 8n + 2  B) 9n + 1  C) 9n + 2  D) 9n + 3  E) 9n + 4

Solution: its C   n items for $8 each   total price $8n   postage and handling of $3 for 1st item and $1 for the rest   total postage and handling = $ [2+ (n-1)]   = $ n+1   total cost   8n+n+1 = 9n+1   9n + 1 8 + +1= 
 8 + +1 = 9
9n+1   9n + 1
Answer: B
Which of the following is satisfied with |x-4|+|x-3|<7?	Choose the correct choice from the following
A) 0<x<7  B) 2<x<5  C) 2.5<x<4.5  D) 2.5<x<4  E) 3<x<4

Solution: --> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<7 -> |x-4+x-3|<7 -> |2x-7|<7, -7<2x-7<7, 0<2x<14, 0<x<7   Therefore, the answer is 0<x<7.
Answer: A
A certain restaurant offers 5 different salads, 4 different main courses, and 7 different desserts. If customers choose one salad, one main course, and two different desserts for their meal, how many different meals are possible?	Options:
A) 300 B) 340 C) 380 D) 420 E) 460

Solution: The number of possible choices for desserts is 7C2 = 21   The number of possible meals is   5*4*21= 
  5*4*21 = 420
420   The answer is 420.
Answer: D
A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?  Choose the correct choice from the following options
A) 3 1/5 Kilometre	B) 2 1/5 Km	C) 3 Km	D) 4 Km	E) 4 1/3 Km

Solution: Formula = S1*S2/ S2-S1 * T1+T2/60   = 4*6/2 * 16/6   = 24/2 * 16/60   = 8 * 2/5   = 16/5 = 3 1/5 Km   3 1/5 Kilometre)
Answer: A
A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 6 inches wide on each side, the total area would have been (M + 200) square inches. What is the perimeter of the photograph, in inches? Choose the correct option.
A) 8	B) 12	C) 16	D) 20	E) 24

Solution: Let x and y be the width and length of the photograph.   (x+2)(y+2)=M and so (1) xy + 2x + 2y + 4 = M   (x+12)(y+12)=M and so (2) xy + 12x + 12y + 144 = M+200   Let's subtract equation (1) from equation (2).   10x + 10y + 140 = 200   2x + 2y = 12, which is the perimeter of the photograph.   The answer is 12.
Answer: B
Find the one which does not belong to that group ?	Pick:  A) 16  B) 28  C) 36  D) 64  E) 4

Solution: Explanation:   16, 36, 64 and 4 are perfect squares but not 28.   ANSWER IS 36
Answer: C
The average of 25 results is 18. The average of first 12 of those is 14 and the average of last 12 is 17. What is the 13th result?	Pick one
A) 74
B) 75
C) 69
D) 78
E) 45

Solution: Solution: Sum of 1st 12 results = 12*14   Sum of last 12 results = 12*17   13th result = x (let)   Now,   12*14+12*17+x = 25*18   Or, x = 78.   Answer: Option 78
Answer: D
The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is -.  Options
A) 0.4869 B) 0.5904 C) 0.6234 D) 0.5834 E) 0.2952

Solution: Explanation:   P(winning prize atleast on one ticket)   = 1 - P("Losing on all tickets")   = 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)   = (1.64)(0.36) = 0.5904   ANSWER IS 0.5904
Answer: B
Wendy begins sanding a kitchen floor by herself and works for 8 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself?
Choose the correct option:
A) 544/49 hours
B) 3/20 hours
C) 20/3 hours
D) 80/9 hours
E) 10 hours

Solution: Let Wendy finishes sanding the floor alone in W hours while B be the hours for Bruce.   Thus in 1 hour Wendy finishes 1/w of the work while Bruce finishes 1/B of the work.   If wendy works for 8 hours and is then joined by Bruce to finish the work in 2 more hours,   8/W + 2/W+2/B = 1 (1 denotes the total amount of work)   10/W + 2/B =1 and given B =20 hours.   Thus W = 544/49 hours , 544/49 hours is the correct answer.
Answer: A
In what time a sum of money double itself at 6% per annum simple interest?  Options.
A) 33 1/8%
B) 16 2/3%
C) 33 7/3%
D) 32 1/3%
E) 23 1/3%

Solution: P = (P*6*R)/100   R = 16 2/3%   Answer: 16 2/3%
Answer: B