MU-NLPC/Calc-aqua_rat huggingface dataset:
The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is? Choose the correct option:
A) 288 B) 208 C) 200 D) 480 E) 261

Solution: 262 – 102 = 242   d1 = 20 d2 = 48   1/2 * 20 * 48= 
1/2 * 20 * 48 = 480
480   Answer: 480
Answer: D
Jane earned enough money by selling seashells at 25 cents each to buy several used paperback books at 55 cents each. If he spent all of the money he earned selling seashells to buy the books, what is the least number of seashells he could have sold ? Choose the correct choice
A) 5  B) 10  C) 17  D) 22  E) 30

Solution: Let's TEST Answer A: 5 seashells...   With 5 seashells, Jamie would have 5(25) = 125 cents. This would allow him to buy 2 books for 110 cents total, but he would then have 15 cents left over. We're told that he spent ALL of his money on books, so this cannot be the correct answer.   Answer D: 22 seashells....   With 22 seashells, Jamie would have 22(25) = 550 cents. This would allow him to buy 10 books for 550 cents total, with no money left over. This is an exact MATCH for what we were told, so this MUST be the answer.   22
Answer: D
Evaluate :	136.09 + 43.9 Choose the correct option:
A) 1000
B) 3000
C) 7000
D) 5000
E) 2000

Solution: 25/0.0005 = (25*10000) / (0.0005*10000) = 25000 / 5= 
25000 / 5 = 5_000
5000   Answer is 5000
Answer: D
A manufacturer of a certain product can expect that between 0.3 percent and 0.5 percent of the units manufactured will be defective. If the retail price is $1,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 20,000 units?
Choose the correct option: A) Between $90,000 and $150,000 B) Between $30,000 and $50,000 C) Between $60,000 and $100,000 D) Between $150,000 and $250,000 E) Between $300,000 and $500,000

Solution: Number of defective units is between = .3 % of 20000 and .5% of 20000   = 60 and 100   Retail Price per unit = 1500 $   Expected price of refund is between = 1500 x 60 and 1500 x 100   =90,000 and 1,50,000 dollars   Between $90,000 and $150,000nswer Between $90,000 and $150,000
Answer: A
If the height of an equilateral triangle WBC is equal in length to the hypotenuse of an isosceles right triangle DEF, a side of ΔWBC is how many times as long as a leg of the right triangle DEF?
Choose the correct choice from the following answers:
A) (√2)/(√3) B) (√3)/(√2) C) √2 D) (2√2)/(√3) E) 2/(√3)

Solution: Side of the equilateral triangle WBC = 2m ----> height = m * sqtr(2)   Hipotenuse of the right triangle WBC = m * sqrt(3) ----> side = m * sqtr(3) / sqtr(2)   Question is 2m/m * sqtr(3) / sqtr(2) = 2*sqrt(2)/sqrt(3)=(2√2)/(√3)
Answer: D
If the length of a rectangle is increased by 10% and the area is unchanged , then its corresponding breadth must be decreased by?	Choose the correct option:
A) 9 1/19
B) 9 1/15
C) 9 1/16
D) 9 1/11
E) 9 1/10

Solution: Suppose length = 100m and breadth = x m   Area = 100 m   New length = 110m and breadth = (x-y% of x)   Then, \inline 110\times (x-\frac{y}{100}x)=100\times x   \inline \Rightarrow \inline 110\times (1-\frac{y}{100})=100   \inline \Rightarrow \inline 1-\frac{y}{100}=\frac{100}{110}   \inline \Rightarrow \frac{y}{100}=1-\frac{100}{110}=\frac{1}{11}   \inline y=\frac{100}{11}=9\frac{1}{10}%   Answer:9 1/10
Answer: E
Find the remainder when 6^50 is divided by 215	Choose the most appropriate option:
A) 34  B) 35  C) 36  D) 37  E) 38

Solution: (6^3)^16*6^2 /215   (215 + 1)^16 * 6^2/215   1^16 * 6^2/215   = 36   ANSWER:36
Answer: C
Payal finished 2/3 of a book. She calculated that she finished 20 more pages than she has yet to read. How long is her book? Choose the correct choice from the following answers.
A) A)60  B) B)150  C) C)130  D) D)90  E) E)210

Solution: Let x be the total number of pages in the book, then she finished 2/3*x pages.   Then she has x−2/3*x=1/3*x pages left.   2/3*x−1/3*x=20   1/3*x=20   x=60   So the book is 270 pages long.   60nswer is 60.
Answer: A
If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word ‘SACHIN’ appears at serial number :
Choose the correct option
A) 603  B) 604  C) 611  D) 511  E) 601

Solution: If the word started with the letter A then the remaining 5 positions can be filled in 5! Ways.   If it started with c then the remaining 5 positions can be filled in 5! Ways.Similarly if it started with H,I,N the remaining 5 positions can be filled in 5! Ways.   If it started with S then the remaining position can be filled with A,C,H,I,N in alphabetical order as on dictionary.   The required word SACHIN can be obtained after the 5X5!=600 Ways i.e. SACHIN is the 601th letter.   ANSW601R:601
Answer: E
A person travels from P to Q at a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips ?	Choose the correct choice from the following choices:  A) 44 km/hour  B) 46 km/hour  C) 48 km/hour  D) 50 km/hour  E) None of these

Solution: Explanation:   Speed while going = 40 km/hr   Speed while returning = 150% of 40 = 60 km/hr   Average speed =   2xy /x+y   =2∗40∗60 /40+60=4800/100= 
4800/100 = 48
48Km/hr   Option 48 km/hour
Answer: C
In a 2000 m race, A beats B by 180 meters or 50 seconds. Find the speed of B?
Choose the correct choice: A) 3.6m/s B) 2m/s C) 5m/s D) 7m/s E) 3m/s

Solution: Since A beats B by 180 m or 50 seconds,   it implies that B covers 180 m in 50 seconds.   Hence speed of B = 180/50= 
180/50 = 18/5 = around 3.6
3.6 m/s.   3.6m/snswer: 3.6m/s
Answer: A
A starts a business with a capital of Rs. 8500. B joins in the business with Rs.8500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?  Pick.
A) 4 months
B) 6 months
C) 7 months
D) 8 months
E) None of these

Solution: Explanation :   Let B joins for x months. Then   A:B = 8500*12 : x* 8500 = 3 : 1   => 85*12 : 85x= 3 : 1   => 85*12/ 85x = 3/1= 
3/1 = 3
3=> 85*4 /85x = 1   => 4/x = 1   => x = 4. 4 monthsnswer : Option 4 months
Answer: A
How many times does the minute hand to go around the clock in one day? Choices:
A) 1355	B) 1416	C) 1432	D) 1400	E) 1300

Solution: The minute hand will go around once. Thus, the second hand will pass the minute hand 59 times in an hour. This means they will meet 59Ã—24=1416 times in a day.   Answer 1416
Answer: B
A person travels equal distances with speeds of 9 km/hr, 10km/hr and 11 km/hr and takes a total time of 47 minutes. The total distance is?	Choose the correct choice from the following answers
A) 6 km	B) 3 km	C) 8 km	D) 9 km	E) 2 km

Solution: Let the total distance be 3x km.   Then, x/9 + x/10 + x/11 = 47/60   29x/96 = 47/60 => x = 2.59   Total distance = 3 *2.59 = 7.78 km.   Answer:8 km
Answer: C
How many cases do you need if you have to pack 240 pairs of shoes into cases that each hold 24 shoes?  Choose the correct choice:
A) 35	B) 15	C) 20	D) 25	E) 30

Solution: C   20   240 pairs of shoes = 480 shoes.   480÷ 24 = 20.
Answer: C
The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.9 kg. the weight of the new student is ?
Choose the correct choice from the following
A) 10.6 kg B) 10.8 kg C) 11 kg D) 13 kg E) None

Solution: Answer   Weight of new student = Total weight of all 20 students - Total weight of initial 19 students   = (20 x 14.9 - 19 x 15) kg   = 13 kg.   Correct Option: 13 kg
Answer: D
In a group of ducks and cows, the total number of legs are 28 more than twice the no. of heads. Find the total no.of buffaloes.  Choose the correct answer:	A) 10	B) 12	C) 13	D) 15	E) 14

Solution: Let the number of buffaloes be x and the number of ducks be y   => 4x + 2y = 2 (x + y) + 28   => 2x = 28 => x = 14   14
Answer: E
A type R machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type R machines and 3 type B machines working together and independently to complete the job?
Choices
A) 1/5 B) 29/35 C) 5/6 D) 35/29 E) 35/12

Solution: now D should be the answer.   R need 5 hours to complete   and B needs 7 hours to compete   so 2R + 3B will complete 2/5 + 3/7 or 29/35 portion of the job in 1 hour   so the whole job will take 35/29 hours....=35/29
Answer: D
3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?  Answers.
A) 34	B) 77	C) 36	D) 49	E) 38

Solution: Explanation:   Let the required length be x meters   More men, More length built (Direct proportion)   Less days, Less length built (Direct Proportion)   \inline \fn_jvn \left.\begin{matrix} Men\: \: \: 20:35\\ Days\: 6:3 \end{matrix}\right\}::56:x   \inline \fn_jvn \therefore (20 x 6 x X)=(35 x 3 x 56) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{35\times 3\times 56}{120} =49   Hence, the required length is 49 m.   Answer: 49
Answer: D
A started a bussiness with a sum of Rs. 14000. After 4 months, B entered with an amount of Rs. 12000 and A added another 2,000 in the business. After 6 months, C entered with Rs. 20000 and 'B' withdrew Rs. 2000 from the business. What will be C's share of profit out of a total profit of Rs. 94000 at the end of 2 years.  Pick one:
A) Rs. 376000
B) Rs. 204000
C) Rs. 36000
D) Rs. 18000
E) Rs. 260000

Solution: Investments--   A=14000x4+16000x20=376000   B=12000x2+10000x18=204000   Rs. 36000=20000x18=360000   So Rs. 36000's Share = 94000xRs. 36000/(A+B+Rs. 36000)=36000   ANSWER:Rs. 36000
Answer: C
A box contains nine slips that are each labeled with one number: 1, 3, 5, 8, 13, 21, 34 and 55. Two of the slips are drawn at random from the box without replacement. What is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box? Pick.
A) 7/72  B) 1/6  C) 5/28  D) 15/36  E) 21/36

Solution: Probability = No: of desired outcomes / Total No: of outcomes.   You are picking two slips out of 8 slips. So   Total No: of outcomes = 8C2 = 28   Desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box. How many such outcomes are there?   If you look at the numbers closely, you will see that the following pair of numbers will give you the desired outcome.   (3,5) (5,8) (8,13) (13,21) (21,34) . There are 7 such pairs. If the two numbers which I pick is from any of these 5 pairs, then I get my desired outcome.   So No: of desired outcomes = 5   Probability = 5/28   Answer :5/28
Answer: C
Given that there are 11 cricket players per team, how many ways can you select 10 cricket players from 2 teams if no more than 2 players can be selected from each team? Pick one.
A) 3025 B) 1500 C) 2600 D) 3500 E) 4200

Solution: Now from each group we have to select 5 persons only: 11C2 * 11C2= 55 * 55= 
55 * 55 = 3_025
3025   Total ways=313444 ways.   3025nswer 3025
Answer: A
The game 'Chunk-a-Luck' is played at carnivals in some parts of Europe. Its rules are as follows:
If you pick a number from 1 to 6 and the operator rolls three dice.
If the number you picked comes up on all three dice, the operator pays you Rs. 3.
If it comes up on two dice, you are paid Rs. 2.
And it comes up on just one dice, you are paid Rs. 1.
Only if the number you picked does not come up at all, you pay the operator Rs. 1.
The probability that you will win money playing in this game is:  Choose the correct option:
A) 0.52
B) 0.753
C) 0.42
D) 0.68
E) None of the above

Solution: Explanation :   If one picks up a number out of six numbers then the only case in which he/she will lose money if none of the three dice shows the picked number on the top surface.   Required probability of losing the game:   =>(5/6) x (5/6) x (5/6).   =>125/216.   Hence, the required probability of winning the game is :-   =>1-(125/216).   =>91/216.   =>0.42.   Answer : 0.42
Answer: C
Jack, Jill, and Sandy each have one try to make a basket from half court. If their individual probabilities of making the basket are 1/6, 1/7, and 1/8 respectively, what is the probability that Jill and Sandy will make a basket but Jack will miss? Pick one.
A) 3/168
B) 5/168
C) 7/168
D) 5/336
E) 7/336

Solution: The probability that Jill and Sandy will make a basket but Jack will miss is 5/6*1/7*1/8=5/336.   The answer is 5/336.
Answer: D
If A = 625 * 7776 * 16 / 1296, How many digits are in A? Choose the most appropriate option:
A) 5  B) 2  C) 3  D) 4  E) 0

Solution: 5 = 625 * 7776 * 16 / 1296   5 = 5^4 * 6^5 * 2^4 / 6^4   5 = 10^4*6 = 60000   Option: 5
Answer: A
34.95+240.016+23.98=? Pick one.
A) 298.0946
B) 298.111
C) 298.946
D) 299.09
E) None of them

Solution: 34.95   240.016   23.98   ----------   298.946   Answer is 298.946
Answer: C
a,b,c,d,e,f,g sitting in a row what is the probability that a,b & c sitting together.	Select:
A) 3/7
B) 5/7
C) 6/7
D) 2/7
E) 1/7

Solution: total number of arrangement is= 7!= 5040   Favorable event i.e a,b and c can be arranged together in 3! and the remaining can be arranged in5! since abc can be in any of the five positions.   so 5!*3!/7! = 2/5   ANSW1/7R:1/7
Answer: E
If A is a positive integer, which of the following must be divisible by 6?
Pick one
A) A(A^2−2)  B) A^2*(A−5)  C) A(A+2)^3  D) A^2*(A−5)  E) (A−1)*A*(A+1)

Solution: option E) (A−1)*A*(A+1) which represents the product of three consecutive integers   the product of 3 consecutive integers is divisible by both 2 and 3 and so also divisible by 6.   Answer is (A−1)*A*(A+1)
Answer: E
The circulation for magazine P in 1971 was 4 times the average (arithmetic mean) yearly circulation for magazine P for the years 1972-1980. What is the ratio of the circulation in 1971 to the total circulation during 1971-1980 for magazine P ?	Choose the correct choice from the following
A) 4/7
B) 5/7
C) 3/7
D) 2/7
E) 1/7

Solution: There are 9 years from 1972-1980, inclusive. Let's say the average circulation every year between 1972-1980 inclusive is x.   So the total circulation is 9x from 1972-1980, inclusive.   In 1971, the circulation is 4x.   So total circulation for 1971-1980 is 4x + 9x = 13x.   Ratio of circulation in 1971 to total circulation during 1971-1980 is 4x to 14x or 4/14 4  + 9= 
 4  + 9 = 13
13x.   Ratio of circulation in 1971 to total circulation during 1971-1980 is 4x to 14x or 4/14=2/7   Answer : 2/7
Answer: D
A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 6, 4 and 3, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created?  Pick one:	A) 20	B) 22	C) 26	D) 24	E) 30

Solution: Total # of codes possible is 3*3*3= 
3*3*3 = 27
27. Oit of those 27 codes only the product of 333 and will be odd, the remaining 26 will have either 2 or 4 in them, which ensures that their product will be even. Therefore the number of codes where the product of the digits is even= (total) - (restriction) = 27 - 1= 
27 - 1 = 26
26.   Answer: 26
Answer: C
Which is greater than 16
Choose the correct answer:  A) 1.6  B) 66  C) 6  D) -6  E) 6.1

Solution: 66 greater than 16.   Answer: 66
Answer: B
A clothing store originally bought 100 jackets at a total cost of j dollars. If each jacket was sold for 30 percent more than its original cost, what was the individual price, in terms of j, of each jacket sold?	Pick: A) j/77 B) 7j/500 C) 140j D) j/100+40 E) 140j/100

Solution: lets take j=1000, as decided by you..   now 30% increase makes it 1300..   this is the price for 100 jackets, so selling price for each jacket=1300/100=$13..   so ans is correct as j/77..
Answer: A
John spent a total of $135 on baseball tickets. The price of a ticket is either $12 for the field seats or $5 for the balcony. What is the minimum amount W of dollars he could have spent for the $12 tickets? Choose the correct choice from the following choices
A) $48  B) $60  C) $84  D) $96  E) $120

Solution: 60 ..... 12 *5 W= 60. (min). Thus answer .$60
Answer: B
A certain stock exchange designates each stock with a one-, two-, or three- letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?	Choose the correct option.
A) 2951
B) 8125
C) 15600
D) 16302
E) 18278

Solution: Remember that Numbers can be repeated.   Number of 1 Digit Codes = 26   Number of 2 Digit Codes = 26 * 26= 
26 * 26 = 676
676   Number of 2 Digit Codes= 26 * 26 * 26= 
26 * 26 * 26 = 17_576
17576   Total= 26 + 676 + 17576= 
26 + 676 + 17576 = 18_278
18278   ANS:18278
Answer: E
Out of three given numbers, the first one is twice the second and three times the third. If the average of these numbers is 88, then the difference between first and third is. Choose one:
A) 92
B) 39
C) 87
D) 96
E) None

Solution: Sum of three number is=88*3= 
88*3 = 264
264   Let three numbers are a, b,c and a is the highest and c is the lowest   Then,   2b=a so b=a/2 and 3c=a so c=a/3   we can write,   a+b+c=264   a+a/2+a/3=264   11a/6=264   a=144   So, c=144/3= 
144/3 = 48
48   So there difference is=144-48= 
144-48 = 96
96   Answer 96
Answer: D
If x is the interest on y and y is the interest on z, the rate and time is the same on both the cases. What is the relation between x, y and z?  Select:
A) Y2 = xz	B) Y2 = xy	C) Y2 = Yz	D) Y3 = xz	E) Y5 = xY

Solution: X = (Y*NR)/100 Y = (Z*NR)/100   X/Y = NR/100 Y/Z = NR/100   X/Y = Y/Z   Y2 = XZ.Y2 = xznswer:Y2 = xz
Answer: A
H(x, y) is the intersection point between the circle (x^2 + y^2 = 4) and the line (y = x +2). Which of the following can be the point H?
Choose the most appropriate option:
A) (1, 2).
B) (2, 0).
C) (0, -2).
D) (-2, 0).
E) (2, 2).

Solution: A quick glance at the options, H(x, y)and we can see that A and E do not satisfy the circle equation. Now we are left with B, C and D. Now B and C do not satisfy the line equation. So we are just left with D. And thats the answer=(-2, 0).
Answer: D
Of the films Empty Set Studios released last year, 60% were comedies and the rest were horror films. 75% of the comedies were profitable, but 75% of the horror moves were unprofitable. If the studio made a total of 45 films, and broke even on none of them, how many of their films were profitable?
Choose the most appropriate option:
A) 18  B) 19  C) 20  D) 21  E) 44

Solution: After fiddling some more, this is how I got to answer choice 44...but did I get here using voodoo math or is it sound?   (.60*.75) + (.40*.25) = .44 + .10 = .55   55/100 = 11/20   Then subtract from 45:   45 - 11/20 = 44 (answer 44)
Answer: E
Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1344?	Choose the most appropriate option
A) 1000  B) 2217  C) 1200  D) 2777  E) 2991

Solution: 1344 = P [1 + (5*12/5)/100]   P= 1200   Answer: 1200
Answer: C
If k is the greatest positive integer such that 4^k is a divisor of 16! then k =  Choose the correct choice from the following: A) 3 B) 4 C) 5 D) 6 E) 7

Solution: 16/4= 
16/4 = 4
4   16/16= 
16/16 = 1
1   4+1= 
4+1 = 5
5   k=5   Answer: 5
Answer: C
How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed? Pick.
A) 577 B) 567 C) 360 D) 376 E) None of these

Solution: Explanation :   The smallest number in the series is 1000, a 4-digit number.The largest number in the series is 4000, the only 4-digit number to start with 4.The left most digit (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.Hence, there are 3×5×5×5 or 375 numbers from 1000 to 3999.Including 4000, there will be 376   Answer : 376
Answer: D
If m^(-1) = -1/4 then m^(-2) is equal to  Pick one
A) -9  B) -3  C) -1/9  D) 1/16  E) 9

Solution: You made a mistake here.   You're right till   m^-2 = 1/m^2 and m^-1 = 1/m^1 = 1/m   given m^-1 1/  1= 
1/  1 = 1
1/m   given m^-1= -(1/4) so, 1/m = -(1/4) solving this, m = -4   Now, m^-2 = 1/m^2 = 1/(-4)^2 = 1/16 ANS 1/16
Answer: D
If the cost price of 50 articles is equal to the selling price of 30 articles, then the gain or loss percent is? Choose the correct choice from the following answers.
A) 16
B) 127
C) 12
D) 18
E) 67

Solution: Percentage of profit = 20/30 * 100 = 67%   Answer: 67
Answer: E
A package contains 8 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white? Choose the correct choice from the following answers.
A) 3/5	B) 1/2	C) 6/8	D) 7/9	E) 1/3

Solution: Let number of balls = (8+8)= 
(8+8) = 16
16.   Number of white balls= 8.   P (drawing a white ball) =	8/16	= 1/2   1/2
Answer: B
How many different 5 letter combinations can be created from the letters A,B,C,D and E?	Pick:	A) 625	B) 125	C) 3125	D) 25	E) 5

Solution: This is a case of number of arrangements possible with repetition.   Thus you have 5 options each for the 1st,2nd,3rd,4th and 5th letter giving you a total of   5*5*5*5*5= 
  5*5*5*5*5 = 3_125
3125 number of possible combinations.   Answer : 3125
Answer: C
Find the odd man out. 7,13,19,25,29,37,43 Select the correct option.
A) 19	B) 29	C) 25	D) 43	E) 37

Solution: Explanation :   All given numbers except 25 are prime numbers.   Answer : Option 25
Answer: C
When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 15-inch boxes. If the university pays $0.60 for every box, and if the university needs 3.06 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes?
Choose the correct choice from the following answers
A) $306	B) $275	C) $510	D) $1,250	E) $2,550

Solution: Total no. Of boxes = 3060000/(20×20×15) = 510   Total cost = 510×$0.6=$306   $306nswer $306
Answer: A
Nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw. If the total weight of one screw and one nail is half that of 6 screws and one nail, then the total weight of 3 screws, and 3 nails is how many times that of 4.5 screws and 1.5 nails?
Choose the correct choice from the following
A) a. 4/3
B) b. 5/2
C) c. 2
D) d. 3/2
E) e. 5/4

Solution: let the weight of nail be n and that of screw be s..   so s+w=1/2 * (6s+1n)...   or 1n = 4s..   lets see the weight of 3 s and 3n= 3s+3*4s=15s..   and weight of 4.5s and 1.5n3 +3*4= 
3 +3*4 = 15
15s..   and weight of 4.5s and 1.5n= 4.5s+1.5*4.5s=11.25s..   ratio4.5 +1.5*4.5= 
4.5 +1.5*4.5 = 11.25
11.25s..   ratio= 15s/11.25s=15/11.25=4/3   a. 4/3
Answer: A
Find the area of circle whose radius is 4m? Choose the correct choice from the following options.
A) 50.28  B) 51.54  C) 51.77  D) 52.88  E) 52.98

Solution: 22/7 * 4 * 4   = 50.28   50.28nswer:50.28
Answer: A
If a 4-digit integer is selected at random from the integers 6000 through 6999, inclusive, what is the probability that the first digit and the last digit of the integer are each equal to three times the tens digit and two times the hundreds digit?  Pick.
A) 1/999 B) 3/6000 C) 1/1000 D) 3/2000 E) 2/3000

Solution: Thousand digit has to be 6 . So units digit needs to 6 as well   Both Hundreds and Units digit needs to be 3 times the tens digit   6/3= 
6/3 = 2
2   The tens digit is 2   Both Hundreds and Units digit needs to be 2 times the hundreds digit    6/2= 
 6/2 = 3
3   The hundreds digit is 3   The number is 6326   Total numbers between 6000 and 6999= (6999-6000)+1= 
(6999-6000)+1 = 1_000
1000   Probability= 1/1000   Answer 1/1000
Answer: C
A vessel of capacity 2 litre has 25% of alcohol and another vessel of capacity 6 litre had 50% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
Answers
A) 31%.	B) 71%.	C) 49%.	D) 29%.	E) 35%.

Solution: 25% of 2 litres = 0.5 litres   50% of 6 litres = 3.0 litres   Therefore, total quantity of alcohol is 3.5 litres.   This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 35%   ANSW35%.R:35%.
Answer: E