MU-NLPC/Calc-aqua_rat huggingface dataset:
A miniature gumball machine contains 5 blue, 4 green, and 1 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color?	Answers.
A) 1/3  B) 1/4  C) 1/5  D) 1/6  E) 1/10

Solution: The total number of ways to dispense 3 gumballs is 10C3=120.   The number of ways to choose one of each color is   5*4*1= 
  5*4*1 = 20
20.   P(dispensing one of each color)=20/120=1/6.   The answer is 1/6.
Answer: D
What is the maximum number E of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?
Choose the most appropriate option.
A) 36 B) 32 C) 24 D) 21 E) 15

Solution: 27 cubic centimetre cubes gives side = 3cm   so if:   L*W*H is 9*12*8, then max. cube we can have are  3*4*2= 
 3*4*2 = 24
24   L*W*H is 9*8*12, then max. cube we can have are  3*2*4= 
 3*2*4 = 24
24   L*W*H is 12*8*9, then max. cube we can have are  4*2*3= 
 4*2*3 = 24
24   L*W*H is 12*9*8, then max. cube we can have are  4*3*2= 
 4*3*2 = 24
24   L*W*H is 8*12*9, then max. cube we can have are  2*4*3= 
 2*4*3 = 24
24   L*W*H is 8*9*12, then max. cube we can have are  2*3*4= 
 2*3*4 = 24
24   In all cases we get E=24 cubes.   Ans. 24
Answer: C
A person can swim in still water at 20 km/h. If the speed of water 12 km/h, how many hours will the man take to swim back against the current for 40km?	Select the correct option: A) 3 B) 4 C) 5 D) 6 E) 7

Solution: M = 20   S = 12   US = 20 - 12= 
20 - 12 = 8
8   D= 40   T = 40/8= 
40/8 = 5
5 Answer:5
Answer: C
Evaluate: 11 + sqrt(- 4 + 6×4÷3)	Answers.
A) 9 B) 10 C) 11 D) 12 E) 13

Solution: According to order of operations, inner brackets first where 6×4÷3 is first calculated since it has a multiplication and a division.   6×4÷3 = 24÷3 = 8   Hence   11 + sqrt(- 4 + 6×4÷3) = 11 + sqrt(- 4 + 8)   = 11 + sqrt(4) = 11 + 2= 
11 + 2 = 13
13   correct answer 13)13
Answer: E
If n = 2p, where p is a prime number greater than 2, how many different positiveevendivisors does n have, including n ?
Choose the correct choice from the following options: A) Two B) Three C) Four D) Six E) Eight

Solution: This is an interesting question because we are immediately given the option to insert any prime number we wish for p. Since this is a problem-solving question, and there can only be one correct answer, we can select any value for p, as long as it is a prime number greater than 2. We always want to work with small numbers, so we should select 3 for p. Thus, we have:   n = 4 x 3   n = 12   Next we have to determine all the factors, or divisors, of P. Remember the term factor is synonymous with the term divisor.   1, 12, 6, 2, 4, 3   From this we see that we have 4 even divisors: 12, 6, 2, and 4.   If you are concerned that trying just one value of p might not substantiate the answer, try another value for p. Let’s say p = 5, so   n = 4 x 5   n = 20   The divisors of 20 are: 1, 20, 2, 10, 4, 5. Of these, 4 are even: 20, 2, 10 and 4. As we can see, again we have 4 even divisors.   No matter what the value of p, as long as it is a prime number greater than 2, n will always have 4 even divisors.   The answer is Two.
Answer: A
The product of all the prime numbers less than 25 is closest to which of the following powers of 10? Choose one:	A) a) 10^9	B) b) 10^8	C) c) 10^8*2.23	D) d) 10^6	E) e) 10^5

Solution: Group these numbers so as to get product close to a multiple of 10, so they can be rewritten as (2*5)(3*7)(11*19)(13*17)*23 or 10*21*209*221* 23   Now take out power of 10 from each number and rewrite   10*10*100*100*10 (1*2.1*2.09*2.21*2.3) or 10^7*(1*2.1*2.09*2.21*2.3)=10^7*10*2.23   =2.23*10^8   c) 10^8*2.23
Answer: C
Somehow or other I got talked into buying something on the installment plan. I'm notsure I got a good deal. The payments to date,according to my checkbook, have reached Rs.96.The second year cost Rs.2.00 more than the first year; the third year cost Rs.3.00 more thanthe second; and the fourth year cost me Rs.4.00 more than the third. What were mypayments the first year? Choose the correct option
A) 18  B) 20  C) 22  D) 24  E) 26

Solution: let payments for the first year=x   given,x+x+2+x+5+x+9=96   4x+16=96   x=20   ANSWER:20
Answer: B
A cubical block of metal weighs 7 pounds. How much will another cube of the same metal weigh if its sides are twice as long? Choose the correct choice: A) 48 B) 32 C) 24 D) 56 E) 12

Solution: For example our cube have a side 1 meter, so we have 1 cubical meter in this cube   and this cubical meter weigth 7 pounds   If we take cube with side 2 meters we will have 8 cubical meters in this cube   8 meters * 7 pounds = 56 pounds   So answer is 56   And similar but more theoretical approach:   if we have sides a and b than they have equal ration with their areas:   a/b = a^2/b^2   and they have equal ration with their volumes:   a/b = a^3/b^3   we have two sides 1/2 so their volume will be in ratio 1/8   weight of one cube * volume of another cube     7 * 8= 
  7 * 8 = 56
56   So answer is 56
Answer: D
The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 2500 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Choose the correct choice from the following
A) 140
B) 150
C) 160
D) 170
E) 200

Solution: Given that the area of the square =2500 sq.units   => Side of square = √2500 = 50 units   The radius of the circle = side of the square = 50 units   Length of the rectangle = 2/5 * 50= 
2/5 * 50 = 20
20 units   Given that breadth= 10 units   Area of the rectangle = lb = 20 * 10= 
20 * 10 = 200
200 sq.units   Answer: Option 200
Answer: E
A, B and C shared profits in ratio of 5 : 7 : 8. Theypartnered for 10months, 8months and 7months respectively. What was he ratio of their investments ?
Choices
A) 10 : 49 : 45	B) 20 : 49 : 64	C) 10 : 19 : 64	D) 20 : 35 : 64	E) 30 : 29 : 63

Solution: Simply multiply profit sharing ratio with investment ratio to get investment amount ratio.   Let X is the total investment   â‡’10 x = 5   â‡’ 8 x = 7   â‡’ 7x = 8   â‡’ Final investment ratio = 20 : 35 : 64   20 : 35 : 64
Answer: D
In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If B receive 18000,how much amount was their profit? Options: A) 58000 B) 48200 C) 60400 D) 58500 E) None of these

Solution: Explanation :   Assume that investment of C = x   Then, investment of A =2x   Investment of B = 4x/3   A:B:C = 2x : 4x/3 : x = 2 : 4/3 : 1 =6 : 4 : 3   Let their profit was y   18000 = y*4/(6+4+3)   y = 18000*13/4= 
18000*13/4 = 58_500
58500   Answer : Option 58500
Answer: D
Arun makes a popular brand of ice cream in a rectangular shaped bar 6cm long, 5cm wide and 2cm thick. To cut costs, the company had decided to reduce the volume of the bar by 19%. The thickness will remain same, but the length and width will be decreased by some percentage. The new width will be, Pick:	A) 33	B) 87	C) 99	D) 367	E) 72

Solution: 33nswer:33
Answer: A
The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 26. Which of the following integers is the higher of the remaining two integers? Choose one:
A) 32
B) 85
C) 44
D) 22
E) 55

Solution: Let the four integers be A, B, C and D where A > B > C > D.   (A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)   A = 93, D = 39 and B - C = 26   (1) => B + C = 276 - (A + D) = 276 - 132= 
276 - 132 = 144
144.   85 + 85 -26= 
85 + 85 -26 = 144
144   85= (144 + 26)/2= 
(144 + 26)/2 = 85
85   Answer:Option 85
Answer: B
Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 5 days before the completion of the work. How long did the work last? Select the correct option:
A) 6	B) 7	C) 8	D) 8 1/9	E) 10

Solution: Abel in the 2 days that he worked completed 1/5 of the job = 4/5 remains   Then if Ben had to leave 5 days before the completion, this means that Carla had to work alone for these 5 days in which she completed 1/3 of the job.   Now together, Ben and Carla completed the job in (1/12 + 1/15)(t) = 7/15   3/20 (t) = 7/15 ---> t = 3 1/9   Therefore, these 3 1/9 days worked plus the 5 days that Carla had to work by herself add to 8 1/9 days   Answer: 8 1/9
Answer: D
Robert ate 13 chocolates, Nickel ate 4 chocolates. How many more chocolates did Robert ate than nickel?
Select:
A) A)4	B) B)7	C) C)9	D) D)5	E) E)2

Solution: 13-4= 
13-4 = 9
9. Answer is 9
Answer: C
The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 54. What is the rate of interest per annum? Answers:
A) 8
B) 2
C) 9
D) 4
E) 6

Solution: 6xplanation:   [15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 54   15000[(1 + R/100)2 - 1 - 2R/100] = 54   15000[(100 + R)2 - 10000 - 200R]/10000 = 54   R2 = (54 * 2)/3= 
(54 * 2)/3 = 36
36=> R = 6   Rate = 6%   Answer: Option 6
Answer: E
The average age of 21 students of a class is 21 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 21th student is	Choose one:
A) 164
B) 152
C) 100
D) 182
E) 195

Solution: Explanation:   Age of the 21th student = [21 * 21 - (14 * 5 + 16 * 9)] = (378-214)= 
(378-214) = 164
164 years.   164nswer: 164
Answer: A
The average (arithmetic mean) of 20, 40, and 60 is 9 more than the average of 10, 70, and what number? Choose the most appropriate option.
A) 15	B) 25	C) 35	D) 13	E) 55

Solution: a1 = 120/3= 
120/3 = 40
40   a2= a1 -9 = 31   sum of second list = 31*3= 
31*3 = 93
93   therefore the number= 93 -80= 
93 -80 = 13
13   ANSWER:13
Answer: D
What is the unit digit in(7^95 - 3^58)?
Choose the correct answer.
A) 6  B) 4  C) 7  D) 9  E) 10

Solution: Explanation:   Unit digit in 7^95 = Unit digit in [(7^4)23 x 73]   = Unit digit in [(Unit digit in(2401))23 x (343)]   = Unit digit in (123 x 343)   = Unit digit in (343)   = 3   Unit digit in 3^58 = Unit digit in [(3^4)14 x 32]   = Unit digit in [Unit digit in (81)14 x 32]   = Unit digit in [(1)14 x 32]   = Unit digit in (1 x 9)   = Unit digit in (9)   = 9   Unit digit in (795 - 358) = Unit digit in (343 - 9) = Unit digit in (334) = 4.   4
Answer: B
Ben and Shari have invited three other couples to their apartment for a game of charades. Everyone is to be split into two equal teams, but each team must consist of either two couples or no couples. How many different pairs of teams are possible? Answers: A) 11 B) 14 C) 22 D) 35 E) 70

Solution: Ben and Shari can be paired with any of the other three couples, leaving the remaining two for the other team. So, the number of ways to split 4 couples into two teams is 3:   {1, 2} - {3, 4}   {1, 3} - {2, 4}   {1, 4} - {2, 3}   The number of teams where there are no couples:   {Ben, any from couple 2, any from couple 3, any from couple 4} and the remaining 4 people form team #2. The number of team for Ben = 2*2*2= 
2*2*2 = 8
8.   Total= 3 + 8= 
3 + 8 = 11
11.   11nswer: 11
Answer: A
If xx is chosen at random from the set {1,2,3,4} and yy is to be chosen at random from the set {5,6,7}, what is the probability that xy will be even? Choices:
A) 24  B) 29  C) 28  D) 23  E) 22

Solution: SS ={(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)}   Total element n(S)=12   xy will be even when even xx or yy or both will be even.   Events of x,y being even is E.   E ={(1,6),(2,5),(2,6),(2,7),(3,6),(4,5),(4,6),(4,7)}   n(E)=8   So, Probability,   P=n(E)n(S)   P=812   P=23   23
Answer: D
Calculate the circumference of a circular field whose radius is 5 centimeters.  Choose the correct choice from the following options
A) 5 π cm B) 6 π cm C) 7 π cm D) 8 π cm E) 10 π cm

Solution: Circumference C is given by   C = 2πr = 2π*5 = 10 π cm   correct answer 6 π cm2 *5= 
2 *5 = 10
10 π cm   correct answer 6 π cm
Answer: B
Find the odd man out. 9, 12, 15, 18, 21, 25 Choose the correct answer:
A) 9
B) 25
C) 12
D) 15
E) 18

Solution: All numbers except 25 are multiples of 3   Answer is 25
Answer: B
Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?	Choose the correct answer: A) Rs.5000 B) Rs. 38,000 C) Rs.6300 D) Rs.9000 E) Rs.12000

Solution: Explanation:   Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.   Then, 2x+4000/3x+4000=40/57   57(2x + 4000) = 40(3x + 4000)   6x = 68,000   3x = 34,000   Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.   Answer:Rs. 38,000
Answer: B
There are 9 women and 8 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible? Answers:
A) 836
B) 942
C) 1008
D) 1224
E) 1450

Solution: 910082 * 810082 = 36*28= 
36*28 = 1_008
1008   The answer is 1008.
Answer: C
A completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be
Options
A) 8 days  B) 9 days  C) 10 days  D) 12 days  E) 13 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days   Therefore, here, the required number of days = 12 × 24/ 36 = 8 days.   8 days
Answer: A
A train 225 m long running at 90 kmph crosses a platform in 25 sec. What is the length of the platform?	Choose the correct answer:	A) 271	B) 266	C) 400	D) 277	E) 232

Solution: Length of the platform= 90 * 5/18 * 25= 
90 * 5/18 * 25 = 625
625 – 225= 400   Answer:400
Answer: C
The parameter of a square is equal to the perimeter of a rectangle of length 20 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)	Choose the correct choice from the following options:
A) 77.14 cm  B) 47.14 cm  C) 26.71 cm  D) 94.94 cm  E) 23.57 cm

Solution: Let the side of the square be a cm.   Parameter of the rectangle = 2(20 + 14) = 68 cm Parameter of the square = 68 cm   i.e. 4a = 68   A = 17   Diameter of the semicircle = 17 cm   26.71 cmircimference of the semicircle   = 1/2(∏)(17)   = 1/2(22/7)(17) = 374/14 = 26.71 cm to two decimal places   ANSWER:26.71 cm
Answer: C
The length and breadth of a rectangle is increased by 30% and 45% respectively. What is the increase in the area?  Answers:
A) 88.25
B) 87.5
C) 86.0
D) 88.0
E) 88.5

Solution: 100*100= 
100*100 = 10_000
10000   130*145= 
130*145 = 18_850
18850   -----------   8850   10000----8850   100-----88.50   Answer 88.5
Answer: E
9 engines consume 24 metric tonnes of coal, when each is working 8 hours day. How much coal is required for 8 engines, each running 13 hours a day, if 3 engines of former type consume as much as 4 engines of latter type?	Choose the most appropriate option:
A) 20 metric tonnes	B) 22 metric tonnes	C) 24 metric tonnes	D) 26 metric tonnes	E) None of these

Solution: Explanation :   Let required amount of coal be x metric tonnes   More engines, more amount of coal (direct proportion)   If 3 engines of first type consume 1 unit, then 1 engine will consume 1/3 unit which is its the rate of consumption.   If 4 engines of second type consume 1 unit, then 1 engine will consume 1/4 unit which is its the rate of consumption   More rate of consumption, more amount of coal (direct proportion)   More hours, more amount of coal(direct proportion)   ⇒ 9 × (1/3) × 8 × x = 8 × (1/4) × 13 × 24   ⇒ 3 × 8 × x = 8 × 6 × 13   ⇒ 3 × x = 6 × 13   ⇒ x = 2 × 13 = 26. Answer : Option 26 metric tonnes
Answer: D
Every letter in the alphabet has a number value that is equal to its place in the alphabet. Thus, the letter A has a value of 1, the letter B has a value of 2, the letter C has a value of 3, etc... The number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word. What is the number value of the word "HEN"? Choose the most appropriate option
A) 69
B) 72
C) 75
D) 78
E) 81

Solution: "HEN" = (8+5+14)*3= 
(8+5+14)*3 = 81
81.   The answer is 81.
Answer: E
Kamal obtained 66, 65, 77, 62 and 75 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Choices.
A) 65
B) 69
C) 72
D) 75
E) NOne

Solution: Sol.   Average   = 66 + 65 + 77 + 62 + 75 / 5)   = (345 / 5)= 
(345 / 5) = 69
69.   Answer 69
Answer: B
Louie takes out a three-month loan of $1000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louis have to pay each month?  Choose the correct choice from the following answers:
A) 333 B) 383 C) 402 D) 433 E) 483

Solution: After 1st month: (1000)(1.1)-X = 1100-X   After 2nd month: (1100-X)(1.1)-X = 1210-2.21X   After 3rd month: (1210-2.21X)(1.1)-X = 1331-3.31X   Now, the amount after the last payment in 3rd month must bring the total to 0. Hence:   1331-3.31X = 0   X = 1331/3.31 = 402.11   The answer is 402
Answer: C
Express 15 mps in kmph?  Choose one
A) 22	B) 88	C) 90	D) 21	E) 54

Solution: 15 * 18/5= 
15 * 18/5 = 54
54 kmph   Answer: 54
Answer: E
If 2 (A's capital) = 4 (B's capital) = 6 (C's capital). Then the ratio of their capitals is?	Choose the most appropriate option.
A) 6:3:2	B) 5:3:2	C) 6:3:5	D) 6:4:2	E) 6:2:2

Solution: 26:3:2 = 4B = 6 C   6:3:2:B:C = 1/2:1/4:1/6   = 6:3:2   6:3:2nswer: 6:3:2
Answer: A
In how many ways can 7 different objects be dived among 3 persons so that either one or two of them do not get any object?  Choose the correct choice.
A) 381
B) 180
C) 36
D) 84
E) 94

Solution: case 1: for all obj are given to one person 3   case 2: choose two out of 3 3c2=3   naw no of ways to distribute 7 obj to two person=2^7   sub two way when no obj is given to both   so no of ways=3+3c2(2^7-2)=381   381NSWER:381
Answer: A
A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 12km?
Choices.
A) 3
B) 5
C) 8
D) 9
E) 6

Solution: M = 4   S = 2   US = 4 - 2= 
4 - 2 = 2
2   D= 12   T = 12/2= 
12/2 = 6
6   Answer:6
Answer: E
A train is 360 meter long is running at a speed of 90 km/hour. In what time will it pass a bridge of 140 meter length?	Choose the correct choice:	A) 87	B) 69	C) 40	D) 72	E) 20

Solution: Speed = 90 Km/hr = 90*(5/18) m/sec = 25 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   = 500 * (1/25)= 
500 * (1/25) = 20
20 seconds   Answer: 20
Answer: E
A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 7 years ago? Choose the correct choice from the following answers.
A) 8 B) 10 C) 12 D) 14 E) 7

Solution: Let's say   Age of Richard isR   Age of David isD   Age of Scott isS   Now   Richard is 6 years older than David,   i.e. R = D +6   David is 8 years older than Scott   i.e. D = S +8   If in 8 years, Richard will be twice as old as Scott   i.e. R+8 = 2x(S+8)   i.e. R+8 = 2S + 16   i.e. R = 2S+8   But R = D+6 = (S+8)+6 = S+14   therefore, 2S + 8 = S +14   i.e. S = 6   i.e. R = 20   i.e. D = 14   Now,   how old was David 7 years ago?   i.e. D-7 = 14-7= 
14-7 = 7
7 years   Answer: Option   7
Answer: E
A bowl was filled with 10 ounces of water, and 0.014 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period? Choose the correct choice from the following
A) 0.004% B) 0.04% C) 0.40% D) 7% E) 40%

Solution: Total amount of water evaporated each day during a 50-day period = .014 * 50   =.014 * 100/2   = 1.4/2= 
1.4/2 = 0.7
.7   percent of the original amount of water evaporated during this period= (.7/10) * 100= 
(.7/10) * 100 = 7
7 %   Answer 7%
Answer: D
It is well known that a triangle’s area is √(p(p-a)(p-b)(p-c)),
when p=(a+b+c)/2, such that a, b, c are the lengths of sides of the triangle. If the triangle has 360, 360, and 300 as the side’s lengths, what is the triangle’s area?
Pick: A) 34,200 B) 36,200 C) 38,200 D) 42,200 E) 49,089

Solution: It is well known that a triangle’s area is √(p(p-a)(p-b)(p-c)),   when p=(a+b+c)/2,   -> P=(360+360+300)/2= 
(360+360+300)/2 = 510
510, area=√(510(510-360)(510-360)(510-300))=49,089. Therefore, the answer is 49,089.
Answer: E
Oranges are bought at 7 for Rs.4.50. At what rate per hundred must they be sold to gain 33%?	Choose the correct option
A) 57.5  B) 85.5  C) 89.5  D) 94.5  E) 95.0

Solution: 7 oranges bought for rs 4.5   1 orange cost =4.5/7   therefore for 100 oranges =100*(4.5/7)   gain =33%    450/7+(33/100)*450/7= 
 450/7+(33/100)*450/7 = 171/2 = around 85.5
rate per hundred he want to sell   ans :85.50   ANSWER:85.5
Answer: B
If 4 persons can do 4 times of a particular work in 4 days, then, 7 persons can do 7 times of that work in?	Select:
A) 3 days	B) 4 days	C) 6 days	D) 7 days	E) 8 days

Solution: That is, 1 person can do one time of the work in 4 days.   Therefore, 7 persons can do 7 times work in the same 4 days itself   4 days)
Answer: B
An alloy of copper and zinc contains copper and zinc in the ratio 9 : 6. Another alloy of copper and zinc contains copper and zinc in the ratio 6 : 9. In what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc?  Choose the correct choice from the following:
A) 1 : 5
B) 1 : 4
C) 1 : 3
D) 1 : 1
E) 1 : 2

Solution: Let Alloy_1 be x units, and let Alloy_2 be y units.   So, fraction of copper in Alloy_1 = 9x/15, and fraction of zinc in Alloy_1 = 6x/15   Similarly, fraction of copper in Alloy_2 = 6y/15, and fraction of zinc in Alloy_2 = 9y/15.   Mixing them, we get   copper = 9x/15 +6y/15; zinc = 6x/15 + 9y/15   So, 9x+6y = 6x+9y   -> 3x = 3y   -> x/y =3/3= 
3/3 = 1
1/1   So, they must be mixed in the ratio 1 : 1   Answer : 1 : 1
Answer: D
In how many ways can the letters D, I, G, I, K be arranged so that the two I's are not next to each other?
Choose the correct answer:
A) 36
B) 48
C) 72
D) 96
E) 128

Solution: 1 D   2 I   1 G   1 K   Number of ways these letters can be arranged = 5!/2! (2! to account 2 same Is) = 60   Consider 2 Is as 1 entity and thus the number of arrangements for (II)DGK = 4! = 24   Total allowed cases = 60-24= 
60-24 = 36
36   36 is the correct answer.
Answer: A
A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B =6:3 and B:C = 6:5. If the total runs scored by all of them are 118, the runs scored by B are?
Choose the correct choice from the following options.
A) 24 B) 20.13 C) 30.93 D) 20.93 E) 10.93

Solution: 24:B = 6:3   B:C = 6:5   24:B:C = 36:18:15   12/59 * 118= 
12/59 * 118 = 24
24   24NSWER:24
Answer: A
Assume all pieces of rope are equal.
If 44 pieces of rope measure A feet, how long would B pieces of rope be in inches?  Pick:	A) 44/AB	B) 11/3AB	C) 6/11AB	D) AB/44	E) 3AB/11

Solution: 44 ropes measure A feet or 12*A inches   1 rope will measure = 12*A/44 = 6*A/22 = 3*A/11   B piece of rope measure = B*3*A/11 = 3AB/11   Hence, the answer is 3AB/11.
Answer: E
In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?  Choose the most appropriate option
A) 2.5 sec	B) 4.25 sec	C) 5 sec	D) 12.5 sec	E) 12 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 100/40= 
100/40 = 5/2 = around 2.5
2.5 sec.   2.5 secNSWER:2.5 sec
Answer: A
In one hour, a boat goes 15 km along the stream and 5 km against the stream. the sped of the boat in still water (in km/hr) is :
Options:  A) 3  B) 5  C) 8  D) 9  E) 10

Solution: Solution   Speed in still water= 1/2(15+5) km/hr= 10kmph. Answer 10
Answer: E