MU-NLPC/Calc-aqua_rat huggingface dataset:
Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is:
Select:
A) 30%  B) 100/3%  C) 35%  D) 44%  E) None of these

Solution: Explanation :   C.P. of 6 articles = Rs. 5   => C.P. of 1 article = Rs. 5/6   S.P. of 5 articles = Rs. 6   => S.P. of 1 article = Rs. 6/5   Profit earned per article = 6/5 - 5/6 = 11/30   % Profit = 11/30∗6/5∗100% = 44%   Answer : 44%
Answer: D
In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is: Choose one
A) 2
B) 3
C) 4
D) 5
E) 1

Solution: flight ==> x hrs   600/x - 600/x+1/2 = 200   x(2x+1) = 3   2x2+x-3 (2 +1)= 
 (2 +1) = 3
3   2x2+x-3=0   x=1   ANSW1R 1
Answer: E
Three coins are tossed. What is the probability of getting at most two tails?  Pick one:
A) 2
B) 6/7
C) 7/8
D) 25
E) 5/1

Solution: Explanation :   Total number of outcomes possible when a coin is tossed = 2   Hence, total number of outcomes possible when 3 coins are tossed, n(S) = 2 × 2 × 2 = 8   E = event of getting at most two Tails = {TTH, THT, HTT, THH, HTH, HHT, HHH}   Hence, p(E)=n(E)/n(S)=7/8   7/8
Answer: C
At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 38 years. What is the age of Deepak at present? Choose the correct choice from the following answers
A) 77 years  B) 15 years  C) 66 years  D) 24 years  E) 55 years

Solution: Let the present ages of Arun and Deepak be 4x and 3x years respectively.   Then, 4x + 6 = 38 => x = 8   Deepak's age = 3x = 24 years.   Answer: 24 years
Answer: D
A can do a piece of work in 20 days and B can do it in 30 days and C can do it 10 days. They started the work together and A leaves after 2 days and C leaves after 4 days from the beginning. How long will work lost?
Choose the correct choice from the following
A) 13  B) 16  C) 25  D) 14  E) 15

Solution: 2/20 + x/30 + 4/10 = 1   x = 300/20= 
300/20 = 15
15   Answer: 15
Answer: E
Two trains running in opposite directions cross a man standing on the platform in 20 seconds and 18 seconds respectively and they cross each other in 19 seconds. The ratio of their speeds is:  Select:
A) 1 : 1 B) 3 : 2 C) 3 : 8 D) 3 : 25 E) 3 : 4

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 20 x meters, and length of the second train = 18 y meters. (20 x + 15 y) / (x + y) = 19   ==> 20 x + 18 y = 19 x + 19 y ==> x = y ==> x/y = 1/1   1 : 1nswer: Option 1 : 1
Answer: A
A man invested Rs. 14,400 in Rs. 100 shares of a company at 20 % premium . If the company declares 5% dividend at the end of the year , then how much does he get ? Choose the correct option:
A) 500  B) 600  C) 650  D) 700  E) 750

Solution: No of shares = 14400/120= 
14400/120 = 120
120   Face value= 100*120= 
100*120 = 12_000
12000   Annual income= 5/100*12000= 
5/100*12000 = 600
600   ANSWER 600
Answer: B
A trader sells 75 meters of cloth for Rs. 4950 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?	Select.
A) 51 B) 88 C) 90 D) 42 E) 22

Solution: SP of 1m of cloth = 4950/75 = Rs. 66   CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth   = Rs. 66 - Rs. 15 = Rs. 51   51nswer:51
Answer: A
Molly is rolling a number cube with faces numbered 1 to 6 repeatedly. When she receives a 2, she will stop rolling the cube. What is the probability that Molly will roll the die less than 2 times before stopping? Choices:
A) 11/180
B) 1/6
C) 25/216
D) 91/216
E) 27/128

Solution: The probability that Molly will roll the die less than 4 times before stopping is the sum of the following:   The probability that Molly will roll the die once: P=1/6 (she gets 2 on the first roll);   P = 1/6   Answer: 1/6
Answer: B
There are 11 boys and 10 girls in a class. If three students are selected at random, in how many ways that 3 girl & 2 boys are selected ?	Choose the correct choice from the following.
A) 6600	B) 1300	C) 6780	D) 1976	E) 2448

Solution: E = event that 3 girl and 2 boys are selected   n(E) = we have to select 2 boys from 11 and 3 girl from 10   = 11C2 * 10C3   = 6600   6600ns - 6600
Answer: A
What is the sum of the different positive prime factors of 380? Pick
A) 5 B) 10 C) 15 D) 17 E) 26

Solution: Prime factorization of 380   =38 * 10   =2*19 * 10   =2*19 * 2*5   =2^2 * 5 * 19   Sum of the different positive prime factors of 380 = 2+5+19= 
2+5+19 = 26
26   Answer 26
Answer: E
If the population of a certain country increases at the rate of 1 person every 60 seconds, by how many persons does the population increase in 2 Hours?	Select the correct option
A) 120  B) 80  C) 100  D) 150  E) 140

Solution: 120nswer = 1 * 120(2 hour = 120 minutes)= 120   120nswer = 120
Answer: A
Reena and Shaloo are partners in a business, Reena invests Rs, 35,000 for 8 months and Shaloo invests Rs. 42,000 for 10 months, out of a profit of Rs. 31,570, Reena's share is ?  Choices.
A) 12628 B) 12228 C) 22812 D) 12727 E) 11922

Solution: Ratio of their shares = (35000 * 8) : (42000 * 10) = 2 : 3.   Reena's share Rs. 31570 * (2 / 5) = Rs. 12628   12628nswer: 12628
Answer: A
A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?  Choose the correct answer
A) 535 m	B) 178 m	C) 186 m	D) 168 m	E) 150 m

Solution: Speed = 60 * 5/18   = 50/3 m/sec   Length of the train   = speed * time   = 50/3 * 9= 
50/3 * 9 = 150
150 m   Answer:150 m
Answer: E
A four-character password consists of one letter of the alphabet and three different digits between 1 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible? Select the correct option:
A) 5,040  B) 18,720  C) 26,208  D) 37,440  E) 52,000

Solution: 4 character password: DLDD   First digit can be chosen in 9 ways.   The letter can be chosen in 26 ways.   Next digit can be chosen in 8 ways.   Next digit can be chosen in 7 ways.   This gives us 9*26*8*7ways   Now, the letter can also be DDLD so there will be another 9*26*8*7 ways   Total = 9*26*8*7*2 = 26,208 ways 26,208
Answer: C
Factor | Percent of Respondents |
User-friendly | 56% |
Fast response time | 48% |
Bargain prices | 42% |
The table gives three factors to be considered when choosing an Internet service provider and the percent of the 1,100 respondents to a survey who cited that factor as important. If 30 percent of the respondents cited both “user-friendly” and “fast response time,” what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time?” Choose the correct choice from the following options.
A) 286
B) 336
C) 360
D) 384
E) 420

Solution: The way I looked at is is as follows:   UserFriendly(UF) + FastResponse (FR) = 30%   UF leftover = 56 - 30= 
56 - 30 = 26
26%   FR leftover= 48 - 30= 
48 - 30 = 18
18%   Sum these= 74% (ie. 74% were either UF+FR, UF, FR)   26% leftover is the maximum number for Bargain Price   26/100 * 1100 = 26 * 11= 
26 * 11 = 286
286 (286).
Answer: A
A type of extra-large SUV averages 12.2 miles per gallon (mpg) on the highway, but only 7.6 mpg in the city. What is the maximum distance, in miles, that this SUV could be driven on 25 gallons of gasoline?	Choose the correct choice from the following answers:
A) 190 B) 284.6 C) 300 D) 305 E) 312

Solution: To maximize the distance that SUV could be driven on 25 gallons of gasoline , we need consider only highway driving .   Max distance = 25 * 12.2= 
25 * 12.2 = 305
305   Answer 305
Answer: D
Square RSTU shown above is rotated in a plane about its center in a clockwise direction the minimum number of degrees necessary for T to be in the position where R is now shown. The number of degrees through which RSTU is rotated is Choices
A) 135 degree  B) 180 degree  C) 225 degree  D) 270 degree  E) 315 degree

Solution: From the options, I am assuming the positioning of R and T relative to each other to be as shown. To replace R by T, focus on OT. Say, you rotate OT clockwise (and with it the entire square) and bring it in place of OR. How many degrees did you go? You covered 2 right angles i.e. 180 degrees.   Answer : 180 degree
Answer: B
A man swims downstream 35 km and upstream 20 km taking 5 hours each time, what is the speed of the man in still water?
Select the correct option.
A) 6.5 B) 5.5 C) 5.2 D) 4.6 E) 9.7

Solution: 35 --- 5 DS = 7   ? ---- 1   20 ---- 5 US = 4   ? ---- 1 M = ?   M = (7+ 4)/2= 
(7+ 4)/2 = 11/2 = around 5.5
5.5   Answer: 5.5
Answer: B
The ratio of number of students studying Arts, Commerce and Science in a College is 3 : 7 :8. What is the new ratio of the number of students studying Arts, Commerce and Science respectively if there is an increase of 20%, 40% and 25% in the number of students studying Arts, Commerce and Science?  Choose the correct choice from the following answers
A) 18 : 35 : 50 B) 18 : 49 : 50 C) 4 : 8 : 5 D) 32 : 35 : 25 E) None of these

Solution: Suppose the number of students studying Arts, Commerce and Science be 3x, 7x and 8x respectively.   When their numbers are increased by 20%, 40% and 25% respectively the new ratio becomes   3x × 120% : 7x × 140% :   8x × 125% = 36 : 98 : 100   = 18 : 49 : 50   Answer 18 : 49 : 50
Answer: B
For an integer x greater than 1, x* denotes the product of all the integers from 1 to x inclusive. How many prime numbers are there between 7*+2 and 7*+7, inclusive ? Pick
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: Given that x* denotes the product of all the integers from 1 to n, inclusive so, 7* + 2 = 7! + 2 and 7* + 7 = 7! + 7.   Now, notice that we can factor out 2 our of 7! + 2 so it cannot be a prime number, we can factor out 3 our of 7! + 3 so it cannot be a prime number, we can factor out 4 our of 7! + 4 so it cannot be a prime number, ... The same way for all numbers between 7! + 2 and 7! +7, inclusive. Which means that there are no primes in this range.   0nswer: 0.
Answer: A
An investment compounds annually at an interest rate of 33.34% What is the smallest investment period by which time the investment will more than triple in value? Select.
A) 1  B) 2  C) 3  D) 5  E) 4

Solution: Assume initial amount is x   Annual Interest is 34.1% so after 1 year the amount will become x * (100+33.34)/100 => x*4/3   now we need to find n for x * (4/3)^n = 3x   or in other words n = 4   4
Answer: E
In the x- y plane, there are 4 points (0,0), (0,4), (9,4), and (9,0). If these 4 points makes a rectangle, what is the probability that x+y<4? Choose the correct choice from the following
A) 2/5 B) 3/5 C) 3/7 D) 4/7 E) 2/9

Solution: The line y=-x+4 intersects the rectangle and these three points of intersection (0,0), (0,4) and (4,0) form a triangle.   The points below the line y=-x+4 satisfy x+y<4.   The area of this triangle is (1/2)(4)(4)=8   The area of the rectangle is 36.   P(x+y<4) = 8/36 = 2/9   The answer is 2/9.
Answer: E
If (m-8) is a factor of m^2-sm-24, then s=	Choose the correct choice from the following:  A) 3  B) 5  C) 6  D) 11  E) 16

Solution: (m-8)(m-a)=m^2-sm-24   A=-3   s=8+a=5=D=5
Answer: B
A voltage will influence current only if the circuit is: Pick one:
A) 2
B) 7
C) 6
D) 28
E) 22

Solution: Answer:22
Answer: E
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions?	Choose the most appropriate option.
A) 187 m	B) 704 m	C) 179 m	D) 127 m	E) 297 m

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.   = 500 * 2 * 22/7 * 22.4= 
500 * 2 * 22/7 * 22.4 = 70_400
70400 cm= 704 m   Answer:704 m
Answer: B
By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?  Pick one.
A) 28%	B) 25%	C) 95%	D) 75%	E) 45%

Solution: SP = CP + g   150 SP = 150 CP + 30 SP   120 SP = 150 CP   120 --- 30 CP   100 --- ? => 25%   Answer:25%
Answer: B
A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:	Options:
A) 1/13
B) 2/13
C) 1/26
D) 2/26
E) 1/52

Solution: Here, n(S) = 52.   Let E = event of getting a queen of club or a king of heart.   Then, n(E) = 2.   P(E) =	n(E)/n(S)	=2/52=1/26   Option 1/26
Answer: C
A sales staff is composed of a sales manager and two sales people, all of whom earn commission as a percentage of sales. Each sales person earns 5% commission on sales. In a given week, the sales staff earned a total of $1,500 in commissions on $5,000 worth of sales. What commission rate did the sales manager earn during that week?	Answers.
A) 20%  B) 30%  C) 35%  D) 40%  E) 45%

Solution: A for me.   Let managers comminsion rate be M.   m*5000+ 2*0.05*5000=1500   5000*m=1000   m=20/100=20%
Answer: A
A certain lab experiments with white and brown mice only. In one experiment, 2/5 of the mice are brown. If there are 12 white mice in the experiment, how many mice in total are in the experiment?
Answers:
A) 20  B) 12  C) 15  D) 18  E) 16

Solution: Let total number of mice = M   Number of brown mice = 2/5M   Number of white mice = 3/5 M = 12   => M = 20   20nswer 20
Answer: A
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
Select: A) 9000 B) 9400 C) 9600 D) 9800 E) None

Solution: EXPLANATION   Greatest number of 4-digits is 9999.   L.C.M. of 15, 25, 40 and 75 is 600.   On dividing 9999 by 600, the remainder is 399.   Required number (9999 – 399) = 9600.   Answer 9600
Answer: C
What will come in place of the x in the following Number series? 46080, 3840, 384, x Choose the correct choice from the following:
A) 48
B) 3
C) 4
D) 5
E) 6

Solution: 46080 /12= 
46080 /12 = 3_840
3840   3840 /10= 
3840 /10 = 384
384   384 /8= 
384 /8 = 48
48   48
Answer: A
An article is bought for Rs.600 and sold for Rs.500, find the loss percent?  Select:
A) 16 4/3% B) 100/3% C) 16% D) 16 2/3% E) 18%

Solution: Explanation:   600 ---- 100   100 ---- ? => 16 2/3%   ANSWER IS 16 2/3%
Answer: D
Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is? Select the correct option:
A) 887 gallons
B) 176 gallons
C) 120 gallons
D) 289 gallons
E) 976 gallons

Solution: Work done by the waste pipe in 1 minute   = 1/15 - (1/20 + 1/24) = - 1/40   Volume of 1/40 part   = 3 gallons   Volume of whole = 3 * 40= 
3 * 40 = 120
120 gallons.   Answer:120 gallons
Answer: C
The food in a camp lasts for 20 men for 50 days. If twenty more men join, how many days will the food last?	Choose the correct choice from the following answers:	A) 22 days	B) 25 days	C) 28 days	D) 16 days	E) 27 days

Solution: one man can consume the same food in 20*50= 
20*50 = 1_000
1000 days.   20 more men join, the total number of men= 40   The number of days the food will last = 1000/40= 
1000/40 = 25
25 days.   Answer:25 days
Answer: B
What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?  Options:	A) Rs.525	B) Rs.500	C) Rs.550	D) Rs.555	E) Rs.625

Solution: Explanation:   70 = (P*4*7/2)/100   P = 500   Answer IS Rs.500
Answer: B
How many even number in the range between 25 to 100 inclusive are not divisible by 3
Choose the correct choice.
A) 27  B) 30  C) 31  D) 33  E) 46

Solution: We have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)   For 2,   26,28,30...100   using AP formula, we can say 100 = 10 + (n-1) *2   or n=38.   For 6,   36, 42,...96   using AP formula, we can say 96 = 12 + (n-1) *6   or n=11.   Hence, only divisible by 2 but not 3 = 38-11= 
38-11 = 27
27. hence, 27nswer 27
Answer: A
A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?	Select the correct option
A) 3 B) 6 C) 7 D) 8 E) 9

Solution: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr   [66 * 5/18] m/sec = [55/3] m/sec.   Time taken to pass the man = [110 * 3/55= 
110 * 3/55 = 6
6 sec   Answer:6
Answer: B
A woman begins bicycling with a pace of 10 kmph and she increases her pace every two hours by 2 kmph. She rests from bicycling 2 hours after her pace reaches her maximum speed of 14 kmph. She does a cool-down for the final 8 km at a pace of 2 kmph. How far in km did she bicycle?
Choose the most appropriate option:
A) 96 km
B) 100 km
C) 106 km
D) 116 km
E) 126 km

Solution: Distance covered in first two hours = 10 Ã— 2 = 20 km   Distance covered in next two hours = 12 Ã— 2 = 24 km   Distance covered in next two hours = 14 Ã— 2 = 48 km   Distance covered in first six hours     20 + 24 + 48= 
  20 + 24 + 48 = 92
92 km   Remaining distance= 8 km   92 + 8= 
92 + 8 = 100
100 km   Answer 100 km
Answer: B
How many multiples of 2 are there between 1 and 58, exclusive?	Pick one.
A) 21  B) 22  C) 24  D) 26  E) 28

Solution: 28   multiples of 2 between 1 and 58 exclusive.   from 2 * 1 upto 2*28, (1,2,3,4,...,28). Hence, 28 multiples !   correct option is 28
Answer: E
In a series of five football matches between Germany and Argentina , the probability of Germany winning a match is 1/3 and the probability that the match ends in a draw is 1/4. If a win gets the team 2 points, a draw 1 point and a loss 0 Points, What is the probability that Germany will end up in 5 draws in the series? Pick one.
A) 24/576
B) 125/864
C) 1/25
D) 1/1024
E) 1/5

Solution: Since the probability of a draw is 1/4, then the probability of 5 draws in 5 matches is (1/4)^5=1/1024.   Answer: 1/1024.
Answer: D
Number of ways in which the letters of word GALE can be arranged with vowels in alphabetical order, is  Choose one
A) 360	B) 240	C) 12	D) 480	E) None of these

Solution: Solution   Order of vowels of fixed   âˆ´ required number of ways are 4!/2!.   Answer 12
Answer: C
Anand and Deepak started a business investing Rs. 2250 and Rs. 3200 respectively. Out of a total profit of Rs. 1380, Deepak's share is:	Choose the correct option:
A) 3776	B) 810.27	C) 815.21	D) 688.12	E) 267.1

Solution: Ratio of their shares = 2250 : 3200 = 45:64   Deepak's share = 13800 * 64/109= Rs. 810.27.   Answer: 810.27
Answer: B
Jack and Jill work at a hospital with 6 other workers. For an internal review, 2 of the 8 workers will be randomly chosen to be interviewed. What is the probability that Jack and Jill will both be chosen?	Choose the correct choice from the following answers.
A) 1/3 B) 1/4 C) 1/15 D) 1/28 E) 2/3

Solution: 1/8C2=1/28.   Answer: 1/28.
Answer: D
If six persons sit in a row, then the probability that three particular persons are always together is?
Choose the correct choice from the following choices:
A) 1/6	B) 1/1	C) 1/5	D) 1/9	E) 1/2

Solution: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes   = 3!4! Required probability   = 3!4!/6!   = 1/5   Answer: 1/5
Answer: C
Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four brown stripes, four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall? Choose the most appropriate option:	A) 120	B) 350	C) 1050	D) 2,520	E) 5,040

Solution: Number of ways to choose 2 colors among 6 - 6c2   Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4))   Now the order,   the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4   [Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this]   Total number of combinations - 6c2 * 2* 7c4 = 1050   1050
Answer: C
Fom the integer n, if n*n*n is odd, then what is true from below options? Choose one.
A) n is odd and n*n is even	B) n is odd	C) n is even	D) n*n is odd	E) n*n is odd

Solution: n is odd and n*n is even   Option n is odd and n*n is even
Answer: A
A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 85. How many points altogether did the team score?  Choose the correct option.
A) 662	B) 672	C) 652	D) 642	E) 670

Solution: 8 * 85= 
8 * 85 = 680
680 – 10= 670   ANSW670R:670
Answer: E
Roger can read a book in k minutes. What part of the book can he read in 4 minutes? (k>8) Choose the correct option.
A) 8+k	B) 8/k	C) k/8	D) (k+ 8)/k	E) (k-8) / k

Solution: Let's sayk = 24   That is, it takes 24 minutes to read the entire book.   So, in 8 minutes, Roger can read1/3of the book   So, we're looking for the answer choice that yields an OUTPUT of1/3whenk = 24   8+k) 8+24=32ELIMIN8+kTE   B) 8/24=1/3KEEP   C)24/8 =3ELIMIN8+kTE   D) (24+ 8)/24=32/24 = 4/3ELIMIN8+kTE   E) (24-8) /24=16/24 = 2/3ELIMIN8+kTE   8+knswer: 8+k
Answer: A
A person goes to a bank and Quotes x Rs and y paise on a cheque. The cashier misreads it and gives y Rs and x paise. The man comes out and donates 5 paise to a begger. Now, the man has exactly double the amount he has quoted on the cheque. .  Choose the correct choice from the following choices
A) 31 rs 63 paise  B) 30 rs 63 paise  C) 31 rs 33 paise  D) 31 rs 3 paise  E) 33 rs 63 paise

Solution: he gets 100y+x paise instead of 100x+y paise   (100y+x) - (100x+y) - 5 = (100x+y)   99y -99x - 5 = 100x + y   98y = 199x + 5   y = 2x + (3x+5)/98   only an integer value of x = 31   will make y an integer   with the constraints that both x & y < 100   substituing, y = 2*31 + 1= 
2*31 + 1 = 63
63   ans: 31 rs 63 paise   31 rs 63 paiseNSWER:31 rs 63 paise
Answer: A
Two dice are tossed. The probability that the total score is a prime number is?
Pick:
A) 1/2
B) 5/12
C) 7/9
D) 1/6
E) 1/12

Solution: Clearly, n(S) = (6 x 6) = 36.   Let E = Event that the sum is a prime number.   Then E= { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),   (5, 2), (5, 6), (6, 1), (6, 5) }   n(E) = 15.   P(E) =n(E)/n(S)=15/36=5/12   hence:5/12
Answer: B
An art gallery owner is hanging paintings for a new show. Of the nine paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings?	Choose the most appropriate option:
A) 18	B) 30	C) 64	D) 60480	E) 216

Solution: Arrangement means permutations questions..   9P3 = 9!/3! = 60480   .   ANS option 60480 is correct answer..
Answer: D
1=5,2=25,3=253,4=254,5=?  Choices.
A) 1  B) 255  C) 345  D) 445  E) 235

Solution: 1=5,2=25,3=253,4=254,5=?   5=1   check the first eqn.   1NSWER:1
Answer: A
A bag is filled with pennies and nickels in the ratio of 4 to 2. There are 30 nickles in the bag, how many coins are there in that bag?	Choose the correct choice from the following choices:
A) 90
B) 50
C) 65
D) 70
E) 80

Solution: A ratio of pennies to nickels of 4 to 2 means that we can write the number of pennies and nickels in the form   number of pennies = 4x and number of nickels = 2x   But we know the number of nickels, 30. Hence   2x = 30   Solve for x   x = 15   The total number of coins is given by   4x + 2x = 6x  4  + 2= 
 4  + 2 = 6
6x= 6 × 15 = 90   90nswer : 90
Answer: A
If 70% of a number is equal to two-third of another number, what is the ratio of first number to the second number?  Choose the correct choice from the following options: A) 5:7 B) 18:23 C) 17:19 D) 20:21 E) 2:3

Solution: Let 70% of A = 2/3 B. Then,   70A/100 = 2B/3 => 7A/10 = 2B/3   A/B = (2/3 * 10/7) = 20/21   A:B = 20:21.   Answer: 20:21
Answer: D
C invested $600 in a business and D invested $400 in a business. At the end of the year they got $2000 as the profit. Find their share? Select:  A) $800,$1200  B) $900,$1000  C) $700,$1100  D) $1200,$800  E) $600,$1000

Solution: C:$1200,$800 = 600:400   C:$1200,$800 = 3:2   C's share = 2000*3/5= 
2000*3/5 = 1_200
$1200   $1200,$800's share= 2000*2/5= 
2000*2/5 = 800
$800   Answer is $1200,$800
Answer: D