MU-NLPC/Calc-aqua_rat huggingface dataset:
In a school with 5 classes, each class has 2 students less than the previous class. How many students are there in the largest class if the total number of students at school is 115?
Choose the correct choice from the following answers:
A) 25
B) 26
C) 27
D) 28
E) 29

Solution: Let x be the number of students in the largest class.   Then x + (x-2) + (x-4) + (x-6) + (x-8) = 115   5x - 20 = 115   5x = 135   x = 27   The answer is 27.
Answer: C
In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
Choices:
A) 44  B) 58  C) 74  D) 12  E) 23

Solution: Explanation:   Let the capacity of the can be T litres.   Quantity of milk in the mixture before adding milk = 4/9 (T - 8)   After adding milk, quantity of milk in the mixture = 6/11 T.   6T/11 - 8 = 4/9(T - 8)   10T = 792 - 352 => T = 44.   44nswer:44
Answer: A
Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 4 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?  Choose the correct choice from the following:
A) 1:2	B) 1:3	C) 3:1	D) 1:5	E) 1:4

Solution: Quantity of alcohol in vessel P = 62.5/100 * 4 = 5/2 litres   Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres   Quantity of alcohol in the mixture formed = 5/2 + 7/2= 
5/2 + 7/2 = 6
6 litres   As 8 litres of mixture is formed, ratio of alcohol and water in the mixture formed= 6 : 2 = 3:1.   Answer:3:1
Answer: C
If the digits 35 in the decimal 0.00035 repeat indefinitely, what is the value of (10^5-10^3)(0.00035)?	Choose the correct choice from the following options
A) 37	B) 41	C) 3.5e-05	D) 35	E) 3.5e-07

Solution: 99*0.35= 
99*0.35 = 34.65
34.65 approx. 35   Answer : 41
Answer: B
Coins are to be put into 10 pockets so that each pocket contains at least one coin. At most 6 of the pockets are to contain the same number of coins, and no two of the remaining pockets are to contain an equal number of coins. What is the least possible number of coins needed for the pockets?	Choose the correct choice from the following answers:  A) 7  B) 13  C) 20  D) 22  E) 28

Solution: Since at most 6 of the pockets are to contain the same number of coins then minimize # of coins in each, so let each contain just 1 coin;   Next, we are told that no two of the remaining 4 pockets should contain an equal number of coins, so they should contain 2, 3, 4, and 5 coins each (also minimum possible);   Total:   1+1+1+1+1+1+2+3+4+5= 
  1+1+1+1+1+1+2+3+4+5 = 20
20   Answer: 20.
Answer: C
A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is? Choose the correct choice from the following choices:	A) 1	B) 2	C) 3	D) 7	E) 5

Solution: DS = 6   US = 4   S = ?   S = (6 - 4)/2= 
(6 - 4)/2 = 1
1 kmph 1nswer:1
Answer: A
Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen? Choices: A) 55/119 B) 55/221 C) 55/223 D) 55/227 E) 56

Solution: We have n(s) = \inline {\color{Black}52C_{2}} = = 1326.   Let A = event of getting both black cards   55/221 = event of getting both queens   A∩55/221 = event of getting queen of black cards   n(A) = \inline {\color{55/221lack}26C_{2}} = = 325, n(55/221)= \inline {\color{55/221lack}4C_{2}} = = 6 and n(A∩55/221) = \inline {\color{55/221lack}2C_{2}} = 1   P(A) = n(A)/n(S) = 325/1326;   P(55/221) = n(55/221)/n(S) = 6/1326 and   P(A∩55/221) = n(A∩55/221)/n(S) = 1/1326   P(A∪55/221) = P(A) + P(55/221) - P(A∩55/221) = (325+6-1) / 1326 = 330/1326 =   55/221
Answer: B
When the price of an article was reduced by 15% its sale increased by 80%. What was the net effect on the sale?
Select the correct option:
A) 44% increase  B) 44% decrease  C) 53% increase  D) 66% increase  E) 66% decrease

Solution: if n items are sold for $p each, revenue is $np. If we reduce the price by 15%, the new price is 0.85p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.85p)(1.8n) = 1.53np, which is 1.53 times the old revenue, so is 53% greater.   ANSWER:53% increase
Answer: C
How many ways are there to lay four balls, colored red, black, blue and green in a row?  Choose the correct choice from the following answers
A) 11  B) 33  C) 44  D) 23  E) 77

Solution: Answer:33
Answer: B
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? Answers:	A) 25200	B) 210	C) 120	D) 1000	E) 20000

Solution: Required selection = select 3 consonants from 7 and 2 vowels frm 4   = 7C3 * 4C2   = 210   As we have to form 5 letter word the above combination of consonants and vowels can be done in 5! = 120 different ways   Required no. of ways = 210 * 120= 
210 * 120 = 25_200
25200   25200ns - 25200
Answer: A
X, Y, and Z are three different Prime numbers, the product XYZ is divisible by how many different positive numbers?  Choose the most appropriate option
A) 4
B) 6
C) 8
D) 9
E) 12

Solution: PRIME # is the # that has only 2 factors: One is 1 and another is the # itself.   infer that   FOR any given # 1 and the # itself are the definite factors.   Knowing above concepts:   product of X,Y, and Z = XYZ   divisible by 1, xyz, x, y, z, xy,yz,xz ==> total 8   ANSWER "8"
Answer: C
Jane and Ashley take 10 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ?  Choose one:
A) 10.2 Days  B) 15.2 Days  C) 16.2 Days  D) 18 Days  E) 20 Days

Solution: Let us assume that the work is laying 40 bricks.   Jane = 4 bricks per day   Ashley = 1 brick per day   Together = 5 bricks per day   Let's say first 8 days Ashley works alone,   No of bricks = 8   Last 4 days Jane works alone,   No. of bricks = 16   Remaining bricks = 40 - 24= 
40 - 24 = 16
16   So together, they would take   16/5= 
  16/5 = 16/5 = around 3.2
3.2   Total no. of days= 8 + 4 + 3.2= 
8 + 4 + 3.2 = 15.2
15.2   Answer is 15.2 Days
Answer: B
Evaluate 35 / .07 Options:
A) 400  B) 500  C) 505  D) None of these  E) 506

Solution: Explanation:   35/.07 = 3500/7= 
3500/7 = 500
500   Option 500
Answer: B
The number N is 7,6H4, where H represents the ten's digit. If N is divisible by 9, what is the value of H?  Choose the correct option
A) 1
B) 3
C) 5
D) 7
E) 9

Solution: Integer is divisible by 9 - Sum of digits is divisible by 9   1nswer: 1
Answer: A
Rs.585 is divided amongst A, B, C so that 4 times A's share, 6 times B's share and 3 times C's share are all equal. Find C's share?	Choose the most appropriate option:
A) 260
B) 150
C) 817
D) 716
E) 616

Solution: 260+B+C = 5854260 = 6B = 3C = x260:B:C = 1/4:1/6:1/3= 3:2:44/9 * 585= Rs.260260nswer: 260
Answer: A
a = 2^15 - 625^3 and a/x is an integer, where x is a positive integer greater than 1, such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?  Pick:
A) None
B) One
C) Two
D) Three
E) Four

Solution: This is a tricky worded question and I think the answer is should be D not C...   Here is my reason :   The stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . The stem wants to say that X is a PRIME NUMBER . because any prime   Number has no factor grater than 1 and Itself .   On the other hand the stem says that X COULD get how many different number NOT MUST get different number ( this is very important issue )   AS our friends say, if we simplify Numerator more we can obtain : 5^12 ( 5^3-1) = 5^12 (124) = 5^12 (31*2*2) divided by x and we are told that this fraction is   An integer . so, X COULD Onee ( not Must be) 5 , 31 ,or 2 !!! so , X could get 1 different values and answer is One....
Answer: B
A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 16 seconds. What is the length of the platform in meters?
Choose the correct choice from the following choices.
A) 240 meters B) 360 meters C) 280 meters D) 600 meters E) Cannot be determined

Solution: Speed of the train in metres/sec = 72000/3600= 
72000/3600 = 20
20   Distance travelled by train to cross the platform= 30 * 20= 
30 * 20 = 600
600= Length of train + Length of platform   Distance travelled by train to cross the man = 16 * 20= 
16 * 20 = 320
320= Length of train   Length of platform = 600 - 320= 
600 - 320 = 280
280   Answer: 280 meters
Answer: C
IN Common Wealth Games an athlete runs 400 meters in 24 seconds. Hisspeed is ? Answers.
A) 25 km/hr  B) 27 km/hr  C) 60.60 km/hr  D) 32 km/hr  E) None of these

Solution: Explanation :   (400/1000)/(24/3600)=60.60 km/hr   Answer : 60.60 km/hr
Answer: C
If 2^2n + 2^2n + 2^2n + 2^2n = 4^28, then n =  Options
A) 3 B) 6 C) 12 D) 27 E) 24

Solution: 2^2n + 2^2n + 2^2n + 2^2n = 4^28   => 4 x 2^2n = 4^28 = 2^56   => 2^2 x 2^2n = 2^56   => 2^(2n+2) = 2^56   => 2n+2 = 56=> n =27   So. Answer will be 27.
Answer: D
It takes Jim N minutes to prepare one omelet. It takes Cole N/2 minutes to prepare one omelet. It takes Mitch N/2 minutes to prepare 2 omelets. If Jim, Cole and Mitch together prepare a total of 30 omelets in 40 minutes, then how many minutes would it take Mitch alone to prepare 30 omelets?
Select:
A) 70
B) 120
C) 140
D) 160
E) 280

Solution: Cole is twice as fast as Jim and Mitch is 4 times as fast as Jim (it takes Mitch N/2 minutes to prepare 2 omelets, thus N/4 minutes to prepare one omelet).   Say the rate of Jim is x omelet/minute, the rate of Cole 2x omelet/minute, and the rate of Mitch 4x omelet/minute.   Then, from (time)(rate) = (job done):   (40 minutes)(x + 2x + 4x) = (30 omelets);   (40 minutes)(7x) = (30 omelets);   Since it takes 40 minutes to prepare 30 omelets at the rate of 7x omelet/minute, then it would take   40*7/4= 
  40*7/4 = 70
70 minutes to prepare the same 30 omelets at the rate of 7x*4/7 = 4x omelet/minute (the rate of Mitch).   Or:   (40 minutes)(7x) 7 *4/7= 
7 *4/7 = 4
4x omelet/minute (the rate of Mitch).   Or:   (40 minutes)(7x)= (30 omelets);   (40*7/4 minutes)(7x*4/7) = (30 omelets);   (70 minutes)(4x) = (30 omelets);   70nswer: 70.
Answer: A
The dimensions of a field are 10 m by 10 m. A pit 5 m long, 5 m wide and 3 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of field as a result of this operation ? Choose one:
A) 2m
B) 2.5m
C) 1.5m
D) 1.25m
E) 1m

Solution: The volume of the earth removed is 5*5*3= 
5*5*3 = 75
75 m^3.   The remaining area of the field is   10*10 - 5*5= 
  10*10 - 5*5 = 75
75 m^2.   75 m^3 of the earth evenly spread over the area of 75 m^2 will rise the height by (height)= (volume)/(area) = 75/75= 
75/75 = 1
1 m.   Answer: 1m
Answer: E
If a, b and c are even integers, which of the following could be the value of a^2 + b^2 + c^2?
Choose the most appropriate option:
A) a)82 B) b)84 C) c)85 D) d)87 E) e)90

Solution: a, b and c are even integers which means that, supposing that x, y and z are integers, then a=2x, b=2y and c=2z   Therefore we have: a^2+b^2+c^2=2^2*x^2+2^2*y+2^2*z=4x^2+4y^2+4z^2=4(x^2+y^2+z^2).   Which means that the total a^2+b^2+c^2 must be divisible by 4.   The only choice which is divisible by 4 is: b)84)   84=8^2+4^2+2^2   Answer: b)84.
Answer: B
A bag contains 8 red and 5 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Choices:
A) 4/7
B) 2/3
C) 5/8
D) 1/4
E) 5/7

Solution: Total number of balls = 8+6= 
8+6 = 14
14   number of white balls= 8   Probability = 8/14 = 4/7   4/7nswer is 4/7
Answer: A
A farmer planned to plough a field by doing 120 hectares a day. After two days of work he increased his daily productivity by 25% and he finished the job two days ahead of schedule. What is the area of the field?
Answers:
A) 1420
B) 1430
C) 1450
D) 1440
E) 1460

Solution: First of all we will find the new daily productivity of the farmer in hectares per day: 25% of 120 hectares is 25100⋅120=30 hectares, therefore   120+30= 
  120+30 = 150
150 hectares is the new daily productivity. Lets x be the planned number of days allotted for the job. Then the farm is 120⋅x hectares. On the other hand, we get the same area if we add 120⋅2 hectares to 150(x−4) hectares. Then we get the equation   120x=120⋅2+150(x−4)   x=12   So, the job was initially supposed to take 12 days, but actually the field was ploughed in  12 - 2= 
 12 - 2 = 10
10 days. The field's area is 120⋅12=1440 hectares.   Answer is 1440.
Answer: D
The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 42 degrees. Find the temperature on Friday? Choose the correct choice from the following
A) 28 B) 27 C) 22 D) 34 E) 20

Solution: M + Tu + W + Th = 4 * 48= 
4 * 48 = 192
192   Tu + W + Th + F= 4 * 46= 
4 * 46 = 184
184   M= 42   Tu + W + Th = 192 -42= 
192 -42 = 150
150   F= 184 – 150 = 34   Answer:34
Answer: D
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 7 employees to 2 different offices?  Choose the correct option.
A) 215  B) 310  C) 343  D) 243  E) 123

Solution: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 7*7*7=7^3=343.   Answer: 343.
Answer: C
If x is an integer and x + x^2 + x^3 is odd, which of the following must be even? Pick one
A) x
B) x^2
C) x^3
D) 3x
E) x + x^2

Solution: x + x^2 + x^3 = odd   Since each is a power of x, x has to be odd   On checking the options, only   x + x^2 = odd + odd = even   Correct option: x + x^2
Answer: E
If it would take one machine 15 minutes to fill a large production order and another machine 25 minutes to fill the same order, how many minutes would it take both machines working together, at their respective rates, to fill the order?	Choose the correct choice from the following:
A) 4 1/60  B) 5  C) 5 5/11  D) 5 1/2  E) 9 3/8

Solution: Since , Machine 1-M1 take 15 mins to fill the order   The work done by M1 in a min = 1/15   Machine 2- M2 take 25 mins to fill the same order   and work done by M2 in a min = 1/25   Total work done by M1 and M2 in a min = 1/15 + 1/25 = 8/75   Time needed for M1 and M2 to complete the order = 75/8 = 9 3/8   Answer 9 3/8
Answer: E
12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres? Choose the correct choice from the following choices:
A) 8	B) 15	C) 16	D) 18	E) 19

Solution: Capacity of the tank = (12 x 13.5) liters = 162 liters.   Capacity of each bucket = 9 liters.   Numbers of buckets needed = (162/9)= 
(162/9) = 18
18   ANSWER:18
Answer: D
Which of the following number will completely divide (36^9)-1?  Options
A) 5  B) 6  C) 7  D) 9  E) 4

Solution: x^n - 1 will be divisible by x+1 only when n is even.   36^9 - 1 = (6^2)^9 - 1 = 6^18 - 1 which is divisible by 6+1 i.e. 7   Answer is 7
Answer: C
If x is a positive number and 1/3 the square root of x is equal to 3x, then x =
Answers:  A) 1/3  B) 1/9  C) 1/81  D) 1  E) 81

Solution: 1/3 of sqrt(x) = 3x, which means that sqrt(x) = 9x   or x = 81x^2 -> divide by x   1=81x   x=1/81   1/81.
Answer: C
In a software company 4/10 of people know C++, 2/4 of them know java, 2/8 of them know neither,find the total possibility to know C++? Choose the correct choice from the following.
A) 1/4
B) 1/3
C) 1/2
D) 2/3
E) 3/4

Solution: 1/4ssume 100 persons in a company   person knows c++=4/10=100*4/100=20 persons   person knows java=2/4=100*2/4= 
100*2/4 = 50
50 persons   neither=2/8=100*2/8= 
100*2/8 = 25
25 persons   according to our assumption 100 person=20+50+25= 
20+50+25 = 95
95 person covered(5 remaining)   so,total possibility=20 person(c++)+5(remaining)=25 persons   which is 25/100=1/4   1/4NSWER:1/4
Answer: A
Percentage of profit earned by selling a book for $1380 is equal to the percentage loss incurred by selling the same book for $1020. What price should the book be sold to make 20% profit?  Choose the correct option
A) $1260  B) $1440  C) $1500  D) $1680  E) $2000

Solution: Let C.P. be Rs. x.   Then, (1380 - x)	x 100 =(x - 1020) x 100   1380 - x = x - 1020   2x = 2400   x = 1200   Required S.P. = 120% of 1200 = 1.20 x 1200 = $1440   Answer : $1440
Answer: B
In how many ways can five boys and three girls sit in a row such that all girls sit together? Choose the correct answer.
A) A)1972 B) B)9022 C) C)2880 D) D)1097 E) E)4320

Solution: Treat all girls as one unit. Now there are six students and they can be arranged in 6! ways. Again three girls can be arranged among themselves in 3! ways.   Required number of arrangements   = 6! * 3! = 720* 6= 
720* 6 = 4_320
4320.   Answer:4320
Answer: E
If (2^x)(3^y) = 216, where x and y are positive integers, then (2^x-1)(3^y-2) equals:	Select:
A) 12	B) 24	C) 48	D) 96	E) 144

Solution: So I would start attacking this problem by quickly performing the prime factorization of 288. With that it is easy to count the 5 twos and the 2 threes that are the prime factors. So x=3, y=3. now quickly 2^2(3^1)=12. Than answer should be number 1.   12
Answer: A
John 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?  Select:
A) 2 1/5 Km	B) 3 1/5 Km	C) 3 2/5 Km	D) 3 3/5 Km	E) 4 1/5 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 Km
Answer: B
Village A’s population is 300 greater than Village B's population. If Village B’s population were reduced by 600 people, then Village A’s population would be 4 times as large as Village B's population. What is Village B's current population?	Select the correct option.
A) 900
B) 1000
C) 1100
D) 1200
E) 1300

Solution: A = B+300.   A=4(B-600).   4(B-600)=B+300.   3B=2700.   B=900.   The answer is 900.
Answer: A
A business executive and his client are charging their dinner tab on the executive's expense account.The company will only allow them to spend a total of 50$ for the meal.Assuming that they will pay 7% in sales tax for the meal and leave a 15% tip,what is the most their food can cost?	Choose the correct choice from the following choices
A) 39.55$ B) 40.63$ C) 41.63$ D) 42.15$ E) 43.15$

Solution: Let x be the amount the most their food can cost.   x + 0.07x + 0. 15x = 50   Solving for x, x = 40.98$, this is the maximum amount that can be used for food.   Hence 40.63$ is the maximum value less than 40.98$   Hence Option 40.63$
Answer: B
The total of the ages of Mahesh, Suresh, Ramesh is 102 years. Ten years ago, the ratio of their ages was 2:3:4. What is the present age of Mahesh?  Choose the correct choice from the following answers:  A) 32years  B) 42years  C) 45years  D) 35years  E) 30years

Solution: Let ages of Mahesh, Suresh, Ramesh 10years ago be 2x,3x,4x   2x+10 + 3x+10 +4x+10 = 102   x = 8   Ramesh present age = 4*8+10= 
4*8+10 = 42
42 years   Answer is 42years
Answer: B
How many digits will be there to the right of the decimal point in the product of 98 and .08216 ?
Choose the correct choice from the following options:
A) 5	B) 6	C) 9	D) 7	E) 8

Solution: Product of 98 and .08216 is 8.05168.   Therefore number of digits to right of decimal point is 5   5nswer is 5.
Answer: A
If two numbers are in the ratio 5:6. If 10 is added to both of the numbers then the ratio becomes 6:7 then find the smallest number?
Choose the correct option
A) 10  B) 20  C) 30  D) 40  E) 50

Solution: 50xplanation:   5:6   5x + 10 : 6x + 10 = 6 : 7   7[5x + 10] = 6[6x + 10]   35x + 70 = 36x + 60   36x - 35x = 70 - 60= 
70 - 60 = 10
10   Then smallest number is=5   5x = 50   Answer: Option 50
Answer: E
The king of a country and 4 other dignitaries are scheduled to sit in a row on the 5 chairs represented above. If the king must sit in the center chair, how many different seating arrangements are possible for the 5 people?
Choose the correct choice from the following options:
A) 4 B) 5 C) 24 D) 20 E) 120

Solution: IMO 24   Given that one chair is taken, i think the remaining 4 dignitaries can be arranged 4!=24.
Answer: C
X, Y and Z, 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 $2350, what will be Z's share of the earnings?	Select the correct option
A) $525  B) $550.50  C) $1080.02  D) $522.3  E) $1020.2

Solution: The dollars earned will be in the same ratio as amount of work done   1 day work of Z is 1/12 (or 2/24)   1 day work of the combined workforce is (1/6 + 1/8 + 1/12) = 9/24   Z's contribution is 2/9 of the combined effort   Translating effort to $ = 2/9 * 2350 = $522.3   hence:$522.3
Answer: D
3 no. leave remainders of 43, 47 & 49 on division by N. The sum of the three no.'s leaves a remainder 9 on division by N. What are the values N can take?
Choose the most appropriate option.
A) 34 B) 35 C) 38 D) 67 E) More than one value is possible

Solution: In this question, the sum of the three numbers should leave a remainder  43 + 47 + 49= 
 43 + 47 + 49 = 139
139. Or, it should be of the form N * k + 139, where K is an integer.   However, it leaves a remainder 9, or it is of the form N * m + 9.   N * k + 139= N * m + 9   N * (m - k) = 130   Or, N should be a factor of 130. Since the remainders left on division by N are 43, 47 and 49, N should be greater than 49.   The only factors of 130 that are greater than 49 are 65 and 130. So, N can take 2 values – 65 or 130   More than one value is possible
Answer: E
In how many ways can a group of 16 friends be seated round 2 tables if one of the tables can seat 10 and the other can seat 6 people?
Choose the correct choice from the following options:
A) 15C5 * 9! *4! B) 15C3 * 8! *3! C) 15C4 * 9! *3! D) 16C4 * 9! *5! E) 16C5 * 10! *4!

Solution: 10 people can be selected from 16 people in 16C10 ways.   Remaining 6 people can be selected from 6 people in 6C6 ways.   Now, arranging 10 people on a round table = (10-1)= 
(10-1) = 9
9!   Arranging 6 people on a round table= (6-1)= 
(6-1) = 5
5!   Hence, total number of ways= 16C10 * 9! * 6C6 * 5!   = 16C4 * 9! * 5!   16C4 * 9! *5!
Answer: D
Which of the following is(are) true for a@b=b@a?
I. a@b=ab+ba
II. a@b=(a+b)(a-b)
III. a@b=(a/b)+(b/a)	Options:
A) only Ⅰ
B) only Ⅱ
C) only Ⅲ
D) only Ⅰ& Ⅲ
E) only Ⅱ & Ⅲ

Solution: If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (O).   If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (X).   If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O).   Thus, Ⅰ& Ⅲ are the answers. Therefore, only Ⅰ& Ⅲ is the answer.
Answer: D
The first doughnut is priced at $1 and then if you purchase additional doughnuts as dozens then the price is $6/dozen. What is the total number of doughnuts purchased if you paid $25?  Pick:
A) 45
B) 49
C) 53
D) 57
E) 61

Solution: $25 = 4 * $6 + $1   The number of doughnuts is 4*12 + 1= 
4*12 + 1 = 49
49   The answer is 49.
Answer: B
Square A has an area of 65 square centimeters. Square B has a perimeter of 16 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B? Choices:
A) 0.25
B) 0.5
C) 0.75
D) 0.1
E) 0.3

Solution: I guess it's mean that square B is placed within square Aentirely.   Since, the perimeter of B is 16, then its side is 16/4= 
16/4 = 4
4 and the area is 4^2=16;   Empty space between the squares is 65-16=48 square centimeters, so if a random point is in this area then it won't be within square B: P=favorable/total=48/64 = 0.75.   Answer: 0.75
Answer: C