MU-NLPC/Calc-aqua_rat huggingface dataset:
At a certain school 25% of the students join a band, 25% play a sport and 20% both join the band and play a sport. if a randomly selected student is a member of the band, what is the probablility that the student also plays a sport?	Choose the correct option:
A) 1) 3/4 B) 2)1/5 C) 3)2/5 D) 4)1/2 E) 5)4/5

Solution: This is the way to approach the question:   25% of the students join a band => 25% of the students either only join a band or both join a band and play sports   25% of the students play sports => 25% of the students either only play sports or both play sports and join a band   If a randomly selected student is a member of the band, then probability that the student also plays a sport = percentage of cases in which the student can do both/percentage of cases in which the student can just play sports or do both   =20%/25% = 4/5   The answer is therefore (5)4/5)
Answer: E
What is the units digit of 18! + 1 ?	Pick one
A) 1 B) 3 C) 5 D) 7 E) 9

Solution: Any number above 4!, such as 5!, 6!, etc... are always multiples of 10, so their units digit is 0.   The units digit of 18! + 1 is 1.   The answer is 1.
Answer: A
A 14 meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point?
Answers:
A) 5/14  B) 3/14  C) 8/21  D) 6/7  E) 2/5

Solution: A square with an area of 4 has a perimeter of 8.   For the area to be >4, the longer piece must be >8.   The wire must be cut within 6 meters from either end.   The probability of this is 12/14 = 6/7.   The answer is 6/7.
Answer: D
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.50 km and 1.25 km respectively. The time taken by the slower train to cross the faster train in seconds is? Choose the correct choice:
A) 12
B) 77
C) 66
D) 99
E) 11

Solution: Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Distance covered = 1.50 + 1.25= 
1.50 + 1.25 = 2.75
2.75 km= 2750 m.   Required time = 2750 * 3/125= 
2750 * 3/125 = 66
66 sec.   Answer: 66
Answer: C
What is the speed required for a bike to cover a distance of 720 km in 12 hours?  Choose the correct choice from the following answers.
A) 50 kmh B) 40 kmh C) 100 kmh D) 60 kmh E) 80 kmh

Solution: Speed= 60 kmhistance / Time   Speed = 720 / 12= 
720 / 12 = 60
60   Answer: 60 kmh
Answer: D
If a positive integer n is divisible by both 2 and 5, then n must also be divisible by which of the following?
I. 10
II. 7
III. 40  Choices:  A) None  B) I only  C) II only  D) I and II  E) II and III

Solution: A multiple of 2 and 5 is also a multiple of 10, but not necessarily a multiple of 7 or 40.   The answer is I only.
Answer: B
The list price of an article is Rs.70. A customer pays Rs.61.11 for it. He was given two successive discounts, one of them being 10%. The other discount is? Choose the correct option:
A) 8% B) 7% C) 10% D) 3% E) 4%

Solution: Explanation:   70*(90/100)*((100-x)/100) = 61.11   x = 3%   3%
Answer: D
In a party attended by 9 persons, each clinch their glass with every other. How many glass clinches?
Choose the correct choice from the following options
A) 51	B) 52	C) 34	D) 35	E) 36

Solution: Total no. of person = 11   Total no. of glass clinches = n(n-1)/2   =9*8/2= 
9*8/2 = 36
36   ANSW36R:36
Answer: E
Which of the following triples of numbers have the same standard deviation as the numbers p, q, and r?
I. p-2, q-2, r-2
II. 0, p-q, r-q
III. p-4, q+5, r-1  Choose the correct option.
A) I only  B) II only  C) I and III only  D) II and I only  E) I, II, and III

Solution: If we add or subtract a constant to each term in a set the standard deviation will not change.   Set {p-2, q-2, r-2} is obtained by subtracting 2 from each term of {p, q, r}   Set {0, p-q, r-q} is obtained by subtracting s from each term of {p, q, r}   Set {p-4, q+5, r-1} is totally different from {p, q, r}.   Thus the answer is I and II only.   Answer:II and I only.
Answer: D
5.40 can be expressed in terms of percentage as  Choose the correct choice from the following answers:
A) 5.04%
B) 50.4%
C) 209%
D) 540%
E) None of these

Solution: Explanation:   While calculation in terms of percentage we need to multiply by 100, so   5.40 * 100= 
5.40 * 100 = 540
540   Answer: Option 540%
Answer: D
If XY denotes X is raised to the power Y, Find the last two digits of 19413843+ 19614181 Choose the correct option
A) 67
B) 97
C) 55
D) 32
E) 62

Solution: 1721^3856   unit digit= 1^2=1   10th digit=5*6= 
5*6 = 30
30=0 means last two digit =1   and 1982^4181   unit digit=1   10th digit=8*2= 
8*2 = 16
16 mean last two digit= 61   hence,   61+1= 
61+1 = 62
62
Answer: E
What is the rate percent when the simple interest on Rs.780 amount to Rs.130 in 4 Years?	Choose the correct answer.
A) 4.16	B) 5.16	C) 6.16	D) 7.16	E) 8.16

Solution: 130 = (780*4*R)/100   R = 4.16%   4.16nswer: 4.16
Answer: A
Find the fourth proportion to 2,3,6	Choose the correct choice
A) 18	B) 12	C) 9	D) 3	E) 4

Solution: Explanation:   2:3 :: 6:x   => 2/3 = 6/x   => x = 18/2   => x = 9   Option 9
Answer: C
Sekar started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000. In 2001, Sekar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000. What will be Rajeev's share in the profit of Rs.2,10,000 earned at the end of 3 years from the start of the business in 1999? Choose the correct choice from the following answers:
A) Rs.45,000
B) Rs.50,000
C) Rs.70,000
D) Rs.75,000
E) none

Solution: Solution   Sekar:Rajeev:Jatin=	(25000×12+35000×12+45000×12):(35000×24) : (35000×12)   = 1260000 : 840000 : 420000   = 3 : 2 : 1.   Rajeev's share	=Rs.(210000×2/6)   = Rs.70000.   Answer Rs.70,000
Answer: C
If 15 machine can finish a job in 36 days, then how many more machines would be needed to finish the job in one -fourth less time? Pick one:
A) a. 5  B) b. 8  C) c. 10  D) d. 12  E) e. 16

Solution: You might think of this in a management context - we can use the principle of 'person-hours' to solve any problem where we have identical workers. So, using simpler numbers, suppose you know that 6 identical employees, working simultaneously, would finish a job in 5 hours. Then that job requires 6*5= 
6*5 = 30
30 total hours of person-work. If instead you wanted the job done in 3 hours, you'd assign   30/3= 
  30/3 = 10
10 employees to do the job, because you want to get a total of 30 hours of work from the employees.   We can solve this problem identically. If 15 machines (identical ones, I assume) work simultaneously for 36 days, they will do a total of 15*36 machine-days of work. So the job requires 15*36 days of machine work in total. We instead want the job done in 1/4 less time, so in 27 days. So we'll need 15*36/27= 
15*36/27 = 20
20 machines, or 5 additional machines.   a. 5
Answer: A
If k is a multiple of 3 and k=(m2)nk=(m2)n, where m and n are prime numbers, which of the following must be a multiple of 9?  Choose the correct option.
A) m^2  B) n^2  C) mn  D) mn^2  E) (mn)^2

Solution: must be a multiple of 9   m and n are prime...lets have 2 and 3   now either of then can be a 3...   a) m can be 2 and n = 3...out   b) n can be 2 and m = 3...out   c) m = 2 and n=3 ...out   d) n can be 2 and m = 3...out   e) m = 2/3 or n = 3/2 both satisfies .......must be a multiple of 9   ANSW(mn)^2R:(mn)^2
Answer: E
A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 200 kilometers?	Select the correct option:
A) 4.5 B) 5 C) 6.5 D) 7.5 E) 8.5

Solution: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 180 kilometers?   200 ÷ 40 = 5 × 1 gallon = 5 gallons   correct answer 5
Answer: B
A series of number is given: 5, 6, 12, 5, 7, 13, 5,__14, 5, 9, 15.. What number fills the blank? Choose the correct answer: A) 6 B) 5 C) 9 D) 8 E) 11

Solution: Looking at the series we can see 1 is added to 6, then to 7, then to 8 and so on...   The answer is option 8 (8)
Answer: D
A, B and C start a business each investing 2,000. After 6 months A withdrew 1000, B withdrew 1000 and C invests 1000 more. At the end of the year, a total profit of 6600 was recorded. Find the share of B.  Choose the correct choice
A) 20,000  B) 21,200  C) 1,800  D) 20,500  E) None of these

Solution: Ratio of the capitals of A, B and 1,800   = 2000 Ã— 6 + 1000 Ã— 6 : 2000 Ã— 6 + 1000 Ã— 6 : 2000 Ã— 6 + 3000 Ã— 6   = 18000 : 18000 : 30000 = 18 : 18 : 30   Bâ€™s share = (6600 Ã— 18â„66) = 1800   Answer 1,800
Answer: C
A worker is paid x rupees for painting every 5 metres of a wall and y rupees for painting every extra metre. During one week, he painted 5 metres on Monday, 6 metres on Tuesday, 7 metres on Wednesday, 8 metres on Thursday and 9 metres on Friday. What is his average daily earning rupees for the five day week?
Choose the correct option:  A) x + 2y  B) (5x + 9y)/5  C) 10x + (8/5)y  D) None of these  E) Cannot be determined

Solution: Explanation :   On Monday, the payment = Rs x   On Tuesday, the payment = Rs (x + y)   On Wednesday, the payment = Rs (x + 2y)   On Thursday, the payment = Rs (x + 3y)   On Friday, the payment = Rs (x + 4y)   x + 2yverage daily earning during the five-day week = (5x + 10y)/5   = x + 2y   x + 2ynswer : x + 2y
Answer: A
If x is a positive, single-digit integer such that 2/3*x, 2x, x, and x + 2, and 3x – 2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?	Answers
A) 3
B) 4
C) 5
D) 6
E) 8

Solution: The big hints are thatx is a 1-digit integerAND (2/3)x, 2x, x, and x + 2, and 3x – 2 are ALLintegers   For (2/3)x to be an integer, x MUST BE A MULTIPLE OF 3. So, x can equal 3, 6, or 9.   Now let's plug each possible value of x into the terms and see which one yields a list ofconsecutive integers   When x =3, we get the following terms: (2/3)(3), 2(3),3,3+ 2, and 3(3) – 2.   When we evaluate these terms we get: 4, 6, 3, 5 and 7   Rearrange to get: 2, 4, 5, 6, 7. So, when x = 3, we getconsecutive integers.   In this case, the MEDIAN = 5   Since 5 is among the answer choices, we need not test the other 2 values of x (i.e., x = 6 and x = 9)   Answer:   5
Answer: C
The average age of father and his two sons is 38 Years. Five years ago, the average age of the two sons was 16 Years. If the difference between the ages of the two sons is four years, what is the present age of the father?  Choose the correct choice from the following answers:
A) 45	B) 46	C) 72	D) 48	E) 49

Solution: The total present age of father and two sons is 3x38 = 114 yrs   The total present age of sons is (16+5) X 2 = 42Years   so, present age of father is 114 â€“ 42 = 72 yrs   Answer 72
Answer: C
Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?
Pick one.
A) 18	B) 77	C) 66	D) 55	E) 41

Solution: S:E = 1:3   E:M = 3:5   ------------   S:E:M = 3:9:15   3/27 * 162= 
3/27 * 162 = 18
18   18nswer:18
Answer: A
Three persons A, B and C divide a certain amount of money such that A's share is Rs.4 less than half of the total amount. B's share is Rs.8 more than half of what is left and finally C takes the which is Rs.14. Find the total amount they initially had with them?	Answers.
A) Rs.68 B) Rs.85 C) Rs.80 D) Rs.56 E) Rs.29

Solution: Let the total amount be Rs.P   Let shares of A and B be Rs.X and Rs.Y respectively.   Given, C's share was Rs.14.   X + Y + 14 = P --- (1)   From the given data, X = P/2 - 4 --- (2)   Remaining amount = P - (P/2 - 4) = P/2 + 4   Y = 1/2(P/2 + 4) + 8   => P/4 + 10 --- (3)   From (1), (2) and (3)   P/2 - 4 + P/4 + 10 + 14 = P   => 3P/4 + 20 = P   => P - 3P/4 = 20   => P/4 = 20 => P = Rs.80   Answer: Rs.80
Answer: C
In what ratio must rice of Rs.32per kg be mixed with rice of Rs.42 per kg so that cost of mixture is Rs.20 per kg? Choose the most appropriate option
A) 13:6  B) 13:5  C) 11:6  D) 11:5  E) 12:5

Solution: (20-42)/(32-20)=22/12=11:6   ANSWER:11:6
Answer: C
The average weight of a class is x pounds. When a new student weighing 60 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x? Choices.
A) 85
B) 86
C) 88
D) 90
E) 92

Solution: When the student weighs 80 pounds the average weight is x - 1 pounds;   When the student weighs 110 pounds the average weight is x + 4 pounds.   So, the increase in total weight of 110 - 80= 
110 - 80 = 30
30 pounds corresponds to the increase in average weight of (x + 4) - (x - 1) =5 pounds, which means that there are 30/5 (  + 4) - (  - 1)= 
(  + 4) - (  - 1) = 5
5 pounds, which means that there are  30/5= 
 30/5 = 6
6 students (including the new one). So, initially there were 5 student.   Total weight= 5x + 80 = 6(x-1) --> x = 88 pounds.   Answer: 88.
Answer: C
A man's age is 125% of what it was 10 years ago, but 83 1/3%
of what it will be after 10 years. What is his present age?	Choose the correct choice from the following choices
A) 70
B) 60
C) 50
D) 40
E) 35

Solution: Age before 10 years =x   125x/100=x+10   125x=100x+1000   x=1000/25= 
1000/25 = 40
40   Present age=x+10=40+10= 
40+10 = 50
50   answer :50
Answer: C
If the speed of X inch per second is equivalent to the speed of Y meter per hour, what is Y in terms of X? (1 meter=39.3701 inch) Choose the correct choice from the following answers:
A) 21.44X  B) 33.35X  C) 67.77X  D) 91.44X  E) 111.3X

Solution: X inch per second -->   --> 3,600X per hour(as there are 3,600 seconds in one hour);   --> 3,600X/39.3701=91.44X meter per hour (as there are 39.3701 inch in one meter).   Answer: 91.44X.
Answer: D
A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 3500. The difference between the profit shares of A and C is?	Choose the correct choice:  A) 621  B) 1400  C) 236  D) 600  E) 211

Solution: Explanation:   Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6   And also given that, profit share of B is Rs. 3500   => 5 parts out of 15 parts is Rs. 3500   Now, required difference is 6 - 4= 
6 - 4 = 2
2 parts   Required difference= 2/5 (3500) = Rs. 1400   Answer:1400
Answer: B
If x = a!, which of these following values of a is the least possible value (in this list) for which the last 9 digits of the integer x will all be zero?  Choose the correct answer:
A) 26 B) 32 C) 37 D) 44 E) 49

Solution: 2*5 will give one 0 at the end. We need 2^9*5^9 to get 9 zeroes at the end.   There are many 2's, so we need to find the first 9 appearances of 5.   These multiples of 5 are: 5, 10, 15, 20, 5*5, 30, 35, 40...which gives us 9.   To have at least 9 zeroes at the end, a => 40.   The answer is 44.
Answer: D
36 men can complete a piece of work in 18 days. In how many days will 54 men complete the same work ?	Choose one.
A) 24	B) 77	C) 88	D) 29	E) 12

Solution: 12xplanation:   Less Men, means more Days {Indirect Proportion}   Let the number of days be x   then,   54 : 36 :: 18 : x   x = 12   Answer: 12) 12 days
Answer: E
The function f(Z) represents the number of ways that prime numbers can be uniquely summed to form a certain number Z such that Z = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)? Choose the correct choice.
A) 4  B) 5  C) 6  D) 9  E) 7

Solution: Its better to start with 2 and check whether sum of two primes is primes is even.   1) 2(6 times)   2) 2(3 times) + 3(2 times)   3) 2(2 times) + 3 + 5   4) 2 + 3 + 7   5) 2 + 5 + 5   6) 3(4 times)   7) 5 + 7   Answer: 7
Answer: E
Machine A can finish a job in 4 hours, Machine В can finish the job in 12 hours, and Machine С can finish the job in 6 hours. How many hours will it take for A, B, and С together to finish the job?
Choose the correct choice from the following answers:
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: The combined rate is 1/4+1/12+1/6 = 1/2 of the job per hour.   The time to complete the job is   2/1= 
  2/1 = 2
2 hours.   The answer is 2.
Answer: B
A certain protective additive increases from 20 days to 25 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive?	Options:
A) 25%  B) 33 1/3%  C) 50%  D) 66 2/3%  E) 75%

Solution: General formula for percent increase or decrease, (percent change):   percent=Change/Original∗100   So, the time between maintenance checks increased by 25−20/20∗100=25   25%nswer: 25%.
Answer: A
Rahul went to a shop and bought things worth Rs. 30, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? Answers: A) Rs 15 B) Rs 12.10 C) Rs 24.70 D) Rs 36.80 E) None of these

Solution: Explanation :   Let the cost of the tax items = x   Given that tax rate = 6%   Rs 24.70ost of tax items, x*(6/100) = 30/100   x = 5 rs   Now non taxable item = total cost - cost for taxable item - tax   = 30 - 5 - 0.30= 
30 - 5 - 0.30 = 24.7
24.70   Answer : Rs 24.70
Answer: C
A 360 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?	Pick.
A) 229 B) 108 C) 278 D) 216 E) 112

Solution: S = 360/6 * 18/5= 
360/6 * 18/5 = 216
216 kmph   Answer: 216
Answer: D
7 points are marked on a straight line and another 5 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?
Choose the correct choice.
A) 91  B) 105  C) 175  D) 21  E) 14

Solution: getting the answer 175 which is not in the choices, what is the source of the problem?   71752* 51751 + 51752* 71751 = 175   175
Answer: C
It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill 1/32 of the dish?
Choose the correct choice from the following answers
A) 25
B) 26
C) 27
D) 28
E) 29

Solution: The bacteria doubles each day, so after 29 days, the dish was half full.   After 28 days, the dish was one quarter full.   After 27 days, the dish was one eighth full.   After 26 days, the dish was one sixteenth full.   After 25 days, the dish was 1/32 full.   The answer is 25.
Answer: A
Mr. Evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 3 children and 5 grandchildren, then approximately what percentage of Mr. Evans estate will each grandchild receive? Choose the correct choice from the following answers:
A) 20%
B) 17%
C) 5.0%
D) 3.3%
E) 2.8%

Solution: 25/5= 
25/5 = 5
5   Answer : 5.0%
Answer: C
X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?	Select.
A) 6	B) 7	C) 8	D) 9	E) 5

Solution: Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000   Let investment period of Z be x months.   Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)   = 240 : 300 : 30x = 8 : 10 : x   The share of Z in the annual profit of Rs. 50000 is Rs. 14000.   => [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7   => 25x = 7x + (18 * 7) => x = 7 months.   Z joined the business after (12 - 7) months. i.e., 5 months.   Answer:5
Answer: E
Farmer Charlie has a chicken farm. On a certain day, Charlie calculates in how many days he will run out of chicken-food. He notices that if he would sell 75 of his chickens, he could feed the remaining chickens twenty days longer with the chicken-food he has, and that if he would buy 100 extra chickens, he would run out of chicken-food fifteen days earlier.
How many chickens does farmer Charlie have? Choose the correct answer:
A) 100 B) 500 C) 300 D) 400 E) 600

Solution: C   300   Let n be the number of chickens and let d be the number of days in which Charlie will run out of chicken-food with this number of chickens. The total amount of chicken-food always equals the number of chickens multiplied by the number of days the food lasts. Therefore, the total amount of chicken-food equals n × d.   If Charlie would sell 75 of his chickens, he could feed the remaining chickens twenty days longer, so the total amount of chicken-food would then equal   ( n - 75 ) × ( d + 20 ).   But the total amount of chicken-food does not change, so   ( n - 75 ) × ( d + 20 ) = n × d   which can be rewritten to equation 1:   d = 4/15 × n - 20.   If Charlie would buy 100 extra chickens, he would run out of chicken-food fifteen days earlier, so the total amount of chicken-food would then equal   ( n + 100 ) × ( d - 15 ).   But the total amount of chicken-food does not change, so   ( n + 100 ) × ( d - 15 ) = n × d   which can be rewritten to equation 2:   d = 3/20 × n + 15.   Combining equations 1 and 2 gives:   4/15 × n - 20 = 3/20 × n + 15.   Solving this equations gives n = 300, so farmer 300harlie has 300 chickens.
Answer: C
If the perimeter of a rectangular garden is 800 m, its length when its breadth is 100 m is?
Pick one:  A) 300 m  B) 777 m  C) 200 m  D) 167 m  E) 128 m

Solution: 2(l + 100) = 800 => l   = 300 m   300 mnswer:300 m
Answer: A
At an election 2 candidates are participated a candidate got 30% of votes and defeated by 5000 votes. 100 votes are invalid. Find the total polled votes? Answers.
A) 11520	B) 12600	C) 15000	D) 13560	E) 12560

Solution: winners votes = 100-30= 
100-30 = 70
70%   invalid votes= 100   polled votes = [(100*5000)/(2*70-100)]+100 = 12600   Answer is 12600(100*5000)/(2*70-100) +100= 
(100*5000)/(2*70-100) +100 = 12_600
12600   Answer is 12600
Answer: B
The sum of how many terms of the series 6 + 12 + 18 + 24 + ... is 1800 ? Options.
A) 19	B) 23	C) 13	D) 26	E) 24

Solution: This is an A.P. in which a = 6, d = 6 and Sn = 1800   Then,	n/2*	[2a + (n - 1)d] = 1800   n/2*	[2 x 6 + (n - 1) x 6] = 1800   2   3n (n + 1) = 1800   n(n + 1) = 600   n^2 + n - 600 = 0   n^2 + 25n - 24n - 600 = 0   n(n + 25) - 24(n + 25) = 0   (n + 25)(n - 24) = 0   n = 24   Number of terms = 24   Answer is 24.
Answer: E
In the number 11,0AB, A and B represent the tens and units digits, respectively. If 11,0AB is divisible by 55, what is the greatest possible value of B × A?
Select the correct option.
A) 0 B) 5 C) 10 D) 15 E) 25

Solution: You should notice that 55*2= 
55*2 = 110
110 so 11,000 is divisible by 55: 55*200=11,000 (or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55) --> B*A=0*0= 
0*0 = 0
0.   Next number divisible by 55 is 11,000+55=11,055: B*A=5*5= 
5*5 = 25
25 (next number won't have 110 as the first 3 digits so we have only two options 0 and 25).   Answer: 25
Answer: E
If the average (arithmetic mean) of 5 positive temperatures is y degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be: Options
A) 6y
B) 4y
C) 5y/3
D) 3y/2
E) 3y/5

Solution: The sum of three greatest should be more than sum of two lowest.   The total sum is; 5y   A. 6y; 6y is more than 5y. Not possible.   B. 4y; 5y-4y=y(Possible)   C. 5y/3; 10y/3; 10y/3 > 5y/3. Not possible   D. 3y/2; 7y/2; 7y/2 > 3y/2. Not possible   E. 3y/5; 22y/5; 22y/5 > 3y/5. Not possible.   Ans:4y
Answer: B
A trade analyst announced 10% reduction in the unit price of bike. As a result, the sales volume went up by 5%. What was the net effect on the sales revenue?
Choose the correct choice from the following options:
A) no change	B) decreases by 5.5%	C) increases by 5.5%	D) increases by 5%	E) None of these

Solution: Explanation :   Reduction of price = (100 -10)= 
(100 -10) = 90
90%= 0.9   Increase of sale = (100+5)= 
(100+5) = 105
105%= 1.05   Total effect = 0.9 X 1.05 =94.5%, Decreases by 5.5%   Answer : decreases by 5.5%
Answer: B