MU-NLPC/Calc-aqua_rat huggingface dataset:
The ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers is 17:325. the value of n is  Choose the correct choice from the following choices:
A) 15 B) n=25 C) 35 D) 30 E) none of these

Solution: sum of 1st n natural no.s is n(n+1)/2,   sum of sqaures of 1st n natural no.s is n(n+1)(2n+1)/6,   The ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers=n(n+1)(2n+1)*2*2/(n*n*(n+1)*(n+1))   =2(2n+1)/(3n(n+1))   now by hit and trial for the given options,if we put 25 then this will give 17/325   therefore the answer is 25   ANSWER:n=25
Answer: B
An office supply store stocks two sizes of notebooks, each in five colors: blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 4 notebooks of the same size and the same color or 4 notebooks of the same size and of 4 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?  Answers.
A) 10
B) 12
C) 20
D) 24
E) 28

Solution: First let's consider the small notebooks.   There are 5 ways to choose notebooks of the same color.   The number of ways to choose four notebooks with different colors is 5C4=5.   There are 10 different packages we can make with the small notebooks.   We can use the same process to find 10 different packages with large notebooks.   The total number of different packages is 20.   The answer is 20.
Answer: C
How many pieces of 0.85 meteres can be cut from a rod 42.5 meteres long  Choose the correct choice from the following answers.
A) 30  B) 40  C) 50  D) 60  E) 70

Solution: Explanation:   We need so simple divide 42.5/0.85,   =(4250/85)= 
(4250/85) = 50
50   Option 50
Answer: C
What is 120% of 13/24 of 360?	Answers
A) 52 B) 117 C) 234 D) 312 E) 576

Solution: 120% * 13/24 * 360 = 1.2 * 13 * 15= 
1.2 * 13 * 15 = 234
234   The answer is 234.
Answer: C
How many odd numbers between 10 and 1,000 are the squares of integers?  Choose the correct choice from the following.
A) 12 B) 13 C) 14 D) 15 E) 16

Solution: The square of an odd number is an odd number:   10 < odd < 1,000   10 < odd^2 < 1,000   3.something < odd < 31.something (by taking the square root).   So, that odd number could be any odd number from 5 to 31, inclusive: 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, and 31.   14 numbers.   Answer: 14.
Answer: C
Two trains each 150m in length each, are running on two parallel lines in opposite directions. If one goes at the speed of 95km/h while the other travels at 85km/h. how long will it take for them to pass each other completely.  Choose the correct choice from the following answers:
A) 25 sec B) 23 sec C) 34 sec D) 22 sec E) 6 sec

Solution: 6 secxplanation:   D = 150 m + 150 m = 300 m   RS = 95 + 85= 
95 + 85 = 180
180 * 5/18= 
180 * 5/18 = 50
50   T= 300 * 1/50= 
300 * 1/50 = 6
6 sec   Answer: Option 6 sec
Answer: E
The duplicate ratio of 6:4 is?	Select the correct option
A) 1:2 B) 9:4 C) 1:8 D) 1:18 E) 1:13

Solution: 36^2: 4^2 = 36:16=9:4   ANSWER:9:4
Answer: B
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?	Choose the correct choice from the following options.
A) 2877 B) 5760 C) 1797 D) 1797 E) 2972

Solution: Explanation:   1/x - 1/6 = -1/8   x = 24 hrs    24 * 60 * 4= 
 24 * 60 * 4 = 5_760
5760   Answer:5760
Answer: B
A clothing store originally bought 100 jackets at a total cost of j dollars. If each jacket was sold for 50 percent more than its original cost, what was the individual price, in terms of j, of each jacket sold?
Options.
A) j/67  B) 7j/500  C) 140j  D) j/100+40  E) 140j/100

Solution: lets take j=1000, as decided by you..   now 50% increase makes it 1500..   this is the price for 100 jackets, so selling price for each jacket=1500/100=$15..   =j/67   so ans is correct as j/67..
Answer: A
Three unbiased coins are tossed, what is the probability of getting at least 2 tails ?  Options
A) 1/5	B) 1/7	C) 1/8	D) 1/2	E) 1/10

Solution: Total cases are = 2^3=8   favoured cases =[TTH,THT,HTT,TTT]=4   Probability = 4/8=1/2   ANSWER 1/2
Answer: D
The diameter of the driving wheel of a bus in 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 14 kmph?  Choose the correct choice from the following answers
A) 53.03 B) 50.01 C) 23.23 D) 24.23 E) 41.23

Solution: distance covered in 1 min=(14*1000)/60=233.33m   circumference of the wheel=(2*(22/7)*.70)= 
(2*(22/7)*.70) = 4.4
4.4m   no of revolution per min=233.33/4.4=53.03   53.03NSWER:53.03
Answer: A
Find number which is 70% less than 80.	Choose the correct choice from the following choices:  A) 18  B) 22  C) 24  D) 26  E) 98

Solution: Explanation:   70% less is 30% of the given number   Therefore, 30% of 80 is 24.   ANSWER: 24
Answer: C
In a BCCI meeting there are ten people. All shake hands with each other once. How many handshakes will be there altogether?
Pick.
A) 38	B) 676	C) 278	D) 28	E) 21

Solution: Answer:676
Answer: B
A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 2 days. How many more days are required to complete the remaining work if they work together?	Choose the correct choice from the following
A) 3 (5/18)	B) 3 (5/16)	C) 3 (5/11)	D) 3 (5/13)	E) 3 (5/21)

Solution: A can do 1/10 of the work in a day.   B can do 1/12 of the work in a 1 day.   Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60   They take 60/11 days to complete the work together.   Given that they already worked for 2 days.   The number of days required to complete remaining work => 60/11 - 2 = 38/11 = 3 (5/11) days.   Answer:3 (5/11)
Answer: C
The sum of money at compound interest amounts to thrice itself in 2 years. In how many years will it be 6 times itself?
Options:
A) 8 years B) 9 years C) 2 years D) 6 years E) 4 years

Solution: 100 ---- 300 --- 2   600 --- 2   ----   4 years   Answer: 4 years
Answer: E
Three pounds of 05 grass seed contain 1 percent herbicide. A different type of grass seed, 20, which contains 20 percent herbicide, will be mixed with three pounds of 05 grass seed. How much grass seed of type 20 should be added to the three pounds of 05 grass seed so that the mixture contains 15 percent herbicide? Choose the correct choice from the following choices.
A) 3
B) 3.75
C) 4.5
D) 8.4
E) 9

Solution: 05 grass seed contains 5% herbicide and its amount is 3 pound   20 grass seed contains 20% herbicide and its amount is x   when these two types of grass seeds are mixed, their average becomes 15%   thus we have   3(1)+x(20)/(x+3) = 15   3+20x=15x +45   5x=42   or x=8.4   8.4
Answer: D
One night 17 percent of the female officers on a police force were on duty. If 204 police officers were on duty that night and half of these were female officers, how many female officers were on the police force? Choices: A) 420 B) 480 C) 540 D) 600 E) 660

Solution: Let x be the number of female police officers on the police force.   The number of female police officers on duty was 102.   0.17x = 102   x = 600   The answer is 600.
Answer: D
The blood groups of 100 people is distributed as follows: 15 have type A blood, 20 have B blood type, 60 have O blood type and 5 have type AB blood. If a person from this group is selected at random, what is the probability that this person has AB blood type?  Choose the correct choice from the following options:
A) 0.4 B) 0.5 C) 0.05 D) 0.1 E) 0.01

Solution: Blood group -	frequency   A	- 15   B	- 20   O	- 60   AB	- 5   Let P(E) be the event of getting AB blood group   P(E) = Frequency for AB blood group / Total frequencies in the above table   = 5 / (5+60+20+15)   = 5 / 100= 
5 / 100 = 1/20 = around 0.05
0.05   My answer is (0.05)
Answer: C
A traveler changes 150 pounds into rupees at the rate of Rs. 7000 for 100 pounds. He spends Rs. 9060 and changes the remaining amount back to pounds at the rate of 100 pounds to Rs. 7200. How many pounds will he get? Choose the correct choice from the following choices:
A) 18 pounds
B) 20 pounds
C) 25 pounds
D) 30 pounds
E) None of these

Solution: Explanation:   Amount of rupees for exchange of 150 pounds = (150/100)*(7000/1) = Rs. 10,500   Out of these Rs.10,500, traveler spent Rs. 9060   Remaining balance in rupees = 10,500 – 9060 = Rs. 1440   Now these Rs. 1440 are exchanged back to pounds with the rate of 100 pounds for Rs. 7200   Amount in pounds = (1440 * 100) / 7200= 
(1440 * 100) / 7200 = 20
20 pounds   ANSWER: 20 pounds
Answer: B
Bill downloads the movieRevenge of the Avengersto his computer in 2.5 hours, using a download manager that downloads from 3 sources marked A, B and C. Each source provides download at a constant rate, but the rates of different sources are not necessarily identical. If the movie was downloaded from sources A and C alone, it would take 4 hours to complete the download. The next day, source B is available, but the other sources are inactive. How long will it take to download the trailer of the movie, a file that is 80 times smaller, from source B alone?
Choose the correct choice from the following options:
A) 6 hours and 40 minutes B) 15 minutes C) 12 minutes D) 10 minutes E) 5 minutes

Solution: Let the movie size be 400 u.   Given,A+C=4 hrs.   A+C=100 u/hr   And A+B+C=2.5 hrs or   400/2.5= 
  400/2.5 = 160
160 u/hr   B alone=160-100= 
160-100 = 60
60 u/hr   Trailer=80 times smaller or  400/80= 
  400/80 = 5
5 u   B will take 5/60 hrs or 5 minutes.   Ans 5 minutes
Answer: E
A is twice as good workman as B, and together they complete a work in 15 days. In how many days can the work be complete by B alone? Choose the correct option:
A) 35 days
B) 65 days
C) 45 days
D) 75 days
E) 95 days

Solution: 45 days   45 days
Answer: C
In one alloy there is 12% chromium while in another alloy it is 8%. 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.	Pick.
A) 8.8%	B) 9%	C) 9.2%	D) 8.6%	E) 8.4%

Solution: The amount of chromium in the new 15+35= 
15+35 = 50
50 kg alloy is  0.12*15+0.08*35= 
 0.12*15+0.08*35 = 4.6
4.6 kg, so the percentage is  4.6/50*100= 
 4.6/50*100 = 9.2
9.2%.   Answer: 9.2%.
Answer: C
What is the probability of getting a sum 9 from two throws of a dice?
Choices.
A) 1/6  B) 1/9  C) 1/8  D) 5/8  E) 2/9

Solution: In two throws of a dice, n(S) = (6 x 6) = 36.   Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.   P(E)=n(E)/n(S)   =4/36   =1/9   The answer should be 1/9
Answer: B
A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.70 per kg. What will be his gain percent?	Choices
A) 8 1/7 % B) 2 1/3 % C) 11 2/3 % D) 8 1/8 % E) 8 1/9 %

Solution: C.P. of 1 kg = 420/70 = Rs. 6   S.P. of 1 kg = Rs. 6.70   Gain % = 0.70/6 * 100 = 35/3   = 11 2/3 %   Answer:11 2/3 %
Answer: C
There are 20 brown dogs, 10 white dogs, 15 black dogs.Totally how many dogs are there in all? Pick one:
A) 45  B) 15  C) 25  D) 5  E) 30

Solution: 20+10+15= 
20+10+15 = 45
45. 45nswer is 45
Answer: A
The Guests at a football banquet consumed a total of 327 pounds of food. if no individual guest consumed more than 2 pounds of food, What is the minimum number of guests that could have attended the banquet?	Choose the correct choice from the following options:
A) 160 B) 161 C) 162 D) 163 E) 164

Solution: To minimize one quantity maximize other.   163*2 (max possible amount of food a guest could consume) = 326 pounds, so there must be more than 163 guests, next integer is 164.   Answer: 164.
Answer: E
A goods train runs at the speed of 72 km/hr and crosses a 270 m long platform in 26 sec. What is the length of the goods train?  Answers.
A) 278	B) 166	C) 151	D) 250	E) 109

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Time= 26 sec.   Let the length of the train be x meters.   Then, (x + 270)/26 = 20   x = 250 m.   Answer:250
Answer: D
A, B and C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
Choose the correct choice from the following answers.
A) 45 B) 50 C) 55 D) 65 E) none

Solution: Sol.   A : B : C = 10 * 7 : 12 * 5 : 15 * 3 = 70 : 60 : 45 = 14 : 12 : 9.   ∴ C’s rent = Rs. [175 * 9/35] = Rs. 45.   45nswer 45
Answer: A
In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?	Choose the correct choice from the following answers
A) 720 ways
B) 735 ways
C) 767 ways
D) 723 ways
E) 730 ways

Solution: The word 'LEADING' has 7 different letters.   When the vowels EAI are always together, they can be supposed to form one letter.   Then, we have to arrange the letters LNDG (EAI).   Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.   The vowels (EAI) can be arranged among themselves in 3! = 6 ways.   Required number of ways = (120 x 6) = 720.   720 waysnswer:720 ways
Answer: A
A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.13 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost? Choose the correct choice.
A) 1276
B) 1560
C) 2832
D) 1299
E) 1236

Solution: Explanation:   l * 30 = 1200 è l = 40   40 + 30 + 50= 
40 + 30 + 50 = 120
120   120 * 13= 
120 * 13 = 1_560
1560   Answer: Option 1560
Answer: B
The average salary of the employees in a office is Rs.120/month.The avg salary of officers is Rs.460 and of non officers is Rs 110. If the no.of officers is 15,then find the No of nonofficers in the office.	Pick:
A) 450  B) 470  C) 560  D) 700  E) 510

Solution: Let no. of non- officers be x   15 * 460 + x * 110 = (x + 15) 120   x = 510   510
Answer: E
Difference between the length &breadth of a rectangle is 10 m. If its perimeter is 60 m, then its area is??
Pick one
A) 2000 m^2
B) 200 m^2
C) 2520 m^2
D) 2556 m^2
E) 2534 m^2

Solution: l -b = 10   2 (l+b)= 60 => l + b = 30   2 l = 40 => l = 20 so b = 10   area of the rectangle = l x b = 20 x 10 = 200 m^2   Answer : 200 m^2
Answer: B
The bankerâ€™s gain on a sum due 3 years hence at 10% per annum is Rs. 60. The bankerâ€™s discount is  Select the correct option:
A) Rs.960 B) Rs.840 C) Rs.1020 D) Rs.760 E) Rs.260

Solution: Solution   T.D	=(B.G x 100 / R x T)   = Rs.(60x100/10 x 3)   = Rs.200.   B.D   =Rs(200+ 60)   = Rs.260.   Answer Rs.260
Answer: E
In how many ways Chief Minister and Minister be elected from a team of 12 members?	Answers.
A) 124  B) 129  C) 132  D) 142  E) 144

Solution: To do this, if captain is elected first, then we have 12 ways of doing this.   For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)   So, the ans is 12*11= 
12*11 = 132
132 ways.   132
Answer: C
If a,b are positive integers and a/b=77.75 which of the following could be the value of b?  Choices
A) 1. 25	B) 2. 26	C) 3. 27	D) 4. 27	E) 4. 32

Solution: Given a/b = 77.75.   this is 77 and 3/4 = 311/4   Since a and b are integers we know that whatever is the value of b, it must be divisible by 4 completely(to make a an integer)   Ans:4. 32
Answer: E
Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?	Choose the correct option
A) $5500
B) $11000
C) $22000
D) $2750
E) $44000

Solution: Explanatory Answer   Shawn received an extra amount of ($605 - $550) $55 on his compound interest paying bond as the interest that he received in the first year also earned interest in the second year.   The extra interest earned on the compound interest bond = $ 55   The interest for the first year = $550/2= 
550/2 = 275
$ 275   Therefore, the rate of interest= (55/275)*100= 
(55/275)*100 = 20
20% p.a.   20% interest means that Shawn received 20% of the amount he invested in the bonds as interest   If 20% of his investment in one of the bonds= $275, then his total investment in each of the bonds = (275/20)*100= 
(275/20)*100 = 1_375
$ 1375   As he invested equal sums in both the bonds, his total savings before investing= 2*1375= 
2*1375 = 2_750
$ 2750.   correct choice is ($2750)
Answer: D
How is 4% expressed as a decimal fraction?	Choose the correct choice from the following:
A) 0.4  B) 0.04  C) 0.004  D) 0.0004  E) 4

Solution: 4/100= 
4/100 = 1/25 = around 0.04
0.04   ANSWER:0.04
Answer: B
Adam sat with his friends in the Chinnaswamy stadium at Madurai to watch the 100 metres running race organized by the Asian athletics Association. Five rounds were run. After every round half the teams were eliminated. Finally, one team wins the game. How many teams participated in the race? Choose the correct answer:
A) 32  B) 77  C) 279  D) 27  E) 91

Solution: Total five rounds were run. So in the final round 2 teams must have participated. In the penultimate round 4 teams, and 3rd round 8, 2nd round 16 and in the first round 32 teams must have participated as in each round half of the teams got eliminated.   32nswer:32
Answer: A
Two trains A and B are 175 m and 150 m long and are moving at one another at 54 Km/hr and 36 Km/hr respectively. Arun is sitting on coach B1 of train A. Calculate the time taken by Arun to completely cross Train B.	Choose the most appropriate option:
A) 10 s  B) 6 s  C) 4 s  D) 8 s  E) 13 s

Solution: DETAILED SOLUTION   Speed of A = 54∗1000/60∗60 = 15 m/s   Speed of B = 36∗1000/60∗60 = 10 m/s   Relative speed = S1 + S2 = 15 + 10 m/s = 25 m/s   The length that needs to be crossed = length of train B = 150 m. Therefore time taken = 150/25= 
150/25 = 6
6s.   What is the time taken for trains to completely cross each other? The length that needs to be crossed= 175 + 150= 
175 + 150 = 325
325 m. Time taken=325/25= 
325/25 = 13
13 s.   CORR13 sCT ANSW13 sR 13 s.
Answer: E
In how many ways can a committee of 4 people comprising at least 3 boys be formed using a group of 4 boys and 6 girls?	Select the correct option.
A) 67 B) 64 C) 65 D) 66 E) None of these

Solution: There are 2 options: the selected groups have no girls or one girls.   -First case: 1 girl + 3 boys: 6C1 * 5C3 = 6*10= 
6*10 = 60
60   -Second case: 4 boys: 5C4= 5   So there are 60 + 5 = 64 ways in total.   64
Answer: B
A sporting goods store sold 64 Frisbees in one week, some for $3 and the rest for $4 each. If receipts from Frisbee sales for the week totaled $204, what is the fewest number of $3 Frisbees that could have been sold? Select
A) 24 B) 12 C) 8 D) 52 E) 2

Solution: In this question however, because we are told that exactly 64 Frisbees have been sold and revenue was exactly $204, there is only one possible solution for the number of $3 and $4 Frisbees sold.   To solve, we have 2 equations and 2 unknowns   Let x = number of $3 Frisbees sold   Let y = number of $4 Frisbees sold   x + y = 64   3x + 4y = 204   x = 64 - y   3(64-y) + 4y = 204   192 - 3y + 4y = 204   y = 12 x= 64-12= 
64-12 = 52
52   52
Answer: D
water is continuously poured from a reservoir to a locality at the steady rate of 10,000 liters per hour. When delivery exceeds demand the excess water is stored in a tank. If the demand for 8 consecutive three-hour periods is 10000,10000,45000,25000,40000,15000,60000 and 35000 liters respectively, what will be the minimum capacity required of the water tank (in 1000 litres) to meet the demand?  Options
A) 20 B) 30 C) 40 D) 50 E) 60

Solution: in the period of first 3 hrs, the demand of water = 10000.   but the water poured by 10000 per hour.   Thus the end of 3 hours it will poured 30000 ltr then the excess of water = 20000.   Similarly at the end of 2nd 3 hr period the excess of water  20000+20000= 
 20000+20000 = 40_000
40000.   Third, 3 hrs water poured= 30000   already we have 40000 of excess water and demand 45000.   Then the excess water at the end of 3rd 3 hrs   = 40000+30000–45000   = 25000   Fourth 3 hrs. water = 25000+30000–25000   = 30000   Fifth = 30000+30000–40000   = 20000   Sixth = 20000+30000–15000=35000   Seventh = 35000+30000–60000   = 5000   Eighth = 5000+30000–35000   = 0   By analyzing the above results, we have 40000 ltrs is the highest measure of excess water.   So the minimum capacity of water tank = 40000 litres = 40   i.e. = 40   ANSWER:40
Answer: C
If an article is sold at 18% profit instead of 11% profit, then the profit would be $56 more. What is the cost price? Options.
A) $600  B) $800  C) $1000  D) $1200  E) $1400

Solution: 7% * cost price = $56   1% * cost price = $56 / 7= 
56 / 7 = 8
$8   The cost price is $800.   The answer is $800.
Answer: B
If the tens digit of positive integers x, y are 6, how many values of the tens digit of 2(x+y) can be there? Select the correct option:  A) 2  B) 3  C) 4  D) 5  E) 6

Solution: If X=y=60, 2(x+y)=240 is derived. If x=y=69, 2(x+y)=276 is derived, which makes 4,5,6,7 possible for the tens digit. Therefore, the answer is 4.
Answer: C
Three-fourth of a positive number and 25/216 of its reciprocal are equal. The number is: Choose the most appropriate option
A) 5/12.72 B) 12/5 C) 25/144 D) 144/25 E) 146/25

Solution: Let the number be x. Then,   3/4 x = 25/216 * 1/x   x2 = 25/216 * 4/3 = 25/162   x = 5/12.72   5/12.72NSWER:5/12.72
Answer: A
The guidelines at a certain college specify that for the introductory English class, the professor may choose one of six specified novels, and choose two plays from a list of 6 specified plays. Thus, the reading list for this introductory class has one novel and two plays. How many different reading lists could a professor create within these parameters?	Options:
A) 60	B) 70	C) 80	D) 90	E) 100

Solution: 6C1*6C2 = 6*15= 
6*15 = 90
90   The answer is 90.
Answer: D
The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
Choose the correct choice from the following choices.
A) Rs.4589	B) Rs.4528	C) Rs.4528	D) Rs.4530	E) Rs.4537

Solution: Area of the four walls = 2h(l + b)   Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.   Total cost = 906 * 5 = Rs.4530   Answer:Rs.4530
Answer: D
In N is a positive integer less than 200, and 27N/60 is an integer, then N has how many different positive prime factors? Choose the correct choice from the following.
A) 2	B) 3	C) 5	D) 6	E) 8

Solution: (A).   27n/60 must be an integer. => 9n/20 must be an integer. Hence n must be a multiple of 2*5.   => n has 2 different prime integers.
Answer: A
Adding 20% of x to x is equivalent to multiplying x by which of the following?
Choose the correct choice from the following:
A) 12.5
B) 1.05
C) 1.15
D) 1.2
E) 1.25

Solution: 120x/100= 1.2*x   ANSWER:1.2120 /100= 
120 /100 = 6/5 = around 1.2
1.2*x   ANSWER:1.2
Answer: D
Dan has a membership at a local gym that also gives classes three nights a week. On any given class night, Dan has the option of taking yoga, weight training, or kickboxing classes. If Dan decides to go to either one or two classes per week, how many different combinations T of classes are available?
Choices:
A) 3
B) T=6
C) T=7
D) T=9
E) T=12

Solution: I think it should be E only.   No where it is given that he attends different classes on each day.   Experts please provide your views.   --- EDITED my Response. It was a typo. I meant 12 is the answer.   If only T=9ay 1 : 3 options   If T=9ay 1 and T=9ay 2 : 3*3= 
3*3 = 9
9 Options   So, Total= 3+9= 
3+9 = 12
12.
Answer: D