MU-NLPC/Calc-aqua_rat huggingface dataset:
Machine T takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine T to make 40 widgets? Choices:
A) 5
B) 6
C) 8
D) 10
E) 12

Solution: i approached this one by plugging in numbers...started with C.   if 40 are made in 8 hours, then 20 are made in 4 hours. so time of T is 4, and time of B is 2.   rate together: 20/4 + 20/2 = 5+10= 
5+10 = 15
15. so in 1 hour, together make 15 widgets. in 3 hours= 45. way too much. we can eliminate right away C, B, and A - because B and T reduces the time - the total # of widgets made will be even higher.   now between D and E -> try only one ..if it doesn't work, then the other one is the answer.   i picked E:   12h to make 40 widgets, and 6 hours to make 20. this is the time of T. time of B=4 hours.   20/6 + 20/4 = 10/3 + 20/4   find LCM of 3 and 4 = 12. multiply first by 4, and second by 3:   40+60/12 = 100/12   divide by 4:   25/3   so this is the rate given.   12 is the correct answer
Answer: E
A train is 400 meter long is running at a speed of 60 km/hour. In what time will it pass a signal post?	Choose one:	A) 28 seconds	B) 30 seconds	C) 40 seconds	D) 24 seconds	E) 18 seconds

Solution: Speed = 60 Km/hr = 60*(5/18) m/sec = 150/9 m/sec   Total distance = 400 meter   Time = 24 secondsistance/speed   = 400 * (9/150)= 
400 * (9/150) = 24
24 seconds   Answer: 24 seconds
Answer: D
The product of the squares of two positive integers is 900. How many pairs of positive integers satisfy this condition? Choose the correct choice from the following choices:
A) 0 B) 1 C) 2 D) 3 E) 4

Solution: Ans: E - 4 pairs   (xˆ2)(yˆ2) = 900 [square root both sides]   xy = 30   20 = 1x30, 3x10, 6x5, 5x6, 10x3, 30x1, 15x2, 2x15   Cancel the repeats   This leaves us with exactly 4 options.   Hence, 4
Answer: E
An archer is shooting arrows from various distances. She shoots at a target from 40 yards, 50 yards, and 60 yards. The probability that she hits within the bullseye from 40 yards is 4/5, the probability that she hits within the bullseye from 50 yards is 3/4, and the probability that she hits within the bullseye from 60 yards is 2/3. What is the probability that she hits the bullseye at least once in three shots, one from each distance listed.  Choices:
A) 39/40  B) 49/50  C) 59/60  D) 9/10  E) 14/15

Solution: The probability that she hits the bullseye at least once = 1 - (the probability that she misses the bullseye every shot)   The probability that she misses every shot = (prob that she misses from 40 yards)*(prob that she misses from 50 yards)*(prob that she misses from 60 yards)   Prob that she misses from 40 yards = 1 - 4/5 = 1/5; Prob that she misses from 50 yards = 1 - 3/4 = 1/4; Prob that she misses from 60 yards = 1 - 2/3 = 1/3   Thus the probability that she misses all shots = (1/5)*(1/4)*(1/3) = 1/60   Thus the probability that she makes at least one shot = 1 - (1/60) = 59/60   59/60
Answer: C
How many seconds will a 600 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? Select
A) 25  B) 36  C) 40  D) 45  E) 50

Solution: Relative speed of the train=63-3= 
63-3 = 60
60kmph=60*5/18=50/3 m/sec   t=600*3/50= 
600*3/50 = 36
36sec   ANSWER:36
Answer: B
Fortunes, the latest SUV by Toyota Motors, consumes diesel at the rate of 1400×[1000x+x]1400×[1000x+x] litres per km, when driven at the speed of xx km per hour. If the cost of diesel is Rs 35 per litre and the driver is paid at the rate of Rs 125 per hour then find the approximate optimal speed (in km per hour) of Fortuner that will minimize the total cost of the round trip of 800 kms?	Options
A) 34 km per hour B) 54 km per hour C) 49 km per hour D) 65 km per hour E) 67 km per hour

Solution: Given that the diesel consumption is at the rate   1400×[1000x+x]1400×[1000x+x]   Cost of diesel = Rs 35 per litre   Payment to the driver = Rs 125 per hour.   Also given that the SUV is driven at the speed of xx km per hour.   Total cost (c)(c)   =1400×[1000x+x]×800×35+125×800x=1400×[1000x+x]×800×35+125×800x   =70000x+70x+100000x=70000x+70x+100000x   Now differentiating both sides in the above equation with respect to xx.   dcdx=−170,000x2+70=0dcdx=−170,000x2+70=0   ⇒ x=49 km per hour.   49 km per hour
Answer: C
Find the annual income derived by investing $ 6800 in 40% stock at 136.
Choose the correct option.
A) 550  B) 2000  C) 250  D) 3000  E) 400

Solution: By investing $ 136, income obtained = $ 40.   By investing $ 6800, income obtained = $ [(40/136)*6800= 
(40/136)*6800 = 2_000
$ 2000.   Answer 2000.
Answer: B
Express the following as a Decimal 6%
Select the correct option:  A) 0.6  B) 6.0  C) 0.006  D) 6.6  E) 0.06

Solution: 6% = 6/100= 
6/100 = 3/50 = around 0.06
0.06   Answer is 0.06.
Answer: E
Youseff lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work. It is takes him exactly 8 minutes more to walk to work than to ride his bike to work, then x equals?  Choose the correct choice from the following answers:
A) 4	B) 7	C) 12	D) 15	E) 20

Solution: Please follow posting guidelines, link is in my signatures.   As for your question, x/60 = blocks/time/block = block^2/time . This is not what you want. You are given x blocks and 60 seconds PER BLOCK. Thus you need to put it as 60*x to give you units of seconds as you are equating this to 480 (which is TIME in seconds.).   Thus the correct equation is : 60*x-20*x=480 ----> 40x=480--> x = 12.   Option 12
Answer: C
At an examination in which full marks were 500. A got 10% less than B, B got 25% more than C and C got 20% less than D. If A got 360marks, what percentage of full marks was obtained by D?
Pick
A) 40%  B) 44%  C) 80%  D) 90%  E) 100%

Solution: Explanation:   A B 80% D   90 100 80 100   A D   90 ----- 100   360 ------ ? = 400   500 ------ 400   100 ------- ? => 80%   Answer: Option 80%
Answer: C
For any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 525 what is the least possible value of k?
Pick one.
A) 10	B) 14	C) 15	D) 21	E) 25

Solution: 525 = 3*5*5*7   Thus k must include numbers at least up to the number 10 so that there are two appearances of 5.   The answer is 10.
Answer: A
Three models (P, Q, and R) of cars are distributed among three showrooms. The number of cars in each showrooms must be equal and each model must be represented by at least one car in every showroom. There are 19 cars of Model P, 17 cars of Model Q, and 15 cars of Model R. What is the maximum number of cars of model P in any showroom ?  Select:
A) 17 B) 16 C) 15 D) 14 E) 13

Solution: The total number of cars is 51. So each showroom has 17 cars(since the number of cars in each showrooms should be equal   51/3= 
  51/3 = 17
17).   Moreover that the number of model P is maximum means that the numbers of model Q and R should be minimum. Since each model must be represented by at least one car in every showroom that minimum number should be 1.   So Maximum number of model P is   17-2= 
  17-2 = 15
15.   The answer is (15)
Answer: C
A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of B.	Choose the correct choice from the following answers.
A) 240 B) 288 C) 277 D) 390 E) 361

Solution: (3*8 + 2*4):(4*8 + 5*4)   8:13   13/21 * 630= 
13/21 * 630 = 390
390   Answer: 390
Answer: D
In a circuit board factory, all circuit boards that pass a verification process are certified. Every board that fails the verification process is indeed faulty, but 1/8 of those that pass are also faulty.
Approximately how many faulty circuit boards exist in a group of 2,400 circuit boards where 64 fail inspection? Choose one:
A) 72 B) 356 C) 200 D) 256 E) 264

Solution: Total of 2,400 boards. All that fail verification are indeed faulty. So the 64 are indeed faulty. 1/8 those that pass are also faulty.   From the 2,400 we know 64 fail. So 2,336 must pass. Of these 1/8 are faulty. 2,336 divided by 8 gives you 292.   What one must do now is to add to the 292 which were not detected the actually detected faulty ones, namely the 64.   Total faulty: 356.   Answer: 356
Answer: B
Diana is painting statues. She has 7/16 of a gallon of paint remaining. Each statue requires 1/16 gallon of paint. How many statues can she paint?	Select:
A) 7 B) 20 C) 28 D) 14 E) 19

Solution: number of statues=all the paint÷amount used per statue   =7/16 ÷ 1/16   =7/16*16/1= 
7/16*16/1 = 7
7/1= 
7/1 = 7
7   7nswer is 7.
Answer: A
A can do a piece of work in 30 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
Select the correct option.
A) 30 days B) 65 days C) 86 days D) 45 days E) 17 days

Solution: 10/30 + 10/30 + 10/x = 1   x =30 days   30 daysnswer:30 days
Answer: A
In the new budget , the price of kerosene oil rose by 25%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase ? Choose the correct choice from the following
A) 10	B) 20	C) 30	D) 40	E) None of them

Solution: Reduction in consumption = [((R/(100+R))*100]%   =[(25/125)*100= 
(25/125)*100 = 20
20%.   Answer is 20.
Answer: B
If six coins are flipped simultaneously, the probability of getting at least one heads and at least one tails is closest to Choose the correct choice from the following options.
A) 3%	B) 6%	C) 75%	D) 94%	E) 97%

Solution: Probability of getting no heads = 1/64   Probability of getting at least 1 head = 63/64   Probability of getting no tails = 1/64   Probability of getting at least 1 tail = 63/64   Probability of getting at least 1 head and at least 1 tail = 63*63/64*64   63/64 is greater than 98%... So squaring that should be greater than 96%. Answer is 97%.
Answer: E
At present, the ratio between the ages of Arun and Deepak is 4:3. After 7 years, Arun's age will be 19 years. What is the age of Deepak at present?
Answers.
A) 16  B) 14  C) 12  D) 9  E) 15

Solution: Let the present ages of Arun and Deepak be 4x and 3x years respectively.   Then, 4x + 7 = 19 => x = 12   Deepak's age = 3x = 9 years.   Answer: 9
Answer: D
The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.10 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?  Pick one.
A) 399	B) 272	C) 732.6	D) 277	E) 311

Solution: Answer: Option 732.6   Explanation:   a2 = 3136 => a = 56   56 * 4 * 3= 
56 * 4 * 3 = 672
672 â€“ 6= 666 * 1.1= 
666 * 1.1 = 732.6
732.6 Answer: 732.6
Answer: C
The average of 65 numbers is 40. If two numbers, 83 and 30 are discarded, then the average of the remaining numbers is nearly	Options:  A) 28.32  B) 39  C) 38.78  D) 29  E) 39.47

Solution: 39.47xplanation :   Total sum of 63 numbers = (65 * 40) - (83 +30) = 2600 - 113= 
2600 - 113 = 2_487
2487   Average= 2487/63 = 39.47   Answer : 39.47
Answer: E
If W is the set of all the integers between 69 and 99, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?  Choose the correct choice from the following.
A) 20 B) 32 C) 33 D) 34 E) 35

Solution: Multiples of 2 from 69 to 99=Multiples of 2 from 1 to 99-Multiples of 2 from 1 to 68=[99/2]-[68/2]=49-34= 
49-34 = 15
15   Multiples of 3 from 69 to 99=Multiples of 3 from 1 to 99-Multiples of 3 from 1 to 68=[99/3]-[68/3]=33-23= 
33-23 = 10
10   Multiples of2 and 3 bothi.e.6 from 69 to 99=Multiples of 6 from 1 to 99-Multiples of 6 from 1 to 68=[99/6]-[68/6]=16-11= 
16-11 = 5
5   These 8 Numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3   i.e. Total Numbers in W= 15 + 10 - 5= 
15 + 10 - 5 = 20
20   20nswer Option 20
Answer: A
Joshua and Jose work at an auto repair center with 2 other workers. For a survey on health care insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen? Choose the correct choice from the following answers:
A) 1/15 B) 1/12 C) 1/9 D) 1/6 E) 1/3

Solution: Two Methods   1) Probability of chosing Josh first = 1/4   Probability of chosing Jose second = 1/3   total = 1/12   Probability of chosing Jose first = 1/4   Probability of chosing Josh second = 1/3   Total = 1/12   Final = 1/12 + 1/12 = 1/6   1/6
Answer: D
The average of 7 numbers is 25. If each number be multiplied by 5. Find the average of new set of numbers? Choose the most appropriate option:  A) A)110  B) B)122  C) C)120  D) D)125  E) E)145

Solution: Explanation:   Average of new numbers = 25 * 5= 
25 * 5 = 125
125   Answer: Option 125
Answer: D
Solve 2log53 X log9x + 1 = log53
Choices
A) 3/5  B) 4/5  C) 4  D) 4/6  E) 5

Solution: Solution:   We can rewrite the above equation in the below format   => log532 X log9x = log53 - 1   => log59 X log9x = log53 - log55   => log59 X log9x = log5(3/5)   By Using the change of base rule in Left side we get   => log5x = log5(3/5)   The value of X = 3/5   3/5NSWER IS 3/5
Answer: A
The perimeter of a semi circle is 144 cm then the radius is?
Choose one.
A) 22 B) 28 C) 98 D) 37 E) 13

Solution: 36/7 r = 144   => r   = 28   Answer: 28
Answer: B
If log1087.5 = 2.9421, then the number of digits in (875)10 is?	Choose the correct choice from the following:
A) 30  B) 28  C) 27  D) 26  E) 40

Solution: X = (875)10 = (87.5 x 10)10   Therefore, log10X = 10(log2087.5 + 1)   = 10(2.9421 + 1)   = 10(3.9421) = 39.421   X = antilog(39.421)   Therefore, number of digits in X = 40.   ANSW40R:40
Answer: E
The volumes of two cubes are in the ratio 27: 125, what shall be the ratio of their surface areas?
Choose the correct answer:
A) 9:22  B) 9:20  C) 9:25  D) 9:26  E) 9:21

Solution: a13 : a23 = 27 : 125   a1 : a2 = 3 : 5   6 a12 : 6 a22   a12 : a22 = 9:25   Answer:9:25
Answer: C
For every positive odd integer n, the function h(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If p is the smallest prime factor of h(100) +1, then p is?
Choose the correct answer:
A) between 1 and 20	B) between 10 and 20	C) between 20 and 30	D) between 30 and 40	E) 1

Solution: h(100) will have 0 in its unit digit because while doing the calculation of the function we are multiplying by 10 (and 100). So h(100)+1 will have 1 in the units digit so smallest prime factor is 1.   Answer: 1
Answer: E
Set S consists of numbers 2, 3, 6, 48, and 164. Number K is computed by multiplying one random number from set S by one of the first 10 non-negative integers, also selected at random. If Z=6^K, what is the probability that 678,463 is not a multiple of Z?
Pick:
A) 10%  B) 25%  C) 50%  D) 90%  E) 100%

Solution: Probability of any random number being picked from set S = 1   Probability of kk not being 0 = 9/10 ( as there are total of 10 ways to pick up k and 9 ways for k not being 0)   Since it's an AND event , we will multiply the probabilities of both the events.   Hence total probability = 1∗9/10=90%. Answer:90%
Answer: D
In a certain game, a player begins with a bag containing tiles numbered 1 through 15, each of which has an equal probability of being selected. The player draws one tile. If the tile is even, the player stops. If not, the player draws another tile without replacing the first. If this second tile is even, the player stops. If not, the player draws a third tile—without replacing either of the first two tiles—and then stops. What is the probability that at the conclusion of the game, the sum of the tiles that the player has drawn is odd?	Select the correct option:
A) 5/18 B) 13/36 C) 3/8 D) 5/8 E) 23/36

Solution: player begins with containing tiles 1 to 10 and have equal probability of selecting means   Proabability of selecting one number =1/10. here 5 even numbers and 5 odd numbers are there.   Next , player draws one title , if number is even player stops or otherwise title is odd without replacement   player draws second title.   If second title is even , player stops or title is odd without replacement player draws third title.   in third title , without replacement of first and second title, player draws and stops it.   the sum of tilte probability is odd. here two conditions are possible.   1st condition is   1st title is odd+ 2nd title is even stops= probability of selecting one title is 1/10*5c1.   Here are we are not selecting 1st condition as even stops because sum of tile is odd.   Here 5 odd numbers are there we can select 1out of 5 odd numbers.   without replacement of fist we select second tilte is even. is 5/10*5c1/9c1.   here we are selecting one number out of remaining 9 numbers. so probability is 5/18.   we are selecting 1 even number out of 5.   2nd condition is 1stodd without replacement,2nd odd without replacement and 3rd one also odd to get odd as sum of title.   Then probability is 5/10*4/9*3/8=1/12.   Finally sum of probability of two conditions is 5/18+1/12   =23/36.   so option 23/36 is correct.
Answer: E
A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area Q of the triangle in terms of h?	Answers:
A) h/ √2  B) h/2  C) h/4  D) (h)^2  E) (h)^2/4

Solution: IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2).   The AREA Q= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2.   So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches...   (h)^2/4
Answer: E
HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is?
Select the correct option:	A) 36	B) 66	C) 132	D) 264	E) 152

Solution: 12 * 396 = 36 * x   x = 132   ANSWER:132
Answer: C
3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 8 pumps work to empty the tank in 1 day?
Options
A) 6	B) 10	C) 11	D) 12	E) 13

Solution: 3 pumps take 16 hrs total (8 Hrs a day)   If 1 pump will be working then, it will need   16*3= 
  16*3 = 48
48 hrs   1 pump need 48 Hrs   If I contribute 8 pumps then     48/8= 
  48/8 = 6
6 hrs.   answer :6
Answer: A
A bus leaves Los Angeles at 9:00 a.m. traveling north at 50 miles per hour. At 11:00 a.m. a plane leaves Los Angeles traveling north at 200 miles per hour. At what time will the plane overtake the bus?  Choose the correct choice from the following options:
A) 11:40 a.m. B) 12:15 p.m. C) 10:00 a.m. D) 11:25 a.m. E) 10:40 a.m.

Solution: 11:40 a.m.t 11:00am, the bus is 100 miles ahead of plane   The plane travels at 200 mph, which gains 150 mph on bus   100/250=2/5 hours = 40 minutes   11:00 + 0:40 = 11:40   The plane will overtake bus at 11:40am   11:40 a.m.nswer:11:40 a.m.
Answer: A
What is the smallest no. that should be added to 31110 to make it exactly divisible by 9?  Options: A) 1 B) 3 C) 5 D) 6 E) 9

Solution: If a number is divisible by 9, the sum of its digits must be a multiple of 9.   Here, 3+1+1+1+0=6, the next multiple of 9 is 9.   3 must be added to 31110 to make it divisible by 9   3
Answer: B
An bus covers a certain distance at a speed of 240 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?  Options.
A) 600 km/hr	B) 720 km/hr	C) 730 km/hr	D) 750 km/hr	E) 760 km/hr

Solution: Distance = (240 x 5) = 1200 km.   Speed = Distance/Time   Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]   Required speed = 1200 x 3 km/hr = 720 km/hr.   720 km/hr
Answer: B
The below sequence is a bit tricky. Can you solve it to find the next number?
8, 28, 328, 4328, ?
Pick one:	A) 29816	B) 38291	C) 54325	D) 38290	E) 54328

Solution: See the pattern. With every digit, the previous numbers are added after that digit   So the next number in the series is 54328   Answer : 54328
Answer: E
The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
Pick one:
A) 300
B) 230
C) 245
D) 250
E) 260

Solution: Speed = 45 * 5/18 = 25/2 m/sec.   Time = 30 sec   Let the length of bridge be x meters.   Then, (130 + x)/30 = 25/2   x = 245 m.   Answer: Option 245
Answer: C
The curved surface of a sphere is 64 π cm2. Find its radius? Choose the correct option.
A) 9
B) 8
C) 4
D) 5
E) 6

Solution: 4 πr2 = 64 => r = 4   Answer:4
Answer: C
A card is drawn at random from a pack of 52 cards. What is the probability that it is neither a spade nor a jack?
Choose the correct choice
A) 9/13  B) 4/13  C) 2/13  D) 6/13  E) 5/13

Solution: There are 13 spades including a jack and 3 more jacks of other suits.   Probability of getting spade or a jack:   = (13 + 3)/52   = 16/52   = 4/13   Therefore, the probability of getting neither a spade nor a jack:   = 1 − 4/13   = 9/13   9/13NSWER:9/13
Answer: A
At a contest with 3000 participants, 1/2 of the people are aged 8 to 14. Next year, the number of people aged 8 to 14 will increase by 1/6. After this change, what percentage of the total 3000 people will the 8- to 14-year-olds represent? Choose the correct choice from the following:
A) 53.33%  B) 50%  C) 58.33%  D) 55.33%  E) 68%

Solution: I just wanted to mention a couple of things here:   * this is a pure ratio question; the number 3000 is completely irrelevant, and you can ignore it if you like. When we increase something by 1/6, we are multiplying it by 1 + 1/6 = 7/6, so the answer here must be (1/2)*(7/6) = 7/12 = 58.33 %.   Answer : 58.33%
Answer: C
Strawberries are purchased for $5/lb at the Farmer's Market. 4/5 of the strawberries will be used for making jam (1/5 of strawberries are rotten and thrown out). The strawberries are crushed and 1 lb of strawberries produces 2 cups of strawberry juice which is mixed with sugar to make the jam. If 3 cups of strawberry juice can make one jar of jam, how much money is needed to buy strawberries to make x number of jars of jam, in dollars?	Choose the correct answer.
A) 2x
B) 75x/8
C) 8x/15
D) 2x/3
E) x/2

Solution: Initial cost for 1 lb = $5, but ONLY 4/5 is used.   So the cost of 4/5 lb = $5, or 1 lb = $25/4,   and 1 lb of strawberries produces 2 cups of strawberry juice,so 2 cups of strawberry juice costs $25/4, but 3 cups are needed for 1 jar, so cost of 3 cups = $(25/4)(3/2) = $75/8.   If 1 jar costs $75/8, x number of jars will cost $75x/8..   Answer is 75x/8
Answer: B
The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?	Choose the correct choice from the following answers: A) 398 B) 379 C) 237 D) 480 E) 111

Solution: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.   4a = 2(l + b)   2a = l + b   l . b = 480   We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .   Area of the square cannot be found.   Answer: 480
Answer: D
The tax on a commodity is diminished by 20% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?
Choose the correct option:
A) 62%
B) 18%
C) 72%
D) 12%
E) 13%

Solution: 100 * 100= 
100 * 100 = 10_000
10000   80 * 110= 
80 * 110 = 8_800
8800   10000------- 1200   100 ------- ?= 12%   Answer: 12%
Answer: D
If N is a positive integer and 14N/60 is an integer. What is the smallest Value of N for which N has exactly four different prime factors.?
Choose one:
A) 30	B) 60	C) 180	D) 210	E) cannot be determined

Solution: 14N/60 tells us that N must be multiple of 30.   Or N has at least 2 *3 * 5 in it.   To find out the smallest value of N such that it has 4 different prime factors, we will multiple 30 with next smallest prime factor which is 7 here.   So, Least value of N is 30 *7= 
30 *7 = 210
210 .   ANSWER:210
Answer: D
The decimal 0.1 is how many times greater than the decimal (0.01)^4?
Choose the correct choice from the following choices
A) 10^5
B) 10^6
C) 10^7
D) 10^8
E) 10^9

Solution: 0.1 = 10^-1   (0.01)^4 = (10^-2)^4 = 10^-8   10^7 * 10^-8 = 10^-1   The answer is 10^7.
Answer: C