MU-NLPC/Calc-aqua_rat huggingface dataset:
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?	Choose the correct choice from the following
A) 12 sec	B) 24 sec	C) 48 sec	D) 60 sec	E) 62 sec

Solution: Relative speed = 45 + 30= 
45 + 30 = 75
75 km/hr.   75 * 5/18= 125/6 m/sec.   Distance covered = 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000 * 6/125= 
1000 * 6/125 = 48
48 sec.   ANSWER:48 sec
Answer: C
A jeep takes 3 hours to cover a distance of 440 Km. how much should the speed in Kmph be maintained to cover the same direction in 1/2th of the previous time? Select:  A) 48 Kmph  B) 252 Kmph  C) 293 Kmph  D) 263 Kmph  E) 265 Kmph

Solution: Time = 3   Distance = 340   1/2 of 3 hours = 6 * 1/2 = 1.5 Hours   Required speed = 440/1.5 = 293 Kmph   293 Kmph)
Answer: C
There are 3 people A,B & C. Rs.700 is divided among A,B & C so that A receives 1/2 as much as B and B 1/2 as much as C. What is the C's share is?	Choose the correct option:  A) Rs.100  B) Rs.200  C) Rs.400  D) Rs.500  E) Rs.550

Solution: Let C's share = Rs.x. Then   B's share = Rs.x2   And, A's share = Rs.x4   A:B:Rs.400 = x4:x2:x=1:2:4   Hence, Rs.400's share = Rs.(700×47) = Rs.400   Rs.400
Answer: C
Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 17% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?	Choose the most appropriate option
A) 5%	B) 13%	C) 21%	D) 11%	E) 30%

Solution: 60-(x+17+z) + 50-(x+17+y) + 35-(z+17+y) + x + y + z +17 = 100   where x = people who bought MilkChicken   y = people who bought chickenApples   z= people who bought Milk and Apples   x+y+z= the number of people who bought just exactly two products.   Hence solving the above equation we get,   111 -(x+y+z) = 100   Thus, x+y+z= 11   Answer: 11%
Answer: D
A cricket bat is sold for $900, making a profit of $225. The profit percentage would be Choose the correct choice from the following answers
A) 24% B) 25.5% C) 33.33% D) 36.3% E) 40%

Solution: 225/(900 - 225) = 33.33%.   Answer: 33.33%
Answer: C
BILAL spends 30% of his salary on house rent and 55% of the remaining money on food and clothes. He saves the remaining amount. If he saves ?59724 yearly, how much amount does he spend on food and clothes per month ?	Choose the correct choice from the following.
A) 5316
B) 4792
C) 5817
D) 6080
E) 6083

Solution: Let his monthly salary be y.   House rent expenditure = 30/100 y = 3y/10   âˆ´ Remaining = 7y/10   6083xpense of food = 7y/10 x 55/100 = 77y/200   âˆ´ Remaining = 7y/10 - 77y/200   = 140y - 77y/200 = 63y/200   Monthly saving = 59724/12= 
59724/12 = 4_977
4977   âˆ´ 63y/200= 4977 = y= 4977 x 200/63 = 15800   6083xpenditure on food and clothes = 77y/200   = 6083
Answer: E
The angle of elevation of the sun, when the length of the shadow of a tree is √3 times the height of the tree is
Choose the correct choice from the following choices
A) 30°  B) 45°  C) 60°  D) 90°  E) None

Solution: Solution   Let AB be the tree and AC be its shadow.   Then, < ABC	= θ.   Then, 30°C/30°B	= √3   cotθ= √3   θ=30°   30°nswer 30°
Answer: A
If the two-digit integers K and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of K and N?	Choose the correct answer:
A) 181  B) 165  C) 121  D) 99  E) 44

Solution: Since the question asks for the answer that CANNOT be the sum of K and N, and the answers are numbers, we can use a combination of TESTing VALUES and TESTing THE ANSWERS to eliminate the possible values and find the answer to the question.   We're told that K and N are two-digit positive integers and have the SAME DIGITS but in REVERSE ORDER. We're asked which of the 5 answers CANNOT be the SUM of K and N.   Let's start with the 'easiest' answer first:   44. Can we get to 44 in the manner described?   Yes, if the numbers are 13 and 31.....13+31 = 44. Eliminate Answer E   Now let's work through the rest of the list....   Can we get to 99 in the manner described?   Yes, there are several ways to do it. For example, if the numbers are 18 and 81.....18+81 = 99. Eliminate Answer D   Can we get to 121 in the manner described?   Yes, there are several ways to do it. For example, if the numbers are 38 and 83.....38+83 = 121. Eliminate Answer C   Can we get to 165 in the manner described?   Yes, there are a couple of ways to do it. For example, if the numbers are 78 and 87.....78+87 = 165. Eliminate Answer B   There's only one answer left....   181
Answer: A
For any real number x, the operatoris defined as:
(x) = x(3 − x)
If p + 1 =(p + 1), then p =
Pick: A) −3 B) 0 C) 1 D) 2 E) 3

Solution: (x) = x(1 − x)   (p + 1) = (p + 1)(3 - p - 1) =(2 -p)(p+1)   We are given that p + 1 =(p + 1)   Therefore (2-p)(p+1) = (p + 1)   Or (p + 1) + (p-2)(p+1) = 0   (p + 1)(p-2) = 0   p = -1,p=2   Option 2
Answer: D
In how many different number of ways 5 boys and 2 girls can sit on a shopa which can accommodate persons?  Options:
A) 180 B) 190 C) 200 D) 210 E) None

Solution: Option '210'   7p3 = 7 × 6 × 5 = 210
Answer: D
A train traveled the first d miles of its journey it an average speed of 60 miles per hour, the next d miles of its journey at an average speed of y miles per hour, and the final d miles of its journey at an average speed of 160 miles per hour. If the train’s average speed over the total distance was 98 miles per hour, what is the value of y?	Answers:
A) 68
B) 84
C) 90
D) 120
E) 125

Solution: Average speed=Total distance traveled /Total time taken   3d/d/60+d/y+d/160=98   Solving for d and y,   15y=11y+480   4y=500   y=125   Answer 125
Answer: E
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 9 minutes, then the area of the park (in sq. m) is:
Choose the correct answer:
A) 153601
B) 153600
C) 153602
D) 153603
E) 194400

Solution: Perimeter = Distance covered in 9 min. =(12000/60) x 9m = 1800 m.   Let length = 3x metres and breadth = 2x metres.   Then, 2(3x + 2x) = 1800 or x = 180.   Length = 540 m and Breadth = 360 m.   Area = (540 x 360) m2 = 194400 m2.   Answer: 194400
Answer: E
Of the 8 members of teacher in school, 5 can teach Physics, 7 can teach Math, and 4 can teach both subject. If one member is chosen at random, what is the probability that the member chosen will be someone who can not teach either subject? Choose the correct choice from the following answers.
A) a) 5/18
B) b) 7/18
C) c) 1/2
D) d) 0
E) e) 13/18

Solution: You know how to solve for Total number of people who can teach at least one subject:   Total = n(A) + n(B) - n(A and B)   Total people who can teach at least one subject = 5 + 7- 4= 
5 + 7- 4 = 8
8   So 8 people know how to teach at least one subject. Hence, if you pick anyone, the probability is 0 that he/she wouldn't know how to teach any subject.   Answer (d) 0)
Answer: D
In a certain Parallelogram the degree measure of one angle exceeds that of the other by 70 what is the degree measure of the smaller angle?  Choose the correct answer: A) 55 B) 80 C) 85 D) 90 E) 95

Solution: In a parallelogram opposite angles are equal and the angles at each side are supplementary to each other (supplementary angles are two angles that add up to 180°).   Given: x+(x+70)=180 --> x=55.   55nswer: 55.
Answer: A
A man sells 45 lemons for Rs 40 and loses 20%. At how much price should he sell 24 lemons to the next customer to make a 20% profit?
Pick one.
A) 37	B) 299	C) 72	D) Rs 32	E) 01

Solution: Explanation:   Let cost price of lemons be x.   Selling price of lemons becomes CP - loss.   =>SP= x-(20/100)x   =>40=x(80/100)   =>50   So 45 lemons cost Rs 50   Cost of 1 lemon = 50/45 Rs   Cost of 24 lemons = (50/45)*24 =80/3 Rs   Selling Price of 24 lemons =(80/3)+(20/100)(80/3)=Rs 32   ANSWER:Rs 32
Answer: D
If M = 775 × 778 × 781, what is the remainder when M is divided by 14? Choose one
A) 6 B) 7 C) 8 D) 9 E) 10

Solution: M 775/14 leaves a remainder 5   778/14 leaves a remainder 8   781/14 leaves a remainder 11   5*8*11= 
5*8*11 = 440
440   So the remainder will be the remainder of 440/14 which is 6   6ns 6
Answer: A
A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:	Choose the correct choice from the following options
A) 15 hrs	B) 20 hrs	C) 25 hrs	D) 30 hrs	E) 10 hrs

Solution: first pipe = x   ssecond and third (x-5)and (x-9)   1/x+1/(x-5)=1/(x-9)=>X=15   15 hrsNSWER 15 hrs
Answer: A
6 women can do 75 units of work in 8 days by working 5hrs/day. In how many days can 4 women do 30 units of work by working 8hrs/day ? Pick: A) 3days B) 4days C) 5days D) 6days E) 7days

Solution: 6x8x5/75=4x8x3days/30   solve this for 3days then we get 3days=3days   3daysNSWER:3days
Answer: A
If a - b = 3 and a^2 + b^2 = 29, find the value of ab.
Choose the correct choice from the following:
A) 12  B) 15  C) 10  D) 18  E) 13

Solution: 2ab = (a^2 + b^2) - (a - b)^2   = 29 - 9= 
29 - 9 = 20
20   ab= 10.   Answer is 10.
Answer: C
1,257
1,275
1,527
........
........
+7,521
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,5 and 7 exactly once in each integer. What is the sum W of the 24 integers ?  Pick
A) 26,996
B) 44,406
C) 60,444
D) 66,660
E) 99,990

Solution: This is the way i solved it :   Total no. of different combos = 24, total digits 4 therefore each digit must repeat  24/4= 
 24/4 = 6
6 times in each row .. So the right most row would add up to 1x6 + 2x6 + 5x6 + 7x6= 6+12+30+42= 
6+12+30+42 = 90
90 .. Each row would add up to 90, so 90 in the first means we have 9 that carries over and we get 0 , the second time its 90+9 and 9 stays and one 9 goes to the row to the left, so the last two digits of the SUM W should be 90 (E) .. We could go on and solve the exact number but since only one answer choice has the last digits as 90 we needn't go any further..
Answer: E
In an exam, C scored 35 percent, D scored 65 percent and E 50 percent. The maximum score awarded in the exam is 2000. Find the average mark scored by all the three candidates?
Select:
A) 100 B) 500 C) 1000 D) 1500 E) 2000

Solution: Average mark scored by all the three boys   = [35/100 (2000) + 65/100 (2000) + 50/100 (2000)] / 3   = 1000   Answer: 1000
Answer: C
On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is:
Answers:  A) 47619  B) 49619  C) 47719  D) 57619  E) 47611

Solution: Last digit should be 9.   when multiplying 7 with 9 , we get 63.   place 3 at unit place , we get 6 as carry.   Next digit of number should be such that we get product with 7 as a number whose last digit is 13-6= 
13-6 = 7
7.   such number is 1.   when 7 is multiplied with 1 , we get 7.   add carry 6 to it and we get 13.   so 3 will get at tens place and 1 carry for next place.   so next digit should give last digit as 2 (3-1=2).   such digit is 6.   ...   ..   so continuing like this , we get desired number as 47619   47619NSWER:47619
Answer: A
What is the sum of the odd integers from 55 to 65, inclusive? Select.
A) 495 B) 360 C) 555 D) 600 E) 605

Solution: The mean is 60.   Sum=Mean(# of elements)   There are 6 odd numbers between 55-65 inclusive. 6*60=360   360
Answer: B
A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 11 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
Choose the correct choice from the following answers.
A) 6.24
B) 7.4
C) 7.92
D) 6.28
E) 7.24

Solution: Net part filled in 1 hour = (1/4 - 1/11) = 7/44   The cistern will be filled in 44/7 hrs i.e., 6.28 hrs.Answer: 6.28
Answer: D
If Mason is now twice as old as Gunther was 10 years ago, and G is Gunther's current age in years, which of the following represents the sum of Mason and Gunther's ages 10 years from now?	Choose the correct choice
A) 4G-8 B) 3G C) 2G-8 D) AG-8 E) 5F-2

Solution: G is Gunther's current age.   Let Mason's current age be M.   given M = 2(G-10).   four years from now Mason's age will be = 2(G-10) + 10 = 2G-10   four years from now Gunther's age will be = G+10   Sum of ages of Mason and Gunther's after 4 years = 2G-10+G+10 = 3G   Ans : 3G
Answer: B
A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the room? Answers
A) 110 B) 124 C) 96 D) 117 E) 127

Solution: Length = 6 m 24 cm = 624 cm   Width = 4 m 32 cm = 432 cm   HCF of 624 and 432 = 48   Number of square tiles required = (624 * 432)/(48 * 48) = 13 * 9= 
13 * 9 = 117
117   ANSWER:117
Answer: D
If the cp of 12 rubbers is equal to the sp of 8 rubbers, the gain %is ?	Choose the correct choice:
A) 25%
B) 30%
C) 50%
D) 70%
E) 80%

Solution: (Explanation:Friends, we know we will need gain amount to get gain percent, right.   So lets get gain first.   Let the cost price of 1 pen is Re 1 50%ost of 8 pens = Rs 8 Selling price of 8 pens = 12   Gain = 12 - 8= 
12 - 8 = 4
4 Gain%=(Gain50%ost*100)%=(48*100)%=50%   50%
Answer: C
If a: b :: 3 : 7, then what is (5a+6b): (a-3b)?  Pick.
A) -57:2 B) -57:11 C) 11 : 10 D) -11 : 10 E) -1 : 10

Solution: a/b= 3/7   Dividing numerator & denominator of ' (5a+6b)/(a-2b) 'by b,   [5(a/b)+6]/[(a/b)-3]= [5*(3/7)+6]/[(3/7)-3]= -57/2   -57:2NSWER:-57:2
Answer: A
The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?  Choose the most appropriate option:
A) 15 kmph
B) 8 kmph
C) 9 kmph
D) 1 kmph
E) 2 kmph

Solution: Explanation:   Distance=Speed*Time    90 * 10/60= 
 90 * 10/60 = 15
15 kmph   15 kmphNSWER:15 kmph
Answer: A
There are 690 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?	Choose the correct choice:	A) 75	B) 100	C) 115	D) 175	E) 225

Solution: female = x   Male = 690-x   x/2 + 690-x/4 = 1/3* (690)= 
1/3* (690) = 230
230   x= 230   x/2 = 115 is supposed to be the answer   M is missing something   115orrect Option 115
Answer: C
If the price of a computer were reduced by 11 percent, which of the following could not be the final price of the computer? (Assume initial price to be integer in cents)  Choose the correct choice from the following answers
A) $844.10	B) $895.20	C) $1,055.20	D) $1,135.20	E) $1,262.40

Solution: Let X be the initial price of computer without discount   then price (final) after discount should be=X(1-11/100)------->X(8/9)=A(say)   means X=A*(9/8).....   so initial price to be integer(As per stem) final price must be multiple of 8   if we check options all were divisible by 8 except option (A)..which is Ans.   $844.10ns $844.10
Answer: A
The ratio of the present ages of P and Q is 3:4. 5 years ago, the ratio of their ages was 5:7. Find the their present ages?	Answers:
A) 30, 40
B) 30, 46
C) 30, 49
D) 30, 43
E) 30, 43

Solution: Their present ages be 3X and 4X.   5 years age, the ratio of their ages was 5:7, then (3X - 5):(4X - 5) = 5:7   X = 35 - 25 => X = 10.   Their present ages are: 30, 40..30, 40nswer:30, 40
Answer: A
Two cars cover the same distance at the speed of 62 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car. Choose the correct option.
A) 1873	B) 1848	C) 1984	D) 1838	E) 1939

Solution: Explanation:   62(x + 1) = 64x   X = 31   62 * 32= 
62 * 32 = 1_984
1984 km   Answer: Option 1984
Answer: C
In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:  Pick
A) 21	B) 22	C) 28	D) 25	E) 30

Solution: A:B = 100:75   B:28=100:96   A:28 = 100/72 = 100:72   A beats (100-72)= 
 (100-72) = 28
28 m   ANSWER 28
Answer: C
Tom found a box of 220 baseball cards. Being a thoughtful older brother, he wanted to save at least 50 percent of the cards for himself and split the remaining cards evenly among his 6 younger brothers. What is the lowest possible number of cards that Tom can save for himself that will also allow each of his 6 younger brothers to get an equal number of cards?  Pick.
A) 110	B) 112	C) 116	D) 118	E) 120

Solution: This question can be easily solved by looking at the options.   Assuming number of cards to be x   We need to find the option for which (1/6)*(x/2) is an integer   Or x/12 is an integer.   Hence we need the lowest multiple of 12 from the given options.   Let us start from the lowest value:   Option A: 110. This is not a multiple of 12   Option E: 120 = 12*10. This is a multiple of 12. Hence the correct answer.   Correct Option: 120
Answer: E
One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number?
Options:
A) 9
B) 3
C) 2
D) 4
E) 5

Solution: x/2 â€“ x/3 = 6 => x =6   3 + 6= 
3 + 6 = 9
9   9nswer 9
Answer: A
In what ratio must rice at $9.30/kg be mixed with rice at $10.80/kg so that the mixture is worth $10/kg?  Select the correct option.
A) 1:3 B) 9:4 C) 8:7 D) 11:9 E) 11:7

Solution: 9.30x + 10.80y= 10(x+y)   .80y= .70x   x/y= 8/7   8:7 is the answer
Answer: C
What is the difference between local value & face value of 9 in the numeral 65693?
Select
A) 84
B) 89
C) 81
D) 90
E) 10000

Solution: (Local value of 9) - (Face value of 9)   = (90 - 9)= 
(90 - 9) = 81
81   81
Answer: C
Anand finishes a work in 7 days, Bittu finishes the same job in 8 days and Chandu in 6 days. They take turns to finish the work. Anand on the first day, Bittu on the second and Chandu on the third day and then Anand again and so on. On which day will the work get over?
Pick.
A) 3rd	B) 6th	C) 9th	D) 7th	E) 8th

Solution: They completed 146/168 work in 6 days working one by one on eacg day.   On 7 th day , 22/168 work is left which will be completed by Anand on 7th day.   ANSWER:7th
Answer: D
What is the sum of all the multiples of 12 between 30 and 200?  Choose the correct choice from the following answers.
A) 1648  B) 1632  C) 1626  D) 1612  E) 1800

Solution: You first have to know all the multiples of 12 between 30 and 200. They are 12,24,36,48,60,72,84,96,108,120,132,144,156,168,180192. If you add all these numbers together, you get 1632.   Final Answer:   1632
Answer: B
How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 50 m long and 16 1/2 m board?	Choose the correct choice from the following choices: A) 99 B) 18 C) 165 D) 10 E) 15

Solution: 50 * 33/2 = 5/2 * 2 * x => x   = 165   Answer:165
Answer: C
4 buses runs between Chennai and Mysore. If a man goes from Chennai to Mysore by a bus and comes back to Mysore by another bus, then the total possible ways are  Pick one.
A) 4  B) 8  C) 12  D) 16  E) None of these

Solution: Since the man can go in 4 ways and can back in 3 ways. Therefore total number of ways are 4 x3 = 12ways.   Answer 12
Answer: C
If 3x - y = 6 and x+2y = 8, then what is the value of 4x + y?  Choose the correct choice from the following choices: A) 1/7 B) 14 C) 15 D) 52/7 E) 60/7

Solution: 3x-y=6 ...equation 1   x+2y=8 ...equation 2   adding both the equations   4x+y=14   correct answer option 14
Answer: B
A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 21 adults have their meal, find the total number of children that can be catered with the remaining food.
Pick one.
A) 33
B) 54
C) 63
D) 17
E) 01

Solution: Explanation:   As there is meal for 70 adults and 21 have their meal, the meal left can be catered to 49 adults.   Now, 70 adults = 90 children   7 adults = 9 children   Therefore, 49 adults = 63 children   Hence, the meal can be catered to 63 children.   ANSWER: 63
Answer: C
If the number of 37,29n, where n represents the ones digit, is a multiple of 3, then the value of n could be which of the following?
Choose the correct choice
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: Then for any number to be a multiple of 3,The sum of its digits should be the multiple of 3.   i.e 3+7+2+9+n = multiple of three   or, 21 + n = multiple of 3.   If n=3, 21 + n =24,which is a multiple of 3.   Hence answer is 3.
Answer: C
What will the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years.	Choose one.
A) 1:2	B) 2:1	C) 2:2	D) 2:3	E) None of these

Solution: Explanation:   Let the principal be P and rate be R   then   ratio = [(P∗R∗6/100) /(P∗R∗9/100)]   =6PR /9PR=2:3   Option 2:3
Answer: D
Each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 3 fantasy books, there are 8 reference books. If the proportion of history to reference books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes? Choose the correct choice from the following choices: A) 12 B) 21 C) 27 D) 35 E) 36

Solution: For every 2 history books, there are 7 fantasy books:   Originally H:F = 2:7 = 6:21.   For every 3 fantasy books, there are 8 reference books:   F:R = 3:8 = 21:56   H:F:R = 6:21:56   After the changes, H:F:R = 12:21:56   There are fewer than 60 fantasy books, so there are 21 or 42 fantasy books.   The number of history books could be 12 or 24.   The answer is 12.
Answer: A
I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss? Choose the correct option.
A) 267
B) 280
C) 279
D) 177
E) 288

Solution: x*(85/100) = (480 - x)119/100   x = 280   Answer:280
Answer: B
A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 300 revolutions. How many revolutions does the second wheel make in covering d feet?	Choose the most appropriate option.
A) 300xy B) 300x/y C) 300x - y D) 200y/x E) 600x/y

Solution: First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)   Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)   Revolutions = distance/circumference   So, from equation (1)   300 = d/(x*pi)   d = 300 * x * pi ---------- (3)   From equation (2)   Revolutions = d/(y*pi) = (300 * x * pi) / (y*pi) = 300x/y   Answer (300x/y)
Answer: B
Find the average of all prime numbers between 10 and 40 Pick:
A) 15.6  B) 22.5  C) 18.6  D) 32.2  E) 26.9

Solution: Prime numbers between 10 and 40 are 11, 13, 17, 19, 23, 29, 31, 37   Required average = (11+ 13+ 17+ 19+ 23+ 29+ 31+ 37)/8 = 180/8= 
180/8 = 45/2 = around 22.5
22.5   Answer is 22.5
Answer: B
If Log2 x - 5 Log x + 6 = 0, then what would the value / values of x be?	Answers.
A) 5.3296
B) 6.3296
C) 7.3296
D) 8.3296
E) 9.3296

Solution: log(2x)-5log(x)+6=0 (given)   log(2x)-log(x^5)=-6   log(2x/x^5)=-6 [since log(a)-log(b)=log(a/b)]   apply anti log   2/(x^4)=e^-6   2/(x^4)=2.4788*10^-3   x^4=806.85   x=5.3296   5.3296NSWER:5.3296
Answer: A