MU-NLPC/Calc-aqua_rat huggingface dataset:
In a dairy farm, 50 cows eat 50 bags of husk in 50 days. In how many days one cow will eat one bag of husk ? Choose the correct choice:
A) 34 days B) 40 days C) 46 days D) 50 days E) None of these

Solution: Explanation:   Less Cows, More days (Indirect Proportion)   Less bags, Less days (50 daysirect Proportion)   [Cows1 50   Bags 50 1]::50:x   =>x∗50∗1=50∗1∗50   =>x=50   Option 50 days
Answer: D
Given that 2x + 13 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?	Choose the correct choice from the following options.
A) -4 and -1 B) -4 and 4 C) -4 and 1 D) -2 and 5 E) 2 and 5

Solution: 2x + 13 > 5   i.e 2x >5-13   i.e. 2x > -8   i.e. x > -4   Also, 5x - 13 < 7   i.e. 5x <7+13   i.e 5x < 20   i.e x < 4   i.e. -4 < x < 4   Answer: Option -4 and 4
Answer: B
A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was?	Options: A) Rs. 2000 B) Rs. 10,000 C) Rs. 15,000 D) Rs. 20,000 E) Rs. 25,000

Solution: Principal =(100 x 5400)/(12 x 3) = Rs. 15000.   Answer: Option Rs. 15,000
Answer: C
Q. How many 8-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3, 5, 5, 6, 6? Choose the correct choice from the following answers.
A) 180
B) 240
C) 210
D) 270
E) 300

Solution: the number is less than 3000000 so we will have the digit on the left most side to be either 1 or 2   i.e your number can be 1 _ _ _ _ _ _ or 2 _ _ _ _ _ _   case 1 > 1 _ _ _ _ _ _ here the units digit can be either 2 or 6   when the units digit is 2 i.e 1 _ _ _ _ _ 2   number of ways this can be done would be 5! / 2! (as 5 is repeated twice) = 60   when the units digit is 6 i.e. 1 _ _ _ _ _ 6, number of ways would be 5!/(2! * 2!) {both 2 and 5 repeat twice} = 30   case 2 > 2 _ _ _ _ _ _ (here units digit may be 2 or 6)   number of ways this can be done would be 5! / (2!) for 2 =60   and 5! / 2! for 6 ... = 60   adding all of these ... gives the answer 270 ...   the explanation looks difficult but this technique helps if you are familiar with the concept of permutations when the numbers/alphabets repeat   270
Answer: D
If a and b are odd integers, which of the following is an even integer? Pick one:
A) 3(2a+b)
B) 3(2a+b)+2a
C) 3(2a+b)+a+b
D) 3(2a+b)+7a-b
E) 3(2a+b)+ab

Solution: 3(2a+b)+ab=odd(odd)+odd=odd+odd=even   The answer is 3(2a+b)+ab.
Answer: E
If the probability of Sita getting selected to a school is 20% and she applied to 3 schools. What is the probability that she will get selected in at least one school?  Choose the correct choice
A) 24/125	B) 21/125	C) 61/125	D) 12/125	E) 18/125

Solution: The probability that she will be selected by at least one school equals to the sum of the probabilities of the following three events:   1. She is selected by only one school: P(SRR)=3!/2!∗1/5∗4/5∗4/5=48/125 (S stands for selected and R stands for rejected). We are multiplying by 3!/2! since SRR scenario can occur in several ways: SRR, RSR, RRS, (so 3!/2! is # of permutations of 3 letters SRR out of which 2 R's are identical);   2. She is selected by only two school: P(SSR)=3!/2!∗1/5∗1/5∗4/5=12/125, the same reason of multiplying by 3!/2!;   3. She is selected by all three school: P(SSS)=(15)^3=1125, we are not multiplying this time since SSS can occur only in one way.   So P=48/125+12/125+1/125=61/125   Answer: 61/125
Answer: C
Find the largest number of four digits which is exactly divisible by 27,18,12,15  Choose one:  A) 9700  B) 9710  C) 9720  D) 9520  E) 7500

Solution: Explanation:   LCM of 27-18-12-15 is 540.   After dividing 9999 by 540 we get 279 remainder.   So answer will be 9999-279= 
9999-279 = 9_720
9720   Option 9720
Answer: C
Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $120 and $124 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings? Choose the most appropriate option:
A) 600 B) 720 C) 1080 D) 1200 E) 1800

Solution: $120 for 2 years = $60 per year.   Extra $4 yearned with the compound interest is the percent yearned on percent. So, $4 is yearned on $60, which means that the interest = 15%.   This on the other hand means that half of the savings = 60*15= 
60*15 = 900
$900. Twice of that= $1,800.   Answer: 1800.
Answer: E
A can do a piece of work in 12 days. He worked for 15 days and then B completed the remaining work in 10 days. Both of them together will finish it in.	Choose the correct choice from the following answers:	A) 12 1/2 days	B) 5 days	C) 8.5 days	D) 2 days	E) 11.5 days

Solution: 12 1/2 daysnswer: Option 12 1/2 days   15/25 + 10/x = 1 => x = 25   1/25 + 1/25 = 2/25   25/2 = 12 1/2 days
Answer: A
A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it? Pick one: A) 13 1/0 B) 13 1/3 C) 13 1/2 D) 13 1/1 E) 13 1/7

Solution: 5/30 + 20/x = 1   x = 24   1/30 + 1/24 = 3/40   40/3 = 13 1/3 days   Answer:13 1/3
Answer: B
Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 181 cms. What was the ratio of men to women?	Choose the correct choice from the following.
A) 5:2
B) 5:1
C) 4:3
D) 4:1
E) 10:1

Solution: We're given a few facts to work with:   1) The average height of the females is 170cm   2) The average height of the males is 181cm   3) The average of the GROUP is 180cm   We're asked for the RATIO of men to women.   W = number of Women   M = number of Men   (170W + 181M)/(W+M) = 180   170W + 181M = 180W + 180M   1M = 10W   M/W = 10/1   The ratio of men to women is 10 to 1.   10:1
Answer: E
The greatest common factor of two numbers is 4!. Which of the following can be the second number, if one of the numbers is 8!?  Choose the correct answer: A) 3(5!) B) 4(5!) C) 5(5!) D) 6(5!) E) 4(4!)

Solution: GCF is the product of common factors of the numbers involved.   GCF = 4!   a = 8! = 8*7*6*5*4!   b will certainly have 5! and cannot have any more common factors with a (as this will increase the GCF)   Looking at the answers only 4 (4!) and 8! will have GCF as 4!   Ans 4(4!)
Answer: E
Thomas bought a pack of eleven computers for Rs. 500000 and sold it for Rs.550000. What is the % of profit he is making per computer?  Answers:	A) 10	B) 14	C) 19	D) 21	E) 25

Solution: The cost of buying a single computer= Rs(500000/11)=Rs. 45454.5   The cost of selling a selling computer=Rs(550000/11)=Rs. 50000.0   Profit per computer=Rs.(50000-45454.5)=Rs. 4545.5   The % of profit in selling a single computer=(4545.5/45454.5)*100=10%   10nswer:10
Answer: A
Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years. Select the correct option:	A) 306.08	B) 306.03	C) 306.04	D) 306.01	E) 306.09

Solution: Explanation:   A = 5000(51/50)3   = 5306.04   5000   -----------   306.04   Answer:306.04
Answer: C
Insert the missing number.
3, 7, 6, 5, 9, 3, 12, 1, 15, (....) Pick one.
A) 3
B) 7
C) -1
D) 8
E) -45

Solution: Explanation:   There are two series, beginning respectively with 3 and 7. In one 3 is added and in another 2 is subtracted.   The next number is 1 - 2 = -1.   Answer: -1) -1
Answer: C
If BOMBAY is written as MYMYMY, how will TAMIL NADU be written in that code?
Choose the correct choice from the following answers: A) TIATIATIA B) IATIATIAT C) MNUMNUMNU D) ALDALDALD E) None of these

Solution: Letters at multiples of 3 is repeated in the code.   So,   In the code BOMBAY, 3rd and 6th letter repeated for the code.   Like that, in the code TAMIL NADU, 3rd 6th and 9th letter must be repeated.   So, TAMILNADU = MNUMNUMNU   ANSWER:MNUMNUMNU
Answer: C
An bus covers a certain distance at aspeed of 240 kmph in 5 hours. To cover the same distance in 1hr, it must travel at a speed of? Answers.
A) 700 km/hr  B) 650 km/hr  C) 690 km/hr  D) 710 km/hr  E) 720 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.   5   720 km/hr
Answer: E
What is the present worth of Rs. 132 due in 2 years at 5% simple interest per annum?	Pick one.
A) 128	B) 277	C) 120	D) 888	E) 171

Solution: Let the present worth be Rs. x. Then,   S.I. = (132 - x)   (x * 5 * 2) / 100 = (132 - x)   10x = 13200 - 100x   110x = 13200 => x = 120.   Answer: 120
Answer: C
A man can row downstream at the rate of 26 Kmph and upstream at 12 Kmph. Find the man’s rate in still water and rate of current?
Choices
A) 8.5
B) 8.0
C) 9.5
D) 7.0
E) 8.25

Solution: Rate of still water = 1/2 (down stream + upstream)   = 1/2 (26 + 12) = 19 Kmph   rate of current = 1/2 (down stream - upstream)   = 1/2 (26 - 12)   = 1/2 (14)   = 7 kmph   Answer is 7.0.
Answer: D
A car is running at a speed of 120kmph. What distance will it cover in 12sec?  Select the correct option:
A) 396m B) 267m C) 180m D) 200m E) 250m

Solution: Speed = 120kmph = 120*5/18 = 33 m/s   Distance covered in 12sec = 33*12= 
33*12 = 396
396m   396mnswer is 396m
Answer: A
The average of 11 results is 48, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Choose the correct choice from the following options:  A) 21  B) 56  C) 78  D) 25  E) 23

Solution: 1 to 11 = 11 * 48= 
11 * 48 = 528
528   1 to 6= 6 * 49= 
6 * 49 = 294
294   6 to 11= 6 * 52= 
6 * 52 = 312
312   6th= 294 + 312 â€“ 528 = 78   Answer:78
Answer: C
Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit? Choose the correct choice from the following answers:
A) 12000
B) 23000
C) 24000
D) 25000
E) 30000

Solution: SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000   30000
Answer: E
A trader mixes 25 kg of rice at Rs. 20 per kg with 25 kg of rice of other variety at Rs. 30 per kg and sells the mixture at Rs. 30 per kg. His profit percent is: Choose one.
A) No profit, no loss  B) 5%  C) 8%  D) 20%  E) None of these

Solution: C.P. of 50 kg rice = Rs. (25 x 20 + 25 x 30) = Rs. (500 + 750) = Rs. 1250   S.P. of 50 kg rice = Rs. (50 x 30) = Rs. 1500   Gain =250/1250x100% = 20%.   Answer: Option 20%
Answer: D
RAM and GOPAL invested in a business. They earned some profit which they divided in the ratio of 1:2. If RAM invested Rs.25, 000, the amount invested by GOPAL is:  Choose the correct choice from the following answers:
A) Rs. 65,000	B) Rs. 50,000	C) Rs. 80,000	D) Rs. 90,000	E) Rs. 60,000

Solution: Invested by Gopal = 25000/1*2= 
25000/1*2 = 50_000
50000   ANSWER : Rs. 50,000
Answer: B
A company has 15 managers and 75 associates. The 15 managers have an average salary of $90,000. The 75 associates have an average salary of $30,000. What is the average salary for the company?
Pick one:
A) $35,000	B) $40,000	C) $55,000	D) $65,000	E) $75,000

Solution: Another method is to get ratios   Say 30000=a and   We know the # of people are in 1:5 ratio   Average=(3a*1+a*5)/6= 8a/6=40000   Answer is B. $40,000
Answer: B
Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 2 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month? Choose the correct choice from the following options
A) 1/7 B) 1/6 C) 1/5 D) 1/4 E) 1/3

Solution: Suppose the portion of her salary that she saved is X   and the remaining portion is Y   X+Y= total take home salary   given, 12X = 2Y   or 6X = Y   Total take-home salary= X+ 6X= 7X   hence, she saved 1/7-th portion of her take home salary   1/7
Answer: A
A cycle is bought for Rs.1120 and sold for Rs.1200, find the gain percent?  Pick one.
A) 7%	B) 2%	C) 6%	D) 1%	E) 8%

Solution: Explanation:   1120---- 80   100 ---- ? => 7%   7%nswer: 7%
Answer: A
A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 80 meters apart,then at what speed is the train traveling? Choose the correct choice from the following choices.
A) 100km/hr  B) 110km/hr  C) 240km/hr  D) 150km/hr  E) 200km/hr

Solution: Number of gaps between 51 telephone posts = 50   Distance traveled in 1 minute = 50*80= 
50*80 = 4_000
4000m= 4km   Speed = 60*4= 
60*4 = 240
240km/hr   Answer is 240km/hr
Answer: C
A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 9 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
Choose the correct answer.
A) 42 B) 70 C) 140 D) 165 E) 252

Solution: Ans: 252   7C1 * 9C2   Answer 252)
Answer: E
A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number?
Choose the most appropriate option:
A) 3.5 B) 6 C) 8 D) 9 E) None of these

Solution: by option   8*2= 
8*2 = 16
16(number is doubled)   add 9(16+9=25)   if 25 trebled it becomes 75   ANSWER:8
Answer: C
A car covers a distance of 720 km in10 hrs. What is its speed in mps.  Choose the correct choice.
A) 40 m/s	B) 25 m/s	C) 20 m/s	D) 15 m/s	E) 16 m/s

Solution: Explanation:   Distance = Speed x Time   Speed = (720/10)= 
(720/10) = 72
72 kmph   Spees in mps= 72 x 5/18 = 4 x 5 = 20 mps.   Answer: Option 20 m/s
Answer: C
The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).	Choose the correct choice.
A) 8, 20, 28
B) 16, 28, 36
C) 20, 35, 45
D) 20, 45, 55
E) None of these

Solution: Explanation:   Let their present ages be 4x, 7x and 9x years respectively.   Then, (4x - 8) + (7x - 8) + (9x - 8) = 56   ⇒ 20x = 80   ⇒ x = 4.   ⇒ Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.   Answer: 16, 28, 36
Answer: B
If x, y, and z are all factors of 35, which of the following must be true?
Pick one
A) The product xyz > 35 B) Either x = y, y = z, or x = z C) x – y – z = even D) The product xyz is odd E) yz/x is an integer

Solution: All the factors of 35 are odd numbers.   The product of odd numbers is odd.   The answer is The product xyz is odd.
Answer: D
In how many different ways can the letters of the word ‘PREPTY’ be arranged?  Choose the correct choice from the following choices.
A) 230
B) 240
C) 260
D) 280
E) 360

Solution: Number of ways = 61/21 6X5X4X3X2X1 - 360   360
Answer: E
The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, find out the value of x
Choose one
A) 13	B) 14	C) 15	D) 16	E) 17

Solution: Explanation:   Let the Cost Price of one article = Rs. 1   CP of x articles = Rs. x   CP of 20 articles = 20   Selling price of x articles = 20   Profit = 25% [Given]   ⇒(SP−CP /CP)=25/ 100=1/4   ⇒(20−x)/x=1/4   ⇒80−4x=x   ⇒5x=80   Option 16   ⇒x=805=16
Answer: D
What is the maximum number of pieces of birthday cake of size 3” by 3” that can be cut from a cake 21” by 21”?	Choose the most appropriate option
A) 5	B) 7	C) 49	D) 20	E) 25

Solution: The prompt is essentially asking for the maximum number of 3x3 squares that can be cut from a larger 21 by 21 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 7 'pieces' each, we have (7)(7) = 49 total smaller squares (at maximum).   49
Answer: C
If an item that originally sold for r dollars was marked up by p percent and then discounted by q percent, which of the following expressions represents the final price of the item? Choose the correct answer:
A) (10,000r + 100r(p – q) – pqr)/10,000
B) (10,000r + 100r(q – p) – pqr)/10,000
C) (100r(p – q) – pqr)/10000
D) (100r(q – p) – pqr)/10000
E) 10000 /(p – q)

Solution: Assume r=100, p=10, q=10. So final price is 99. Now put these value each option. Only option (10,000r + 100r(p – q) – pqr)/10,000 will give right answer.
Answer: A
The product of n consecutive positive integers is always divisible by?	Choices.
A) n^2 -1  B) (n+1)!  C) 2n +1  D) n!  E) n^2 + 1

Solution: Plug in some vlues and check -   Product of first 2 number is 2*1   Product of first 3 number is 3*2*1   Product of first 4 number is 4*3*2*1   Product of first 5 number is 5*4*3*2*1   So, The product of first n natural numbers is always divisible by n! , answer will be (n!)
Answer: D
A bag marked at $240 is sold for $120. The rate of discount is?	Choose the correct choice.
A) 10%  B) 25%  C) 20%  D) 50%  E) 45%

Solution: Rate of discount = 120/240 * 100= 
120/240 * 100 = 50
50%   Answer is 50%
Answer: D
What is the sum of odd integers from 20 to 80, inclusive? Choose one:
A) 1,550  B) 1,500  C) 1,240  D) 1,120  E) 1,100

Solution: Number of odd integers = (80-20)/2 + 1   = 60/2 + 1= 
60/2 + 1 = 31
31   Sum of odd integers= (20+80)/2 * 31   = 50 * 31= 
50 * 31 = 1_550
1550   1,550nswer 1,550
Answer: A
A box contains 2 white, 3 black and 5 red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?	Choose the correct option.
A) 85	B) 66	C) 27	D) 19	E) 17

Solution: Explanation:   Total balls in a box = 2W + 3B + 5R = 10 balls.   Therefore total number of ways of drawing 3 balls from 10 balls is 10C3 2  + 3  + 5= 
2  + 3  + 5 = 10
10 balls.   Therefore total number of ways of drawing 3 balls from 10 balls is 10C3= 120 ways ........(1)   This includes all types of color combinations of white, black and red.   Now total balls in a box of white and red color = 2W + 5R = 7 balls.   Therefore total number of ways of drawing 3 balls from 7 balls is 7C3 2  + 5= 
2  + 5 = 7
7 balls.   Therefore total number of ways of drawing 3 balls from 7 balls is 7C3= 35 ways ........(2)   This includes all types of color combinations of white and red only.   Therefore from (1) and (2), we get the total number of ways of drawing 3 balls, which includes at least one black ball = 120 – 35 = 85 ways.   85NSWER: 85
Answer: A
Adam, Bryan, Chris, and David are all basketball players. An unknown habit of Adam's is to score 7 more than half as many points as Bryan. Bryan is their star player and will always score at least 50 points plus Chris' score. Chris is a consistent player in that he will score twice as many points as David. Write a general equation that shows the total score of these four players in a game in terms of David, D Pick one:
A) 82 +6D B) 82 +4D C) 82 +8D D) 8D E) 50+4D

Solution: 82 +6D = B/2+7   B = 50+C   C = 2D   D = D   Now compile new equations   82 +6D+B+C+D = (B/2+7) +(50+C) +(2D) +(D)   = (B/2+7) +(50+C) +3D, look back at original equations   =(B/2+7) +(50+2D) +3D   =(B/2+7) +50+5D   = (50+2D)/2+7 +50 +5D   = 25 +D +7+50+5D   =82 +6D   82 +6Dnswer: 82 +6D
Answer: A
A mixture of 70 lts. Of wine and water contains 10% of water. How much water must be added to make 37% of the resulting mixture?
Choose the correct answer:
A) 30	B) 31	C) 32	D) 33	E) 34

Solution: Its given that currently water is 10% of the mixture.   => (10/100)(70) = 7lts   lets say x litres of water is added.   => 7+x = (37/100)(70+x)   => x = 30 liters   30NSWER:30
Answer: A
In a certain pet shop, the ratio of dogs to cats to bunnies in stock is 7 : 7 : 8. If the shop carries 330 dogs and bunnies total in stock, how many dogs are there?  Choose the correct choice from the following options
A) 42  B) 66  C) 98  D) 112  E) 154

Solution: Let us assume the number of dogs, cats and bunnies to be 7x, 7x and 8x   Total dogs and bunnies = 15x.   And we are given that 15x = 330.   Hence x = 22.   Dogs = 7x = 7*22= 
7*22 = 154
154 (Option 154)
Answer: E
During a sale, the price of a pair of shoes is marked down 14% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes? Choose the correct choice from the following options:
A) 9%
B) 10%
C) 11%
D) 16%
E) 90%

Solution: Assume the price = 100   Price during sale = 86   Price after sale = 100   Percent increase = 14/86*100 = 16% approx.   Correct Option: 16%
Answer: D
A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.85 less, he could have gained 25%. What is the cost price? Choose the correct choice from the following answers
A) 372  B) 375  C) 278  D) 425  E) 288

Solution: CP1 = 100 SP1 = 120   CP2 = 80 SP2 = 80 * (125/100)= 
80 * (125/100) = 100
100   20 ----- 100   85 ----- ?=> 425   Answer:425
Answer: D
A car covers a distance of 600 km in 6 hours. Find its speed?
Choices:	A) 104	B) 100	C) 266	D) 288	E) 121

Solution: 600/6= 
600/6 = 100
100 kmph   Answer:100
Answer: B
The function f is defined for all the positive integers n by the following rule: f(a) is the number of positive integers each of which is less than a and has no positive factor in common with a other than 1 . if p is a prime number then f(p)?
Choose the correct choice from the following answers
A) p-1	B) p-2	C) (p+1)/2	D) (p-1)/2	E) 2

Solution: The moment you put a prime number in the function f(a), notice that all the numbers lesser than a have no divisor clashing with divisor of a since a is prime!!.   For instance f(7)= {6, 5, 4, 3, 2, 1}   Thus for f(p) number of integers falling under this set will be p-1   p-1nswer :- p-1
Answer: A
A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 100 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
Pick.
A) 71.5	B) 72	C) 72.5	D) 73	E) 94.7

Solution: Many approaches are possible, one of them:   Let the distance be 1 kilometer.   Time to cover this distance at 100 kilometers per hour is 1/100 hours = 3,600/100 seconds = 36 seconds;   Time to cover this distance at regular speed is 36+2= 
36+2 = 38
38 seconds= 38/3,600 hours = 4/379 hours;   So, we get that to cover 1 kilometer 1/(4/379) hours is needed --> regular speed 94.7 kilometers per hour (rate is a reciprocal of time or rate=distance/time).   Answer: 94.7.
Answer: E
A rectangular circuit board is designed to have width w inches, perimeter p inches, and area x square inches. Which of the following equations must be true? Pick one.
A) w^2 + pw + x = 0
B) w^2 - pw + 2x = 0
C) 2w^2 + pw + 2x = 0
D) 2w^2 - pw - 2x = 0
E) 2w^2 - pw + 2x = 0

Solution: Notice that we can discard options A, and C right away. The sum of 3 positive values Cannot be 0.   Now, assume:   Width =w = 1 inchand length = 1 inch;   Perimeter =p = 4 inches;   Area =x = 1 square inches.   Plug the values of w, p, and x into the answer choices: only for E 2w^2 - pw  + 2= 
 + 2 = 2
2 - 4 + 2= 
2 - 4 + 2 = 0
0.   Answer: 2w^2 - pw + 2x= 0.
Answer: E
All of the students of the Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 98 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only?  Choose the correct choice from the following options:
A) 36
B) 39
C) 42
D) 45
E) 48

Solution: 50% of students are in the band only, so 30% of students are in the orchestra only.   Since 20% of students are in both, then 70% of students are in the band which is 98 students.   The number of students in the orchestra is  (30/70)*98= 
 (30/70)*98 = 42
42.   The answer is 42.
Answer: C
In a group of 80 children and 17 youngsters, each child got sweets that are 15% of the total number of children and each youngster got sweets that are 25% of the total number of children. How many sweets were there?
Choices:
A) 1140
B) 1160
C) 1180
D) 1300
E) 1210

Solution: Number of sweets each child got = 15% of 80 = 15/100 * 80= 
15/100 * 80 = 12
12.   Number of sweets 80 children got= 80 * 12= 
80 * 12 = 960
960.   Number of sweets each youngster got= 25% of 80 = 25/100 * 80= 
25/100 * 80 = 20
20.   Number of sweets 17 youngsters got= 17 * 20= 
17 * 20 = 340
340.   Total number of sweets= 960 + 340= 
960 + 340 = 1_300
1300.   1300)
Answer: D