MU-NLPC/Calc-aqua_rat huggingface dataset:
There are 21 balls in a jar: 14 red, 4 blue and 3 green. If a single ball is drawn from the jar, what is the probability of that it is either blue or red?  Choose the correct choice from the following answers:
A) 1/12
B) 3/4
C) 6/9
D) 6/7
E) 3/4

Solution: Blue + Red =18   Total number of balls is  14+4+3= 
 14+4+3 = 21
21   So the answer is 18/21=6/7   Answer 6/7
Answer: D
A train is walking at 6/7 of its usual speed, the train is 20 minutes too late. Find its usual time to cover the journey.	Options:
A) 1 hour
B) 30min
C) 3 hours 20 min
D) 2 hours 30 min
E) 2 hours

Solution: new speed = 6/7 of the usual speed   new time taken = 7/6 of the usual time taken   so, ( 7/6 of the usual time ) - ( usual time ) = 20min   1/6 of the usual time = 20min   usual time = 20*6= 
20*6 = 120
120 min= 2 hours   correct option is 2 hours
Answer: E
A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?	Answers
A) 109 ways
B) 908 ways
C) 128 ways
D) 108 ways
E) 104 ways

Solution: The boy can select one trouser in nine ways.   The boy can select one shirt in 12 ways.   The number of ways in which he can select one trouser and one shirt is   9 * 12= 
  9 * 12 = 108
108 ways.   Answer:108 ways
Answer: D
How many meters are there in 770 centimeters?  Choose the correct choice from the following:
A) 770 meters B) 7.6 meters C) 700 meters D) 6.5 meters E) 7.7 meter

Solution: Solution:   1 meter = 100 centimeters   Just divide 770 by 100   770 Ã· 100 = 7.7, so there are 7.7 meters in 770 centimeters   Option 7.7 meter
Answer: E
A shopkeeper sold an article at $1800 with 20% profit. Then find its cost price?	Choose the correct choice from the following:
A) $1000 B) $1500 C) $1850 D) $1600 E) $2000

Solution: cost price = selling price *100/(100+profit)   C.P. = 1800*100/120= 
1800*100/120 = 1_500
$1500   Answer is $1500
Answer: B
For what values of k will the pair of equations 3(3x + 4y) = 36 and kx + 12y = 30 does not have a unique solution?
Select
A) 12	B) 9	C) 3	D) 7.5	E) 2.5

Solution: we have 2 equations   1. 3(3x + 4y) = 36 --> 3x + 4y = 12 -- > 9x + 12y = 36   2. kx + 12y = 30   substract 1-2, we get (9-K)x = 6   i.e. x = 6/(9-k)   then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is 9
Answer: B
A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
Options:
A) 32:45
B) 32:47
C) 32:45
D) 32:41
E) 32:42

Solution: 32:45 : B   (8000*4)+(4000*8) : (9000*6)+(6000*6)   64000 : 90000   32 : 45.32:45nswer: 32:45
Answer: A
Workers decided to raise Rs.3lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.25lacs. How many workers were they? Choose the correct choice from the following options:
A) 350
B) 400
C) 500
D) 550
E) 590

Solution: N * 50 = (325000 - 300000)= 
(325000 - 300000) = 25_000
25000   N= 25000 / 50= 
25000 / 50 = 500
500   500
Answer: C
In how many ways can 12 different gifts be divided among four children such that each child receives exactly three gifts?  Select the correct option:
A) 16^3  B) (4!)^3  C) 12!/(3!)^4  D) 12!/4!  E) 4^12

Solution: Total 12 different Gifts, and 4 children.   Thus any one child gets 12C3 gifts,   then the other child gets 9C3 gifts(12 total - 3 already given),   then the third one gets 6C3 gifts,   and the last child gets 3C3 gifts.   Since order in which each child gets the gift is not imp, thus, ans :   1212!/(3!)^43 * 912!/(3!)^43 * 612!/(3!)^43 * 312!/(3!)^43 = 12! / (3!)^4   Ans : 12!/(3!)^4.
Answer: C
The sum of three integers A, B and C is 180. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C? Select
A) 120  B) 125  C) 105  D) 115  E) 110

Solution: A is one third of the sum of B and C..   or A=1/3(B+C)...   But A+B+C=180.   so 1/3(B+C)+B+C=180   4(B+C)/3= 180   B+C =180*3/4= 
180*3/4 = 135
135   A=180-135= 
180-135 = 45
45   2)B is one fifth of the sum of A and C   or B=1/5(A+C)...   125ut A+125+C=180   so 1/5(A+C)+A+C=180   A+C=180*5/6= 
180*5/6 = 150
150   but A=45, so C=150-45= 
150-45 = 105
105   Answer : 125
Answer: B
A man gets a simple interest of Rs.400 on a certain principal at the rate of 5% p.a in eight years. Find the compound interest the man will get on twice the principal in two years at the same rate? Choices:	A) s.256.27	B) s.256.29	C) s.205.00	D) s.256.22	E) s.256.25

Solution: Let the principal be Rs.P   S.I at 5% p.a in 8 years on Rs.P = Rs.400   (P)(8)(5)/100 = 400   P = 1000   s.205.00.I on Rs.2P i.e., Rs.2000 at 5% p.a in two years   =2000{ [1 + 5/100]^2 - 1} =   = 2000(41/ 400)   = Rs.205   Answer:s.205.00
Answer: C
A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability C that out of the two, one is white and one is blue?
Answers.
A) 15/56
B) 41/56
C) 13/28
D) 15/28
E) 5/14

Solution: The required probability C= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls.   Ways to select 6 out of total 8 = 8C6   Ways to select 4 out of 5 white balls = 5C4   Ways to select 2 out of 3 blue balls = 3C2   Thus the required probability = (5C4*3C2)/8C6 = 15/28.   15/28 is thus the correct answer.
Answer: D
Of 120 applicants for a job, 56 had at least 4 years' experience, 72 had degrees, and 12 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?	Choose the correct choice from the following options
A) 10 B) 15 C) 22 D) 20 E) 24

Solution: 120 - 12= 
120 - 12 = 108
108   108 - 56 - 72= -20   Then 20 are in the intersection between 4 years experience and degree.   Answer : 20
Answer: D
Eleven books consisting of 5 financial management, 4 marketing management and 2 system management are placed on a shelf at random order. What is the probability that the books of each kind are all together.
Choose the correct choice from the following answers.
A) 1/1155 B) 1/1255 C) 1/1355 D) 1/1455 E) 1/1555

Solution: (Probability of an event) = (Favorable) / (Total)   The total number of ways to arrange 11 books in a row is 11!.   3 groups of books: financial management (F), marketing management (M) and system management (S), can be arranged in 3! ways: FMS, FSM, MFS, MSF, SFM, and SMF (this way all the books of each kind will be together). Now, books in F itself can be arranged in 5! ways, in M in 4! ways and in S in 2! ways. Hence, the total number of ways to arrange books so that books of each kind are together is 3!*5!*4!*2!.   P = (3!*5!*4!*2!) / 11! = 1/1155.   1/1155nswer: 1/1155
Answer: A
The inverse ratio of 3: 2: 1 is?
Choices:
A) 2:3:8	B) 4:3:6	C) 2:3:2	D) 2:3:6	E) 2:3:1

Solution: 1/3: 1/2: 1/1   = 2:3:6   Answer: 2:3:6
Answer: D
Which of the following MUST yield an integer when divided by 11? Select.
A) The sum of eleven consecutive positive integers.	B) The square of a prime number.	C) The sum of two odd integers.	D) The product of three consecutive odd numbers.	E) The difference between a multiple of 8 and a multiple of 3.

Solution: For option A: Let the numbers be (x-5), (x-4), (x-3), (x-2), (x-1), (x), (x+1), (x+2), (x+3), (x+4), (x+5).   Now, (x-5)+(x-4)+(x-3)+(x-2)+(x-1) + (x) + (x+1) + (x+2)+(x+3)+(x+4)+(x+5) = 11(x). Hence A is true. No need to check other answers since there can only be one correct answer.   So, The sum of eleven consecutive positive integers.ns(The sum of eleven consecutive positive integers.).
Answer: A
A coach must choose five starters from a team of 12 players. How many different ways can the coach choose the starters ? Choose the correct choice from the following choices
A) 722
B) 729
C) 278
D) 299
E) 271

Solution: Explanation:   Choose 5 starters from a team of 12 players. Order is not important.   \inline {\color{729lack} 12C_{5}}= 729   Answer: 729) 729
Answer: B
Barbata invests $2400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 8% of her entire investment?	Answers:
A) 1200	B) 3000	C) 1000	D) 3600	E) 2400

Solution: Let the additional invested amount for 8% interest be x;   Equation will be;   2400+0.05*2400+x+0.08x = 2400+x+0.08(2400+x)   0.05*2400+0.08x = 0.06x+0.08*2400   0.02x = 2400(0.08-0.05)   x = 2400*0.03/0.02= 
2400*0.03/0.02 = 3_600
3600   Ans:3600
Answer: D
One side of the bottom layer of a triangular pyramid has 12 balls. How many are there in the whole pyramid?Note that the pyramid is equilateral and solid.  Options
A) 286 B) 364 C) 504 D) 164 E) 165

Solution: As there are 12 balls along one side, it means that there are 12 layers of balls. The top most layer has 1 ball. The second layer has 3 (1+2) balls. The third layer has 6 (1+2+3) balls. The fourth layer has 10 (1+2+3+4) balls. The fifth layer has 15 (1+2+3+4+5) balls. Similarly, there are 21, 28, 36, 45, 55, 66 and 78 balls in the remaining layers.   Hence, the total number of balls are   = 1 + 3 + 6 + 10 + 15 + 21 +28 + 36 + 45 + 55 + 66 + 78= 
1 + 3 + 6 + 10 + 15 + 21 +28 + 36 + 45 + 55 + 66 + 78 = 364
364 balls   ANSWER:364
Answer: B
Marcella has 25 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left?	Choose the correct choice from the following answers:
A) 21	B) 20	C) 19	D) 16	E) 15

Solution: greatest number of paired shoes means greatest number of lost pairs   9 shoes have 4 pairs and 1 extra shoes of a pair .so a otal of 5 pairs she loses   leftover pair=20   ANSWER:20
Answer: B
A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order Y? (1 cubic meter = 1,000 liters) Choose the correct choice from the following answers
A) 92 B) 90 C) 82 D) 78 E) 75

Solution: I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5.   Y=12.5*6 = 75.75
Answer: E
A merchant can buy goods at the rate of Rs. 20 per good. The particular good is part of an overall collection and the value is linked to the number of items that are already on the market. So, the merchant sells the first good for Rs. 2, second one for Rs. 4, third for Rs. 6…and so on. If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?  Options
A) 24
B) 18
C) 27
D) 32
E) 34

Solution: DETAILED SOLUTION   Let us assume he buys n goods.   Total CP = 20n   Total SP = 2 + 4 + 6 + 8 ….n terms   Total SP should be at least 40% more than total CP   2 + 4 + 6 + 8 ….n terms ≥ 1.4 * 20 n   2 (1 + 2 + 3 + ….n terms) ≥ 28n   n(n + 1) ≥ 28n   n2 + n ≥ 28n   n2 - 27n ≥ 0   n ≥ 27   He should sell a minimum of 27 goods.   Answer 27hoice (27)
Answer: C
65% of x = 20% of 747.50. Find the value of x?	Select:  A) 100  B) 230  C) 150  D) 180  E) 199

Solution: 65% of x = 20% of 747.50   Then, 65/100 * x = 20/100 * 7475/10   x = 230   Answer is 230
Answer: B
The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above conditions is:	Choices:
A) 4	B) 5	C) 6	D) 6	E) 1

Solution: Let the required numbers be 33a and 33b.   Then, 33a + 33b = 528 => a + b = 16.   Now, co-primes with sum 16 are (1, 15), (3, 13), (5, 11) and (7, 9).   Required numbers are (33 * 1, 33 * 15), (33 * 3, 33 * 13), (33 * 5, 33 * 11), (33 * 7, 33 * 9).   The number of such pairs is 4.   4nswer:4
Answer: A
The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 200,000 bacteria Choose one:
A) 10
B) 12
C) 14
D) 16
E) 18

Solution: The question basically asks how many minutes it takes for a population to increase by factor 200 (200,000 / 1,000 = 200).   Now you know that every two minutes the population doubles, i.e. is multiplied by 2. So the equation becomes:   2^x >= 200, where x represents the number of times the population doubles. A lot of people remember that 2^10 = 1,024. Hence, 2^8 = 256, i.e. the population has to double 8 times.   Since it takes the population 2 minutes to double once it takes 8*2= 
8*2 = 16
16 minutes to double 8 times.   Thus, solution 16= 16 is correct.
Answer: D
A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 500 m long?  Choose the correct choice from the following options:
A) 65sec  B) 70sec  C) 74sec  D) 80sec  E) 85sec

Solution: Speed = 240/24= 
240/24 = 10
10 m/sec.   Required time= (240 + 500)/10= 
(240 + 500)/10 = 74
74 sec.   Answer:74sec
Answer: C
The average temperature of a city in the first four days of a month was 36°. The average for the 2nd, 3rd, 4th and 5th day was 38°. If the temperature of the 1st and 5th day were in the ratio 4 : 5, then what is the temperature on the fifth day ?  Choose the correct choice from the following answers:  A) 40°  B) 49°  C) 43°  D) 41°  E) 42°

Solution: Explanation:   The temperature for first 4 days = 4 * 36= 
4 * 36 = 144
144   The temperature for last 4 days= 4 * 38= 
4 * 38 = 152
152   The difference between the temperatures is (152 – 144)= 8   The ratio of temperature between first and fifth day is 4 : 5   The temperature on fifth day is   5*8= 
  5*8 = 40
40   40°NSWER: 40°
Answer: A
A bird shooter was asked how many birds he had in the bag. He replied that there were all sparrows but six, all pigeons but six, and all ducks but six. How many birds he had in the bag in all? Options
A) 9  B) 18  C) 27  D) 36  E) 34

Solution: all sparrows bt six i.e. those six can b 3 pigeons and 3 ducks,   similarly the other 2 conditions will apply..   9NSWER:9
Answer: A
Find the number which multiplied by 15 is increased by 196.	Pick:
A) 14
B) 20
C) 26
D) 28
E) 27

Solution: Let the number be x. Then,   15x - x = 196   x = 14   14NSWER:14
Answer: A
When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy works alone she chops 3 lb. salad in 2 minutes. They start working together, and after some time finish chopping 65 lb. of salad. Of those 80 lb., the salad quantity chopped by Tom is what percent lesser than the quantifying chopped by Tammy?.  Choices
A) 44%  B) 100%  C) 105%  D) 225%  E) 125%

Solution: Tom chops 4 lbs in 6 minutes   Tammy chops 9 lbs in 6 minutes   So in the same amount of time, Tom chops 125% less than Tammy, since 9 is 125% greater than 4. So 125% is the answer.   Note that the actual time doesn't matter. If you multiply the time each work by x, you'll multiply the work each does by x, and 9x is still 125% greater than 4x.   Ans:125%
Answer: E
If a randomly selected non-negative single digit integer is added to {2, 3, 4, 8}. What is the probability that the median of the set will increase but the range still remains the same? Choose the correct choice from the following choices:
A) 0.2  B) 0.3  C) 0.4  D) 0.5  E) 0.6

Solution: We are selecting from non-negative single digit integers, so from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. These 10 digits represent the total number of outcomes.   Hence, the total number of outcomes is 10.   We need to find the probability that the median of the set will increase but the range still remains the same.   The median of the set is  (3 + 4)/2= 
 (3 + 4)/2 = 7/2 = around 3.5
3.5, thus the number selected must be 4 or greater.   For the range to remain the same, the number must be between 2 and 8 inclusive.   To satisfy both conditions, the number selected must be 4, 5, 6, 7, or 8.   The probability is  5/10= 
 5/10 = 1/2 = around 0.5
0.5   The answer is 0.5.
Answer: D
In a survey conducted to find out the readership of three Newspapers A,B and C, it was found that the number of newspaper A is at least 20 and at most 40. The number of people who read newspaper B is at least 50 and at most 70. The number of people who read newspaper C is at least 70 and at most 83. It was also found that 5 people read all three newspapers. Find the minimum number of people who read both A and B but not C.  Answers:
A) A)1	B) B)2	C) C)3	D) D)0	E) E)5

Solution: I wish I could draw a diagram to show you but by giving you number A and B, it might help a little.   A and B and C is 5 - that means A and B is at least 5. This seems trivial given the value intervals of A and B but definitely helps to think through how to minimize A and B but not C   A and B but not C = |A|-|B| - 5   So i would pick A=25 and B =50 to minimize the value to a 0. (ANS 0)
Answer: D
6% of customers that enter a store on any given day must not pay tax. If 1000 people shop every day, how many people pay taxes in the store every week  Pick:
A) 6500
B) 6580
C) 7200
D) 7120
E) 6800

Solution: 6% of customers do not pay taxes.   6/100 * 1000= 
6/100 * 1000 = 60
60   Therefore 1000 - 60= 
1000 - 60 = 940
940   940 * 7= 
940 * 7 = 6_580
6580   6580)
Answer: B
A taxi owner buys diesel at Rs.8.50, Rs. 9 and Rs. 9.50 per litre for three successive years. What approximately is the average cost per litre of diesel if he spends Rs. 5000 each year?  Choose the correct choice from the following choices:
A) 7.98  B) 8.98  C) 9.98  D) 6.98  E) 8.12

Solution: Total Cost = 5000 × 3=15000   Total diesel used = 5000/8.50 + 5000/9 +5000/9.50   =588+555+527= 
588+555+527 = 1_670
1670   Average cost per litre of diesel=15000/1670   =8.98   ANSWER:8.98
Answer: B
With the wind, an airplane travels 1120 miles in seven hours. Against the wind, it takes eight hours. Find the rate of the plane in still air and the velocity of the wind.  Select the correct option:
A) 10 kmph	B) 11 kmph	C) 12 kmph	D) 13 kmph	E) 14 kmph

Solution: 1120 miles in seven hrs that means up speed is  1120/7= 
 1120/7 = 160
160.   for against the wind 1120 miles in 8 hrs so down speed  1120/8= 
 1120/8 = 140
140.   now plain speed in still air=1/2(160+140)=150 kmph   wind speed=1/2(160-140)=10 kmph   10 kmphNSWER:10 kmph
Answer: A
x = 13.165
y = 7.496
z = 11.557
The number A is obtained by first rounding the values of x, y, and z to the hundredths place and then adding the resulting values. The number B is obtained by first adding the values of x, y, and z and then rounding the sum to the hundredths place. What is the value of A – B?	Choose the correct choice:
A) 0.01
B) 0.02
C) 0.03
D) 0.1
E) 0.2

Solution: Rounding off the values:   x = 13.17   y = 7.50   z = 11.56   A = 13.17 + 7.50 + 11.56= 
13.17 + 7.50 + 11.56 = 32.23
32.23   x + y + z= 13.165 + 7.496 + 11.557 = 32.206   0.02 = 32.21   A - 0.02 = 0.02   Option 0.02
Answer: B
If a 3-number code is formed of the integers from 1 to 14 inclusively, and each of the numbers in the code is different, how many possible codes are there?
Select the correct option:
A) 1744
B) 1854
C) 1964
D) 2074
E) 2184

Solution: 14*13*12= 
14*13*12 = 2_184
2184   The answer is 2184.
Answer: E
If a car travels a distance of 300 km in 8 hours, partly at a speed of 40 kmh-1 and partly at 30 kmh-1, what is the distance it travelled at the speed of 40 kmh-1? Pick one.
A) 200 km	B) 210 km	C) 220 km	D) 240 km	E) 250 km

Solution: let the distance travelled at 40 kmph=x km   distance travelled at 30 kmph =300-x km   x/40 + (300-x)/30 = 8   x = 240   ANSWER:240 km
Answer: D
If the length of the longest chord of a certain circle is 18, what is the radius of that certain circle?
Pick.
A) 2.5  B) 9  C) 10  D) 15  E) 20

Solution: Longest chord of a circle is the diameter of the circle   diameter = 2 * radius   If diameter of the circle is given as 18 = 2 * 9   so radius of the circle = 9   correct answer - 9
Answer: B
Nick took a bus from home to market, that travels at 80 kmph. While walking back at 8 kmph,
halfway through, he suddenly realized he was getting late and he cycled back the remaining distance in 60 kmph. Find the average speed.  Choose the correct answer:	A) 49.5 kmph	B) 49.0 kmph	C) 48.5 kmph	D) 48.0 kmph	E) none of these

Solution: Let the distance be 2x(one way)   Time taken by bus = 2x/80, by walking =x/8, by cycling = x/60 hours   :. Average speed = Total 48.0 kmphistance/Total time   = 8x / x/40 + x/8 + x/60   = 8 *60 / 1.5+7.5+1   = 12.0   ANSWER:48.0 kmph
Answer: D
At the faculty of Aerospace Engineering, 310 students study Random-processing methods, 232 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering?
Choose the most appropriate option:
A) 430 B) 432 C) 440 D) 442 E) 446

Solution: 310 + 232 - 112 (since 112 is counted twice )= 430   430 is the answer
Answer: A
In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible A score that Lindsey could have received on her midterm exam?  Choose the correct choice from the following:  A) 52%  B) 64%  C) 72%  D) 76%  E) 80%

Solution: If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have:   100-------------88----------------------------x   And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%.
Answer: A
The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Select.
A) 176 m B) 189 m C) 245 m D) 189 m E) 197 m

Solution: Speed = (45 * 5/18) m/sec   = (25/2) m/sec. Time   = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X)   = 750 ==> X = 245 m.   Answer:245 m
Answer: C
The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 40%, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged? Pick one.
A) 100% decrease B) 50% decrease C) 40% decrease D) 40% increase E) 50% increase

Solution: The rate of reaction is invesrsly proportional to the concentration of chemical B present. It used to have B=1 . Now that B is increased by 40%. So the new equation would be 2B=(1/2). In order for the rate of reaction to still be 1, we need to change the concentration of A to yield a 2. It used to be A^2=1, now the new equation should be (sqrt(2)*A)^2=2. The change in the concentration of A can be calculated as (sqrt(2) -1)/1 or approximately 40% increase. Answer 50% decrease.
Answer: B
Jill works as a waitress at the local diner where she earns an hourly wage of $8.00 per hour and a standard tip rate of 30% of the cost of the orders she serves. If she worked four 12-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week? Choose the correct choice from the following choices:
A) 1120
B) 300
C) 320
D) 350
E) 400

Solution: Jill earns 8 dollars/hour and the hourly tip is (3/10)*40.   Jill thus earns 8*14+14*12 per day(or 8(14)+12(14)=20(14)=280).   Jill has worked for 4 days -> 280*4=1120.   This matches answer choice 1120.
Answer: A
Which number is a factor of 20?	Choose one
A) 3	B) 4	C) 7	D) 18	E) 9

Solution: A whole number that divides exactly into another whole number is called a factor   20/5= 
20/5 = 4
4   answer 4
Answer: B