MU-NLPC/Calc-aqua_rat huggingface dataset:
A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 10 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese? [Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)] Choose the most appropriate option:
A) 1/4  B) 7/12  C) 2/3  D) 7/27  E) 8/7

Solution: Let' take the Number of geese to be 100.   Male = 30. Female = 70.   Now the second part of the Q, Let's take the Number migrated to be 20.   So we have 20 geese that migrated and out of that 10% are male i.e 10/100 *20 = 2 Geese (Males)   And now we know out of the total 20 geese , 2 are male , then 18 have to be female.   Now the ratio part , Male Geese Ratios = 2/30 = 1/15. - A   Female Geese Ratios =18/70=9/35 - B   Cross Multiply Equations A and B and you get = 7/27.   Ans 7/27
Answer: D
If Mel saved more than $10 by purchasing a sweater at a 15 percent discount, what is the smallest amount the original price of the sweater could be, to the nearest dollar?  Choose the correct choice from the following choices:
A) 45  B) 67  C) 75  D) 83  E) 150

Solution: We are told that 15 percent discount from the original price is more than $10:   0.15*{price} > 10;   {price} > 1,000/15;   {price} > 66 2/3.   Answer: 67.
Answer: B
If the average marks of three batches of 45, 60 and 45 students respectively is 50, 55 and 60, then the average marks of all the students is
Choose one:
A) 53.33	B) 54.68	C) 55	D) 57	E) None

Solution: Sol.   Required average = [55x50 + 60x55 + 45x60 / 45 + 60 + 45]   = [2250 + 3300 + 2700 / 150]   = 8250 / 150= 
8250 / 150 = 55
55   Answer 55
Answer: C
Raj has bought the product and sold it for a profit of Rs.30. His cost of buying and selling is in the ratio of 8:9 respectively. How much did Raj spent for buying A? Select:
A) 200 B) 240 C) 250 D) 270 E) 300

Solution: Let cost of buying of product A be x, (x+30/x)=9/8   Up on cross multiplication and solving for x, we get x=240   Answer: 240
Answer: B
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women? Choose one
A) 1/14
B) 1/7
C) 2/7
D) 3/7
E) 1/2

Solution: P=Favorable outcomes / Total # of outcomes   Favorable outcomes: 2 women and 2 men = C^2/5∗C^2/3=30   Total # of outcomes: 4 people out of 5+3= 
5+3 = 8
8= C^4/8=70   P=30/70=3/7   Answer: 3/7.
Answer: D
A truck owner will refuel his vehicle at a rate of 2 gallons of diesel fuel every 5 seconds. If diesel fuel costs $ 2 per gallon, how long will it take for the truck owner to refuel his vehicle with $ 100 worth of diesel fuel? Choose the correct choice from the following choices.
A) 20 seconds	B) 2 minute 5 seconds	C) 1 minute 20 seconds	D) 20 minutes	E) 1 hour 20 minutes

Solution: 2 gal / 5 sec   $2 / gal   $100/$2 = 502 gal   2 gal / 5 sec with 50 gal = 125 sec   B. 2 minute 5 seconds
Answer: B
Arabica coffee costs $0.4 per ounce while Robusta coffee costs $0.3 per ounce. If the blend of Arabica and Robusta costs $0.36 per ounce, what is the share of Arabica in this blend?
Choose the correct choice:
A) 20%
B) 24%
C) 30%
D) 33%
E) 60%

Solution: a= amount of arabica coffee   1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta   therefore:   .4a + .3(1-a) = .36   .4a + .3 - .3a = .36   a= .6   therefore: .6/1 ounce = 60%. Therefore, the answer should be 60%
Answer: E
Which one of the fractions has the highest value?
Choose the correct choice from the following answers
A) A)23/77	B) B)23/78	C) C)23/84	D) D)23/87	E) E)23/25

Solution: 23/25   Now, all options have the same numerator 23. If numerator is same, the fraction with the highest value will be the one with the lowest denominator.   Answer (23/25).
Answer: E
If a is an odd integer and b is an odd integer which of the following must not be an odd integer : Choose the correct answer:	A) a/b	B) ab	C) 2a+b	D) 2(a+b)	E) 3a/b

Solution: only when two odd number added then we get even number.   Therefore answer is 2(a+b)
Answer: D
Jane started baby-sitting when she was 16 years old. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 32 years old, and she stopped baby-sitting 10 years ago. What is the current age of the oldest person for whom Jane could have baby-sat? Choices: A) 20 B) 21 C) 22 D) 23 E) 24

Solution: Check two extreme cases:   Jane = 16, child = 8, years ago = 32-16= 
32-16 = 16
16 --> child's age now= 8+16= 
8+16 = 24
24;   Jane= 22, child = 11, years ago = 32-22= 
32-22 = 10
10 --> child's age now= 11+10= 
11+10 = 21
21.   Answer: 24.
Answer: E
A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction.In how much time will the train pass the jogger?  Answers.
A) 3.6 sec B) 18 sec C) 36 sec D) 72 sec E) none

Solution: speed of the train relative to jogger = (45-9)km/hr=36km/hr.   (36*5/8)m/sec.   10m/sec.   Distance to be covered = (240 + 120)= 
(240 + 120) = 360
360 m.   time taken=(360/10)= 
(360/10) = 36
36sec.   Answer: 36 sec
Answer: C
Two people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L Choose the correct choice from the following answers:  A) 1/3.  B) 1/2.  C) 2.  D) 3.  E) 6.

Solution: Difference = Average   H - L = (H + L)/2,   Solving for H/L gives 3. A quick check, H be 21 and L be 7, 21- 7= (21 + 7 )/2   3.
Answer: D
Of the films Empty Set Studios released last year, 60% were comedies and the rest were horror films. 75% of the comedies were profitable, but 75% of the horror moves were unprofitable. If the studio made a total of 60 films, and broke even on none of them, how many of their films were profitable?	Choose the correct option:	A) 18	B) 19	C) 20	D) 21	E) 59

Solution: After fiddling some more, this is how I got to answer choice 59...but did I get here using voodoo math or is it sound?   (.60*.75) + (.40*.25) = .44 + .10 = .55   55/100 = 11/20   Then subtract from 60:   60 - 11/20 = 59 (answer 59)
Answer: E
10 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?  Pick one:
A) 144
B) 131
C) 115
D) 90
E) 45

Solution: there are 10 business exec and in each handshake 2 business execs are involved.   hence 10C2=45   Also, each of 10 exec will shake hand with every 7 other chairmen for total of 70 handshake.   total=45+70= 
45+70 = 115
115   ANS: 115
Answer: C
For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of (( 90 Θ 33 ) Θ 17 ) - ( 97 Θ (33 Θ 17)) ?  Choose the correct choice from the following:
A) 0
B) 2
C) 4
D) 6
E) 8

Solution: (( 90 Θ 33 ) Θ 17 )   The remainder of 90 divided by 33 is 24;   The remainder of 24 divided by 17 is 7;   ( 97 Θ (33 Θ 17))   The remainder of 33 divided by 17 is 16;   The remainder of 97 divided by 16 is 1.   7 - 1= 
7 - 1 = 6
6.   Answer: 6.
Answer: D
Two trains A and B are 150 m and 150 m long and are moving at one another at 54 Km/hr and 36 Km/hr respectively. Arun is sitting on coach B1 of train A. Calculate the time taken by Arun to completely cross Train B.
Choose one
A) 10 s  B) 6 s  C) 4 s  D) 8 s  E) 12 s

Solution: DETAILED SOLUTION   Speed of A = 54∗1000/60∗60 = 15 m/s   Speed of B = 36∗1000/60∗60 = 10 m/s   Relative speed = S1 + S2 = 15 + 10 m/s = 25 m/s   The length that needs to be crossed = length of train B = 150 m. Therefore time taken = 150/25= 
150/25 = 6
6s.   What is the time taken for trains to completely cross each other? The length that needs to be crossed= 150 + 150= 
150 + 150 = 300
300 m. Time taken= 300/25= 
300/25 = 12
12 s.   CORR12 sCT ANSW12 sR 12 s.
Answer: E
At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other? Choose the correct answer:
A) 16 4/19
B) 16 4/18
C) 16 4/10
D) 16 4/11
E) 16 4/14

Solution: Formula : θ=∣∣∣30h−112m∣∣∣θ=|30h−112m|   Here angle is 0. So   11/2 m – 30 h = 0   11/2 m – 30 × 3 = 0   m = 180/11   = 16 4/11   Ans:: 16 4/11
Answer: D
In a barrel of juice there is 60 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer? Options:
A) 3:2.	B) 1:1.	C) 3:1.	D) 4:3.	E) 3:4.

Solution: Juice barrel : beer Barrel = 60:80 i.e. 3:8   price of Juice : Price of Beer = 3 : 4   so for 6/8 costs 3/4, ie 6J / 8B = 3/4.   Solving for J/1:1., we get 2:2=1:1   Answer 1:1..
Answer: B
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required?	Choose the correct choice from the following choices
A) 34  B) 40  C) 68  D) 88  E) None

Solution: Solution   We have:L =20 ft and lb = 680 sq.ft	b = 34ft   Length of fencing	= (l + 2b)   = (20 + 68)= 
(20 + 68) = 88
88 ft.   Answer 88
Answer: D
A river 2m deep and 45 m wide is flowing at the rate of 3 kmph the amount of water that runs into the sea per minute is?  Choose the correct choice
A) 4500 M3	B) 4580 M3	C) I8500 M3	D) 4900 M3	E) 4700 M3

Solution: Explanation:   (3000 * 2 * 5)/60 = 4500 M3   4500 M3nswer: Option 4500 M3
Answer: A
You and your friend spent a total of $19 for lunch. Your friend spent $3 more than you. How much did your friend spend on their lunch?	Choose the correct choice from the following
A) $9 B) $3 C) $4 D) $6 E) $11

Solution: My lunch = l, my friends lunch = l+3   (l)+(l+3)=19   l+l+3-3=19-3   2l=16   l=8   My friends lunch l+3 = 8+3= 
8+3 = 11
$11, the answer is $11
Answer: E
A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations F are possible? Choose the correct choice from the following answers:	A) 3	B) 4	C) 5	D) 6	E) F=8

Solution: The combinations could be F{(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6),(48,5),(60,4),(80,3),(120,2),(240,1)}   Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with.   {(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)}   Hence 8..F=8
Answer: E
Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 21 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel?
Choose the correct choice from the following answers.
A) 54 B) 66 C) 68 D) 60 E) 63

Solution: 63   63   It takes 3 hours for the friends to meet; so the pigeon flies for 3 hours at 21 MPH = 63 miles
Answer: E
Two wheels are connected via a conveyor belt. The larger wheel has a 36cm diameter and the smaller wheel has a 24cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per hour in terms of r?	Options:
A) 1280π
B) 75r
C) 48r
D) 90r
E) (64π)/3

Solution: Interesting to note that the larger wheel has a diameter of 36 (6*6) while the smaller one has a diameter of 24 (6*4)...   If the large wheel has a diameter of 36 and the small wheel, 24, then their circumferences are 36pi and 24pi respectively. In order for them to move the conveyor belt at the same rate, the smaller wheel would need to rotate 1.5 times as fast as the larger wheel. Lets say the large wheel makes 10 revolutions per minute, the smaller wheel would need to make   10*1.5= 
  10*1.5 = 15
15 revolutions per minute. If the large wheel makes 10 revolutions per minute it makes 600 per hour. Therefore, the smaller wheel would need to make   600*1.5= 
  600*1.5 = 900
900 revolutions per hour.   If r= 10, then the answer choice must be d.   D. 90r
Answer: D
Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work?  Choose the correct choice from the following choices:
A) 12 days B) 5 days C) 8 days D) 11 days E) 6 days

Solution: Answer: Option 11 days   (5 + x)/20 + 5/25 = 1 => x = 11 days
Answer: D
Ajay can complete a piece of work in 4 days. Balu takes double the time taken by Ajay, Charan takes double that of Balu, and Danush takes double that of Charan to complete the same task. They are paired in groups of two each. One pair takes two thirds the time needed by the second pair-to complete the work. Which is the first pair?	Choose the correct choice from the following options.
A) A, B B) A, C C) B, C D) A, D E) None of these

Solution: Time taken by Ajay, Balu, Charan, Dhanush is 4 days, 8 days, 16 days and 32 days respectively.   Therefore, grouping Ajay and Dhanush work will be two third of the work that will be completed by grouping Balu and Charan.   ANSWER:A, D
Answer: D
A Bell Curve (Normal Distribution) has a mean of − 1 and a standard deviation of 1/8 . How many integer values M are within three standard deviations of the mean?  Options
A) 0	B) 1	C) 3	D) 6	E) 7

Solution: Got the question correctly -- the second item -- [highlight]bthe list of elements in the set is required.[/highlight] is not required.   With the new information, there is only one integer value (-1) that is between (-1.375, -0.625) i.e., falls within the three 3 SD range.1
Answer: B
A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
Choose the correct answer
A) 7	B) 8	C) 5	D) 2	E) 4

Solution: 30 --- 3 DS = 10   ? ---- 1   18 ---- 3 US = 6   ? ---- 1 M = ?   M = (10 + 6)/2= 
(10 + 6)/2 = 8
8   Answer:8
Answer: B
A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.20. For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount. What is the total for a book on the third day it is overdue?
Pick:  A) $0.60  B) $0.70  C) $0.80  D) $0.90  E) $1.00

Solution: 1st day fine - 0.2   2nd day fine - 0.2*2 = 0.4 (as doubling gives lower value)   3rd day fine - 0.4+3 = 0.7 (as doubling gives higher value)   Answer: $0.70.
Answer: B
The sides of a rectangle are in the ratio of 6 : 5 and its area is 1331 sq.m. Find the perimeter of rectangle.	Pick one
A) 121	B) 123	C) 125	D) 122	E) 126

Solution: Let 6x and 5x be sides of the rectangle   6x × 5x = 1331   11xpower2 = 1331   xpower2 = 1331/11= 
1331/11 = 121
121=> x = 11   Length = 6x = 6 × 11 = 66   Breadth = 5x => 5 × 11 = 55   Perimeter = 2 (l+b) => 2 (66+55) = 121 m   121nswer is 121.
Answer: A
A CAN FINISH A WORK IN 21 DAYS AND B CAN DO THE SAME WORK IN15 DAYS. B WORKED FOR 10 DAYS AND LEFT THE JOB. IN HOW MANY DAYS, A ALONE CAN FINISH THE REMAINING WORK?
Choose the most appropriate option.
A) 5	B) 5 1/2	C) 7	D) 8	E) NONE OF THESE

Solution: B'S 10 DAY'S WORK=(1/15*10)=2/3 REMAINING WORK = (1-2/3)=1/3   NOW, 1/18 WORK IS DONE BY A IN 1 DAY   1/3 WORK IS DONE BY A IN  (21*1/3)= 
 (21*1/3) = 7
7 DAYS.   7ORRE7T OPTION:7
Answer: C
The volume of a large cube is 125 cubic inches. A new
shape is formed by removing a smaller cube from one
corner of the large cube. The surface area of this new
shape in square inches is Choose one
A) 120
B) 150
C) 180
D) 225
E) 250

Solution: Note that the surface area of the shape is the same as the surface area of the   large cube. Also, the large cube has side 5, and surface area 6 × 5-2round = 150.   correct answer 150
Answer: B
The first four numbers in a regular sequence are 4, 10, 22, and 46. What is the next number in the sequence?	Choose the correct answer.
A) 94 B) 54 C) 176 D) 82 E) 190

Solution: it is a good Q to learn to pick up number properties in the given set, even if we do not get a Q on these line in actuals..   when we see the sequence 4, 10, 22, 46, we see that each succeeding number is some value more than twice the previous number..   10=2*4+2..   22=2*10+2..   and so on..   so next number= 2*46+2=94..   94
Answer: A
What least number must be added to 1056, so that the sum is completely divisible by 23 ?
Select the correct option
A) 23  B) 24  C) 12  D) 2  E) 6

Solution: 23) 1056 (45   92   ---   136   115   ---   21   ---   Required number = (23 - 21)= 
(23 - 21) = 2
2   ANSWER 2
Answer: D
A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 6 runs. His new average is:	Choose the correct choice
A) 46 B) 50 C) 52 D) 54 E) 30

Solution: Let average for 10 innings be x. Then,   (10x + 108)/11 = x + 6   = 11x + 66 = 10x + 108   = x = 42.   New average = (x + 6) = 48 runs.   46NSWER 46
Answer: A
How many four-digit numbers that do not contain the digits 2, 3, 4, 5, 6, 7, or 8 are there? Choose the correct choice.
A) 30
B) 36
C) 42
D) 48
E) 54

Solution: The 1st digit can be filled up by the numbers: {1,9} = 2 ways   The 2nd digit can be filled up by the numbers: {0,1,9} = 3 ways   The 3rd digit can be filled up by the numbers: {0,1,9} = 3 ways   The 4th digit can be filled up by the numbers: {0,1,9} = 3 ways   The total number of such four-digit numbers is   2*3*3*3= 
  2*3*3*3 = 54
54   The answer is 54.
Answer: E
How many three letter words are formed using the letters of the word THREE?  Choose the correct choice from the following answers:
A) A)117
B) B)118
C) C)119
D) D)120
E) E)121

Solution: The number of letters in the given word is five.   The number of three letter words that can be formed using these four letters is 5P4   = 5 * 4 * 3*2= 
5 * 4 * 3*2 = 120
120.   Answer:120
Answer: D
In a pair of fractions, fraction A is twice the fraction B and the product of two fractions is 2/25. What is the value of fraction A?	Choose the correct choice from the following choices
A) 1/5	B) 1/25	C) 2/5	D) Data inadequate	E) None of these

Solution: A = 2B => B = 1/2 A, so, AB = 2/25   1/2 A2 = 2/25   A2 = 4/25   A = 2/5   ANSWER:2/5
Answer: C
The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?  Pick one
A) 28882
B) 27772
C) 23123
D) Rs.13500
E) 28811

Solution: P = (184*106) / [6 2/3 * 6 2/3 *(300*6 2/3)]   P = 13500   Answer: Rs.13500
Answer: D
What is the maximum number Q of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ? Answers:
A) 36 B) 32 C) 24 D) 21 E) 15

Solution: 27 cubic centimetre cubes gives side = 3cm   so if:   L*W*H is 9*12*8, then max. cube we can have are  3*4*2= 
 3*4*2 = 24
24   L*W*H is 9*8*12, then max. cube we can have are  3*2*4= 
 3*2*4 = 24
24   L*W*H is 12*8*9, then max. cube we can have are  4*2*3= 
 4*2*3 = 24
24   L*W*H is 12*9*8, then max. cube we can have are  4*3*2= 
 4*3*2 = 24
24   L*W*H is 8*12*9, then max. cube we can have are  2*4*3= 
 2*4*3 = 24
24   L*W*H is 8*9*12, then max. cube we can have are  2*3*4= 
 2*3*4 = 24
24   In all cases we get Q=24 cubes.   Ans. 24
Answer: C
In a can, there is a mixture of milk and water in the ratio 3:2. If the can is filled with an additional 6 liters of milk, the can would be full and the ratio of milk and water would become 2:1. Find the capacity of the can? Options:  A) 36  B) 34  C) 32  D) 30  E) 28

Solution: Let C be the capacity of the can.   (3/5)*(C-6)+6=(2/3)*C   9C-54+90=10C   C=36   The answer is 36.
Answer: A
The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?	Choose the correct choice from the following answers
A) 2:5  B) 2:8  C) 2:4  D) 2:1  E) 2:2

Solution: The volume of the cone = (1/3)πr2h   Only radius (r) and height (h) are varying.   Hence, (1/3)π may be ignored.   V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2   => h1/h2 = 2/5   i.e. h1 : h2 = 2:5   2:5nswer: 2:5
Answer: A
To mail a package, the rate is 40 cents for the first pound and 5 cents for each additional pound. Two packages weighing 4 pounds and 6 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved? Choose the correct choice from the following options:
A) Combined, with a saving of 20 cents B) Combined, with a saving of 35 cents C) Separately, with a saving of 5 cents D) Separately, with a saving of 15 cents E) Combined, with a saving of 25 cents

Solution: 4 pounds cost = 40+3*5= 
40+3*5 = 55
55   6 pounds cost= 40+5*5= 
40+5*5 = 65
65   Total= 120   10 pounds cost = 40+ 9*5= 
40+ 9*5 = 85
85 dif. 35   Answer : Combined, with a saving of 35 cents
Answer: B
Twenty eight years ago,a father was three times as old as his son.Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is : Choose the correct choice from the following answers:	A) 120	B) 176	C) 168	D) 105	E) 86

Solution: Let the present ages of the father and son be 2x and x years respectively.   then,(2x-28)=3 (x-28)   x=56.   Required sum =(2x+x)=3x=168 years.   Answer is 168
Answer: C
In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 8720 votes were polled, then how many valid votes did B get?
Choose the correct option:
A) 1888  B) 2999  C) 2834  D) 2777  E) 2991

Solution: Let the total number of votes polled in the election be 100k.   Number of valid votes = 100k - 20% (100k) = 80k   Let the number of votes polled in favour of A and B be a and b respectively.   a - b = 15% (100k) => a = b + 15k   => a + b = b + 15k + b   Now, 2b + 15k = 80k and hence b = 32.5k   It is given that 100k = 8720   32.5k = 32.5k/100k * 8720 = 2834   The number of valid votes polled in favour of B is 2834.   Answer: 283432.5 /100  * 8720= 
32.5 /100  * 8720 = 2_834
2834   The number of valid votes polled in favour of B is 2834.   Answer: 2834
Answer: C
The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.04. There are 40 brand A widgets, 35 brand B widgets, 25 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x?	Answers:
A) 0.05	B) 0.055	C) 0.07	D) 0.1	E) 0.2

Solution: Given probability of defective items in each brand,   So, the number of items defective in brand A=x*40, in brand 0.055=0.06*35 and brand C=0.04*25   Total number of widgets=40+35+25= 
40+35+25 = 100
100   the probability that the widget selected is defective is 0.053=(x*40+0.06*35+0.04*25)/100   => 40x+2.1+1=5.3   =>40x = 2.2   >x=2.2/40= 
2.2/40 = 0.055
0.055   Ans 0.055
Answer: B
Rachel drove 40 1/4 kilometres in 45 minutes. What was her average rate of speed in kilometres per hour? Choose the correct choice:
A) 52
B) 52 2/3
C) 53
D) 53 2/3
E) 54 1/3

Solution: 53 2/3 = 40(1/4) = 161/4   T = 3/4   S = 53 2/3/T = 53 2/3   Answer = 53 2/3
Answer: D
What number must be added to 6, 16 and 8 to get an average of 13? Choose the correct choice from the following:
A) 23
B) 22
C) 44
D) 33
E) 55

Solution: 22   22
Answer: B