MU-NLPC/Calc-aqua_rat huggingface dataset:
How many integers between 324,700 and 436,600 have tens digit 1 and units digit 3?  Choose the correct choice from the following options
A) 327	B) 645	C) 987	D) 1119	E) 1339

Solution: The integers are:   324,713   324,813   etc...   436,513   The number of integers is   4366 - 3247= 
  4366 - 3247 = 1_119
1119   The answer is 1119.
Answer: D
If the area of circle O is 16π, what is the length of an arc on the circle formed by a central angle measuring 15 degrees?  Pick:
A) π/3 B) 3π/2 C) 2π D) 5π/2 E) 8π

Solution: Area = 16π   Radius = 4   Circumference = 2 x 4 x π = 8π   Angle forming the arc = 15 degrees. 15/360 = 1/24.   Therefore length of arc = 1/24 * 8π = π/3 - π/3nswer choice π/3.
Answer: A
Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.143 per kg, the price of the third variety per kg will be  Choose the correct choice from the following options.
A) Rs.165.50	B) Rs.1700	C) Rs. 175.50	D) Rs. 180	E) None

Solution: Solution   Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50   So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.   x-143/22.50 = 1 =â€º x - 143 = 22.50 =â€º x=165.50.   Hence, price of the third variety = Rs.165.50 per kg.   Rs.165.50nswer Rs.165.50
Answer: A
Set L is composed of nine numbers, labeled L1 through L9. Set M is also composed of nine numbers, labeled M1 through M9. Set M is defined as follows: M1 = 1 + L1; M2 = 2 + L2; and so on, including M9 = 9 + L9. How much larger is the sum of set M's mean and range than the sum of set L's mean and range?  Choose the correct option
A) 3 B) 4 C) cannot be determined D) 6 E) 8

Solution: Yes, the correct answer is cannot be determined
Answer: C
If x^3 > y^2 > z, which of the statements could be true?
I. x < y = z
II. x = z < y
III. y < x < z	Options
A) I only	B) III only	C) I and II only	D) II and III only	E) I, II and III

Solution: Given : x^3 > y^2 > z   I. x < y = z is not true i.e. Answers can not be Options A, C or E   II. x = z < y is not true i.e. Answers can not be Options A, C or E   III. y < x < z is true for x=4, y=3, z=5 i.e. Answers can only be Options III only   Answer: option III only
Answer: B
A rectangular tank needs to be coated with insulation. The tank has dimensions of 4 feet, 5 feet, and 2 feet. Each square foot of insulation costs $20. How much will it cost to cover the surface of the tank with insulation?	Choose the correct choice from the following choices:
A) $1520	B) $1640	C) $1780	D) $1850	E) $1960

Solution: The total surface area is 2(2*4 +4*5 + 2*5) = 76 square feet   The total cost is 76*$20 = $1520   The answer is $1520.76* 20= 
76* 20 = 1_520
$1520   The answer is $1520.
Answer: A
A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag? Pick:
A) 76 ways  B) 65 ways  C) 54 ways  D) 28 ways  E) 30 ways

Solution: The word contains five consonants. Three vowels, three consonants can be selected from five consonants in ⁵C₃ ways, two vowels can be selected from three vowels in ³C₂ ways.   3 consonants and 2 vowels can be selected in ⁵C₂ . ³C₂ ways i.e., 10 * 3 = 30 ways.   Answer: 30 ways
Answer: E
A person climbs up to a pole of 88 m high. In every min he climbs 12 m but slips down 8 m...how much time will he take to reach d top?	Choose one:
A) 20th minute  B) 21th minute  C) 22th minute  D) 24th minute  E) 25th minute

Solution: in every min person climbs up 12m and slips 8m . hence net displacement becomes 4m.   in 19 minutes person would climb  (19*4)= 
 (19*4) = 76
76m   in 20th minute person would climb 12m up.. and it will be on top.   hence in 20th minute. person will reach on pole.   20th minuteNSWER:20th minute
Answer: A
If z is a multiple of 7899, what is the remainder when z^2 is divided by 9?
Choose the correct choice from the following answers.
A) 0	B) 2	C) 3	D) 6	E) 7

Solution: The sum of the digits is 7+8+9+9= 
7+8+9+9 = 33
33.   Thus 3 is a factor of 7899, so 3 is a factor of z.   Then 3^3= 9 is a factor of z^2.   Then the remainder when z^2 is divided by 9 is 0.   The answer is 0.
Answer: A
A bag contains 3 red, 4 green and 4 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball?
Pick:
A) 6/11	B) 27/55	C) 31/55	D) 91/165	E) 109/165

Solution: P(no red balls) = 8/11*7/10*6/9 = 56/165   P(at least one red ball) = 1 - 56/165 = 109/165   The answer is 109/165.
Answer: E
In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 7 consecutive days in Rwanda?	Choose the correct answer:  A) 4/7  B) 3/7  C) 35/128  D) 4/28  E) 28/135

Solution: using Binomial. theorem   n35/128r (p)^r (q)^n-r   735/1284 (1/2)^4 (1/2)^r   which is 35/128   Answer is 35/128.
Answer: C
In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 83 more candidates got selected than A. What was the number of candidates appeared from each State?  Choose the correct choice.
A) 7000
B) 8300
C) 6000
D) 5000
E) 4000

Solution: State A and State B had an equal number of candidates appeared.   In state A, 6% candidates got selected from the total appeared candidates   In state 8300, 7% candidates got selected from the total appeared candidates   8300ut in State 8300, 83 more candidates got selected than State A   From these, it is clear that 1% of the total appeared candidates in State 8300 = 83   => total appeared candidates in State 8300 = 83 x 100 = 8300   => total appeared candidates in State A = total appeared candidates in State 8300 = 8300
Answer: B
What is the Mode of the following data set R- {1,2,7,9,6,6,7,7}	Choose the correct choice from the following choices:	A) 1	B) 2	C) 7	D) 6	E) 9

Solution: Mode of a set is the data point that is repeated the most number of times. In the set given, 7 is repeated.   Answer: 7
Answer: C
624 people are protesting outside of the White House. If they are standing in a rectangle in which the rows are no less than 6 people and no more than 104, how many different combinations of rectangular shapes are possible?
Choices
A) 6  B) 7  C) 8  D) 9  E) 10

Solution: firstly factors of 624 = 1,2,3,4,6,8,12,13,16,24,26,39,48,52,78,104,156,208,312,624   the question says each row will have people no less than 12 and no more than 52,   therefore, we should be interested in the factors between 12 and 52 (inclusive)   12(in each row) * 52(number of columns) =624, similarly   13 * 48   16 * 39   24 * 26   26 * 24   39 * 16   48 * 13   52 * 12   total possibilities = 8   option 8
Answer: C
The average age of a group of 10 students was 25. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?  Choose the correct choice from the following options:
A) 37 years
B) 30 years
C) 32 years
D) 44 years
E) None of these

Solution: The total age of 10 students with average 25 = 250   The total age of 12 students with average 27 = 324   The total age of 2 new students = 74   Their average =37   Correct Option 37 years
Answer: A
In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 4 ounces of corn syrup, how many ounces of water does it contain?
Pick one:  A) 45  B) 50  C) 55  D) 60  E) 63

Solution: F:C:W   1:12:30   Sport version:   F:C   3:12   F:W   1:60   OR 3:180   So C:F:W = 12:3:180   C/W = 12/180 = 3 ounces/x ounces   x = 4*180/12= 
4*180/12 = 60
60 ounces of water   60
Answer: D
A circular rim 14 inches in diameter rotates the same number of inches per second as a circular rim 42 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?	Choose the correct choice from the following options.
A) 48pi/x  B) 75x  C) 48x  D) 24x  E) 20x

Solution: Let's try the explanation. We have two wheels. One with 14pi and the other one with 42pi. They have the same speed. In the smaller wheel it's 14pi*x, which must be equal to the speed of the bigger one (42pi*a number of revolutions).They are asking that number of revolutions (but in minutes, which makes the question even harder).   Anyway, we have 14pi*x=42pi*a.   (14pi*x)/(42pi). As I said, that's in seconds. So, to convert it to minutes we multiply by 60 and we get the result, 20x.   Ans :20x
Answer: E
Find the least number which when divided by 34 and 5 leaves a remainder of 4 in each case.	Choose the correct choice from the following
A) 170  B) 172  C) 174  D) 176  E) 178

Solution: The least number which when divided by different divisors leaving the same remainder in each case   = LCM(different divisors) + remainder left in each case.   Hence the required least number   = LCM(31, 5) + 4 = 174.   ANSWER:174
Answer: C
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? Choose one: A) 5.79 B) 5.77 C) 5.76 D) 5.72 E) 5.71

Solution: M = 6   S = 1.2   DS = 7.2   US = 4.8   x/7.2 + x/4.8 = 1   x = 2.88   D = 2.88 * 2 = 5.76.Answer:5.76
Answer: C
At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants? Choose the correct choice from the following answers:	A) 2	B) 3	C) 4	D) 5	E) 6

Solution: 39 = 19 + 18 + 12 - 4 - 2x   2x = 19 + 18 + 12 - 4 - 39   = 45 - 39= 
45 - 39 = 6
6   x= 3   ANSWER:3
Answer: B
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green? Options:
A) 3/4  B) 1/4  C) 1/3  D) 7/19  E) 1/7

Solution: Total number of balls = (8 + 7 + 6)= 
(8 + 7 + 6) = 21
21.   Let E= event that the ball drawn is neither red nor green   = event that the ball drawn is blue.   n(E)=7   P(E)=n(E)/n(S)   =7/21   =1/3   The answer should be 1/3
Answer: C
In how many ways 5 boys and 5 girls can be seated in a row so that boys and girls are alternate? Choose the correct choice from the following answers
A) 28400	B) 28500	C) 28600	D) 28700	E) 28800

Solution: number of ways = 2*5!*5! = 28800   Answer is 28800
Answer: E
For how many integers k is (k^2)+3 = 3+(2^k) ?	Select
A) None  B) 1  C) 2  D) 3  E) 4

Solution: (2^2)+3= 3+(2^2)   (2^4)+3= 3+(4^2)   For k= 2 and 4 the above equality holds true.   Answer:Option 2
Answer: C
There are two pipes which are functioning simultaneouly to fill a tank in 12 hours, if one pipe fills the tank 10 hours faster than other then how many hours second pipe will take to fill the tank ?
Choices
A) 30 hours  B) 35 hours  C) 40 hours  D) 42 hours  E) 41 hours

Solution: Explanation:   Lets suppose tank got filled by first pipe in X hours,   So, second pipe will fill the tank in X + 10 hours.   =>1/X+1/X+10=1/12   =>X=20   30 hoursNSWER IS 30 hours
Answer: A
A train of length 180 metres takes 54 seconds to cross a tunnel of length 270 metres. What is the speed of the train in km/hr?
Choose the correct choice from the following answers.
A) 50 km/hr.  B) 20 km/hr.  C) 30 km/hr.  D) 40 km/hr.  E) None

Solution: Sol.   Speed = [180 + 270 / 54] m/sec = [450 / 54 * 18/5] km/hr =30 km/hr.   Answer 30 km/hr.
Answer: C
If 7 ministers are to be seated at a round table conference, then how many different ways can they be seated?  Options
A) 24	B) 60	C) 720	D) 520	E) 180

Solution: Simple formula:   There are (n - 1)! ways to arrange n distinct objects in a circle.   so its  (7-1)= 
 (7-1) = 6
6!= 720=720
Answer: C
The number which exceeds 12% of it by 52.8 is:	Choices:
A) 60
B) 77
C) 269
D) 26
E) 91

Solution: Explanation:   Let the number be x. Then, x – 12% of x = 52.8   x – (12/100)x = 52.8   x (1– 12/100) = 52.8   (88/100)x = 52.8   x = (100 X 52.8) / 88 = 60   60NSWER: 60
Answer: A
How many prime numbers are between 15/7 and 131/6?  Options
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: 15/7= 3-   131/6= 22-   Prime numbers between 3 and 22 are 5, 7, 11, 13, 17, and 19   - sign signifies that the number is marginally less .   Answer 6
Answer: D
A boy has Rs. 320 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? Options.
A) 60  B) 110  C) 140  D) 130  E) 120

Solution: Let number of notes of each denomination be x.   Then x + 5x + 10x = 320   16x = 320   x = 20.   Hence, total number of notes = 3x = 60.   60
Answer: A
Find the odd man out. 1, 3, 10, 13, 19, 29
Select the correct option
A) 12
B) 9
C) 1
D) 3
E) 10

Solution: 10 is an even number. All other given numbers are odd   Answer : Option 10
Answer: E
What is the probability that their sum of two numbers, randomly selected from the set {3,6,9,12,15,18} will be greater than 9?  Choose one: A) 7/6 B) 7/9 C) 7/8 D) 7/10 E) 6/7

Solution: First7 problem is 6C2 = 12 .. Not 20..   Point 2, you sum should be greater than 9, so these are the following possibilities you have   ({3,9},{3,12},{3,15},{3,18},{6,9},{6,12},{6,15},{6,18},{9,12},{9,15},{9,18},{12,15},{12,18},{15,18}) which leads to 14 pairs   So the probability is 14 on 12 or 7/6..   7/6NSWER:7/6
Answer: A
Two letters from the word KHANTKAR are selected at random. What is the probability that at least one of the selected letters is a consonant?
Choices:
A) 25/28	B) 27/28	C) 30/28	D) 40/28	E) 50/28

Solution: There are 6 consonants and 2 vowels in KHANTKAR .   probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels)   Probability of both vowels = 2C2/8C2 = 1/28   So,Answer is 1 - 1/28 = 27/28   Answer : 27/28
Answer: B
Working alone, Jim finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Jim alone cleans the entire house in 6 hours. How many hours will it take Nick and Jim to clean the entire house if they work together?
Select the correct option.
A) 1.5 B) 2 C) 2.4 D) 3 E) 3.6

Solution: Answer is 3.6 hours.   Jim does the complete house in 6 hours while Nick does it in 9 hours. 1/ (1/6+1/9)= 3.6   answer is 3.6
Answer: E
In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital? Answers
A) 11758
B) 11759
C) 11755
D) 11750
E) 11751

Solution: 200 + 130= 
200 + 130 = 330
330   800 - 330= 
800 - 330 = 470
470   200 ---- 5000   470 ---- ?=> 11750   Answer: 11750
Answer: D
Choose the missing terms out of the given alternatives.
CMW, HRB, ?, RBL, WGQ, BLV	Choose the correct choice from the following choices:
A) MWS
B) MWG
C) SJE
D) HHW
E) YSH

Solution: MWG   MWG   The letters move five steps forward.
Answer: B
Which of the following will divide evenly into 407,406,520?  Answers.
A) 11 B) 21 C) 4 D) 31 E) 41

Solution: Rule:   4: Last two digits should be divisible by 4   the last two digits are 00, which are divisible by 4   Answer: 4
Answer: C
Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is  Choose the correct answer:
A) 30 Km/hr	B) 36 Km/hr	C) 80 Km/hr	D) 90 Km/hr	E) None of these

Solution: Explanation:   Distance covered = 120+120= 
120+120 = 240
240 m   Time= 12 s   Let the speed of each train = x.   Then relative velocity = x+x = 2x   2x = distance/time = 240/12= 
240/12 = 20
20 m/s   Speed of each train= x = 20/2= 
20/2 = 10
10 m/s= 10*18/5 km/hr = 36 km/hr   Option 36 Km/hr
Answer: B
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?  Pick one
A) 128  B) 177  C) 199  D) 178  E) 150

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 15 => y = x/15   x + 100 / 25 = x / 15   x = 150 m.   Answer:150
Answer: E
Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
Choose one.
A) Rs.200
B) Rs.250
C) Rs.300
D) Rs.350
E) Rs.370

Solution: Let the amount paid to X per week = x   and the amount paid to Y per week = y   Then x + y = 550   Rs.250ut x = 120% of y = 120y/100 = 12y/10   ∴12y/10 + y = 550   ⇒ y[12/10 + 1] = 550   ⇒ 22y/10 = 550   ⇒ 22y = 5500   ⇒ y = 5500/22 = 500/2 = Rs.250   Rs.250)
Answer: B
The area of playground is 5700 sq. meters. What will be the cost of covering it with grass sheet 1cm deep, if cost of grass sheet is $2.80 per cubic meter.  Choose the most appropriate option: A) a) $144 B) b) $150.50 C) c) $159.6 D) d) $158.60 E) e) $160.70

Solution: total volume * unit cost = total cost   or, 5700 * 0.01 * 2.8 = total cost = 159.6=c) $159.6
Answer: C
A man has Rs. 400 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? Pick one
A) 45  B) 60  C) 75  D) 90  E) 105

Solution: Answer : C   Let number of notes of each denomination be x.   Then, x + 5x + 10x = 400   16x = 400   x = 25.   Hence, total number of notes = 3x = 75.
Answer: C
An design manager has 10patterns of chairs & 9patterns of tables. In how many ways can he make a pair of table & chair?	Choose the most appropriate option:
A) 20
B) 40
C) 80
D) 90
E) 100

Solution: He has has ten patterns of chairs and eight patterns of tables   Hence, A chair can be arranged in 10 ways and   A table can be arranged in 9 ways   Hence one chair and one table can be arranged in 10 x 9 ways = 90 ways   90
Answer: D
The perimeter of a square is 52 m. Find the area of the square.  Choose the most appropriate option:
A) 161 m².
B) 164 m².
C) 166 m².
D) 169 m².
E) 273 m².

Solution: Perimeter of square = 52 m   But perimeter of square = 4 × side   Therefore, 4 × side = 52 m   Therefore, side= 52/4= 
52/4 = 13
13m   Now, the area of the square= (side × side)   Therefore, area of the square = 13 × 13 m² = 169 m².   ANSWER : OPTION 169 m².
Answer: D
Find the distance covered by a man walking for 36min at a speed of 10km/hr? Pick one:
A) 1km
B) 3km
C) 6 km
D) 5km
E) 6km

Solution: Distance = 10*36/60= 
10*36/60 = 6
6 km   Answer is 6 km
Answer: C
A train 2500 m long can cross an electric pole in 100 sec and then find the speed of the train?  Choose the correct choice from the following choices
A) 90  B) 60  C) 120  D) 180  E) 360

Solution: Length = Speed * time   Speed = L/T   S = 2500/100= 
2500/100 = 25
25 M/Sec   Speed= 25*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 90 Kmph   90nswer:90
Answer: A
The list price of an article is Rs.70. A customer pays Rs.59.22 for it. He was given two successive discounts, one of them being 10%. The other discount is?	Choose the correct choice from the following:
A) 8%  B) 7%  C) 10%  D) 12%  E) 6%

Solution: Option 6%   6%xplanation:   70*(90/100)*((100-x)/100) = 59.22   x = 6%
Answer: E
Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science? Choose the correct choice from the following choices:	A) 18	B) 68	C) 67	D) 55	E) 56

Solution: S:E = 1:3   E:M = 3:5   ------------   S:E:M = 3:9:15   3/27 * 162= 
3/27 * 162 = 18
18   18nswer:18
Answer: A
Kail purchased n items from a catalog for $10 each. Postage and handling charges consisted of $4 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?
Pick one:	A) 11n + 2	B) 11n + 4	C) 11n + 3	D) 9n + 3	E) 9n + 4

Solution: its 11n + 3   n items for $10 each   total price $10n   postage and handling of $4 for 1st item and $1 for the rest   total postage and handling = $ [4+ (n-1)]   = $ n+3   total cost   10n+n+3 = 11n+3
Answer: C
In a school of 850 boys, 46% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?  Pick one
A) A)136	B) B)627	C) C)153	D) D)721	E) E)159

Solution: 46 + 28 + 10= 
46 + 28 + 10 = 84
84%   100 – 84= 16%    850 * 16/100= 
 850 * 16/100 = 136
136   136nswer:136
Answer: A
A tank can be filled by pipe A in 5 hours and by pipe B in 8 hours, each pump working on its own. When the tank is full and a drainage hole is open, the water is drained in 20 hours. If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how long does it take for the tank to be filled?
Choose the most appropriate option:	A) 2.6 hours	B) 3.6 hours	C) 4.6 hours	D) 5.6 hours	E) None of these

Solution: Let's first find the rates of the pumps and the drainage hole   pump A: 1 / 5 , pump B: 1 / 8 , drainage hole: 1 / 20   Let t be the time for the pumps to fill the tank. The pumps ,add water into the tank however the drainage hole drains water out of the tank, hence   t ( 1 / 5 + 1 / 8 - 1 / 20) = 1   Solve for t   t = 3.6 hours   Answer 3.6 hours
Answer: B
A certain company’s profit in 1996 was 15 percent greater than its profit in 1995, and its profit in 1997 was 20 percent greater than its profit in 1996. The company’s profit in 1997 was what percent greater than its profit in 1995?
Choose the correct option.
A) 5%
B) 18%
C) 33%
D) 35%
E) 38%

Solution: Soln:-   Profit in 1995 - 100   Profit in 1996 - 115   %increase Profit in 1997 in comparison to 1995 = 15 + 115*20%= 38%   ANSW38%R:38%
Answer: E
What is the value of x?
Data 1: x - 2y = 7
Data 2: 4x – 28 = 8y
Choices:
A) 89 B) 10 C) 12 D) 15 E) no solution exists

Solution: both are same equations   4X(x-2y=7) is 4x-8y=28   so no solution exists   ANSWno solution existsR:no solution exists
Answer: E
The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is  Choose one.
A) 4/5 B) 7/11 C) 7/13 D) 7/15 E) 8/11

Solution: Let the required fraction be x. Then	1	- x =	9   x	20   1 - x2	=	9   x	20   20 - 20x2 = 9x   20x2 + 9x - 20 = 0   20x2 + 25x - 16x - 20 = 0   5x(4x + 5) - 4(4x + 5) = 0   (4x + 5)(5x - 4) = 0   x =	4/5   4/5)
Answer: A
A box contains 8 apples, 7 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n?	Pick one:
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: P(choosing a red apple 5 times in a row) = 7/8*6/7*5/6*4/5*3/4 = 3/8 < 0.5   The answer is 5.
Answer: C
When not moving on the sidewalk, Maya can walk the length of the sidewalk in 7 minutes. If she stands on the sidewalk as it moves, she can travel the length in 4 minutes. If Maya walks on the sidewalk as it moves, how many minutes will it take her to travel the same distance? Assume she always walks at the same speed, and express your answer as a decimal to the nearest tenth.	Pick one.
A) 2.9
B) 2.5
C) 2.7
D) 2.1
E) 2.2

Solution: Explanation:   Assume distance of sidewalk "x"   Speed 1 (moving on sidewalk)   Speed 2 (moving off sidewalk)   Since both the movements are in same direction, we can do speed 1 + speed 2   Speed 1 = x4x4   Speed 2 = x7x7   Speed 1 + speed 2 = 11x2811x28 = = 0.39286x   Now new time while moving on sidewalk = x0.39286xx0.39286x = 2.54544   Hence, the answer is 2.5   Answer: 2.5
Answer: B