MU-NLPC/Calc-aqua_rat huggingface dataset:
In a game of billiards, A can give B 20 points in 70 and he can give C 30 points in 70. How many points can B give C in a game of 100?	Answers
A) 18
B) 27
C) 25
D) 20
E) 17

Solution: A scores 70 while B score 50 and C scores 40.   The number of points that C scores when B scores 100 = (100 *40)/50= 
(100 *40)/50 = 80
80.   In a game of 100 points, B gives (100 - 80)= 
(100 - 80) = 20
20 points to C.   Answer: 20
Answer: D
How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?  Choices.
A) 25 sec B) 28 sec C) 30 sec D) 35 sec E) 45 sec

Solution: Let length of tunnel is x meter   Distance = 800+x meter   Time = 1 minute = 60 seconds   Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s   Distance = Speed*Time   800+x = (65/3) * 60   800+x = 20 * 65= 
20 * 65 = 1_300
1300   x= 1300 - 800= 
1300 - 800 = 500
500 meters   ANSWER:30 sec
Answer: C
The area of a circle is increased by 1500%. By what percent has the radius of the circle increased?	Pick:
A) 100%
B) 200%
C) 300%
D) 600%
E) 800%

Solution: The area of the circle is increased by 1500%, thus the area is increased 16 times.   The area of a circle it proportional to the square of the radius (area=πr^2), therefore the radius must increase 4 times (diameter increase 4 times = area increase 16 times), which is increase by 500%.   Answer: 300%
Answer: C
The sides of a cube are in the ratio 1:2 the ratio of their volume is?
Pick
A) 1:9  B) 1:5  C) 1:8  D) 1:1  E) 1:2

Solution: 1:8   Answer: 1:8
Answer: C
If 10,000 microns = 1 decimeter, and 10,000,000angstroms = 1 decimeter, how many angstroms equal 1 micron?  Choose the correct choice from the following answers
A) 1.0e-08  B) 1.0e-05  C) 100,000  D) 10,000  E) 1,000

Solution: 10,000 microns = 1 decimeter, and 10,000,000 angstroms = 1 decimeter   10,000 microns = 10,000,000 angstroms   1 micron = 1,000   Answer : 1,000
Answer: E
A student got twice as many sums wrong as he got right. If he attempted 24 sums in all, how many did he solve correctly ?  Choose the correct choice from the following choices
A) 12	B) 16	C) 8	D) 24	E) 26

Solution: Explanation:   Suppose the boy got x sums right and 2x sums wrong.   Then, x + 2x = 24 3x = 24 x = 8.   Answer:8
Answer: C
At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $6.50 per hour, how much less than a manager does a chef earn each hour?
Choose the correct choice from the following.
A) $2.6
B) $2.40
C) $3.40
D) $4.40
E) $5.40

Solution: Manager wages per hour = $6.50   Dishwasher wages per hour = half of manager's wages. = 1/2($6.50) ==> $3.25   Chef wages per hour = 20% greater than Dishwasher wages   --> 20% of $3.25 = (20*($3.25)) /100   --> ($65)/100   --> $0.65   Therefore,   Chef wages per hour = $3.25 + $0.65 ==> $3.9   Difference of wages between manager and chef = $6.50 - $3.9 ==> $2.6   $2.6NSWER:$2.6
Answer: A
If four students are made to sit in a row, then 7 don't have seats. If 7 students are made to sit in a row, then two rows are empty. How many students have to sit a row such that each row has equal number of students and all students are seated?  Choices.
A) 0  B) 1  C) 4  D) 5  E) 9

Solution: Let there be a rows.   Then 4a + 7 = 7(a-2) [equating the number of students]   => a= 7   and total number of students = 35   Therefore 5 students much sit in each row such that each row has an equal number of students and all students are seated.   Option (5)
Answer: D
Find the odd man out. 1, 9, 16, 51, 121, 169, 225	Choose the correct choice from the following choices:
A) 169
B) 51
C) 16
D) 1
E) 2

Solution: Explanation :   Each of the given numbers except 51 is a perfect square. Answer : Option 51
Answer: B
One man traveled a distance of 61 km in 9hrs. He traveled partly on footat 4 km/hr and partly on bicycle ta 9 km/hr. The distance traveled on foot is?  Choose the correct option:
A) 10 km B) 12 km C) 16 km D) 18 km E) 20 km

Solution: Let the distance travelled on foot be x km.   Then, distance travelled on bicycle = (61 -x) km.   So, x + (61 -x) = 9   4 9   9x + 4(61 -x) = 9 x 36   5x = 80   x = 16 km.   16 km
Answer: C
A train passes a station platform in 36 sec and a man standing on the platform in 21 sec. If the speed of the train is 54 km/hr. What is the length of the platform?	Pick one
A) 288
B) 225
C) 881
D) 1277
E) 121

Solution: Speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/sec.   Length of the train= 15 * 21= 
15 * 21 = 315
315 m.   Let the length of the platform be x m . Then,   (x + 315)/36= 15 => x = 225 m.   Answer: 225
Answer: B
The area of the house of a hall is 20 m2 that of a longer wall 10 m2 and of the shorter wall 8 m2, find the edge of the new cube?  Choose the correct choice from the following
A) 45 m3 B) 40 m3 C) 60 m3 D) 600 m3 E) 300 m3

Solution: lb = 20 ; lh = 10 ; fh = 8   (lbh)2 = 20 * 10 * 8 => lbh = 40 m3   ANSWER:40 m3
Answer: B
A boat can move upstream at 40 kmph and downstream at 56 kmph, then the speed of the current is?  Choose the correct choice.
A) 5	B) 6	C) 8	D) 4	E) 2

Solution: US = 40   DS = 56   M = (56 - 40)/2= 
(56 - 40)/2 = 8
8 Answer:8
Answer: C
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 choice from the following.
A) 2 kmph	B) 8 kmph	C) 16 kmph	D) 4 kmph	E) 6 kmph

Solution: 30 --- 3 DS = 10   ? ---- 1   18 ---- 3 US = 6   ? ---- 1 M = ?   M = (10 + 6)/2= 
(10 + 6)/2 = 8
8   ANSWER:8 kmph
Answer: B
What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?
Choose the correct choice from the following options.
A) 1 : 3 B) 1 : 4 C) 2 : 3 D) Data inadequate E) None of these

Solution: Let the principal be P and rate of interest be R%.   ∴ Required Ratio = [(P×R×6/100) /(P×R×9/100)]=6PR/9PR=69=2:3   Answer 2 : 3
Answer: C
A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10^4 -10^2)(0.0016)? Choose the correct answer:
A) 15	B) 15.84	C) 17	D) 18.5	E) 19

Solution: You get 10^2 (100-1) (.0016)   we know   16/10000= 
  16/10000 = 1/625 = around 0.0016
.0016   10^2 (99) * (16/10000)   10^2= 100 and 100^2 = 10000   Cancel out the 100 with the 10^2   Left with 99(16/100).   0.99*16= 
0.99*16 = 15.84
15.84   Answer : 15.84
Answer: B
For any number y, y* is defined as the greatest positive even integer less than or equal to y. What is the value of 8.2 – 8.2*?
Choose the correct choice from the following options:
A) 0.2	B) 1.2	C) 1.8	D) 2.2	E) 4.0

Solution: Since y* is defined as the greatest positive even integer less than or equal to y, then 8.2* = 4 (the greatest positive even integer less than or equal to 5.2 is 4).   Hence, 8.2 – 8.2* = 8.2 - 6= 
8.2 - 6 = 2.2
2.2   Answer: 2.2.
Answer: D
A bakery opened yesterday with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon, and 65 percent of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?	Answers:	A) 5	B) 6	C) 7	D) 8	E) 9

Solution: answer is C ...7 dozens ....   half sold by noon --> 20 dozens (20 *12 =240)   remaining --> 20 dozens i.e 240 eggs...   65% sold --> 65*240/100 =156 eggs   remaining 35 % --> 84 eggs (7 dozens ) --> answer --  65*240/100= 
 --  65*240/100 = 156
156 eggs   remaining 35 % --> 84 eggs (7 dozens ) --> answer
Answer: C
A candy company sells premium chocolate at $5 per pound and regular chocolate at $2 per pound in increment of whole pound only.If Barrett buys a pack of candies which costs him $31, how many pounds of premium chocolates are in the box?  Choose the correct choice:	A) [A] 1	B) [B] 2	C) [C] 3	D) [D] 4	E) [E] 5

Solution: This question is a bit of Special equations with a single set of unique values.   the Equation stands : 5X + 2Y = 31   Subtract multiple of 5 from 31 and check whether the remaining total is divisible by 4   31 - 5= 
31 - 5 = 26
26 -> Not divisible by 4   31 - 10= 
31 - 10 = 21
21 -> Not divisible by 4   31 - 15= 
31 - 15 = 16
16 -> Divisible by 4   31 - 20= 
31 - 20 = 11
11 -> Not divisible by 4   31 - 25= 
31 - 25 = 6
6 -> Not divisible by 4   31 - 30= 
31 - 30 = 1
1 -> Not divisible by 4   Any multiple of 5 hereon will give a negative value for regular chocolates bought and hence, inadmissible   Thus Amount spent on regular chocolate= $16   Amount spent on Premium chocolate= $15   Price per premium chocolate = $5   No. Of boxes of premium chocolate bought = 10 / 5= 
10 / 5 = 2
2   Correct Option : [B] 2
Answer: B
A company, Chauncy Co., has an annual travel budget of $50,000. The accounting department estimates that transportation expenses will increase 5 percent in the coming year, and nontransportation travel expenses will increase by 15 percent in the coming year. Last year, Chauncy Co. spent $19,500 on transportation-related expenses, and $35,000 on nontransportation travel expenses. If the annual travel budget does not increase this year, and if the accounting department’s estimates are correct, how far over the annual travel budget will expenses be this year? Choose the correct choice from the following:  A) Expenses will not go over the budget.  B) $500  C) $4,225  D) $5,725  E) $10,725

Solution: annual travel budget of $50,000   Let, Transportation expenses = T = 19500   and Non-Transportation expenses = N=35000   i.e. Increased Transportation expenses = 1.05T = 20475   and Increased Non-Transportation expenses = 1.15N = 40250   Total $10,725xpense = 20475+40250= 
20475+40250 = 60_725
60725   $10,725xpense over Budget= Budget - expense = 50000-60725 = 10725   Answer: Option $10,725
Answer: E
The cost of an item is Rs 12.60. If the profit is 10% over selling price what is the selling price ?	Select the correct option: A) 13 rupees B) 17 rupees C) 16 rupees D) 15 rupees E) 14 rupees

Solution: C.P+PROFIT=S.P   given,   PROFIT=10*S.P/100   so, S.P=12.60+10*S.P/100   90*S.P=1260   S.P=14 rupees   ANSW14 rupeesR:14 rupees
Answer: E
A vendor bough toffees at 6 for a rupee. how many for a rupee must he sell to gain 20%?  Choose the correct choice from the following choices
A) 3  B) 8  C) 5  D) 9  E) 1

Solution: C.P or toffees = Rs.1, S.P of 6 toffee = 120% of Rs.1 = Rs.6/5   for Rs. 6/5, toffees sold=6, for Rs.1, toffees sold= (6*5/6)= 
(6*5/6) = 5
5   5orrect answer (5)
Answer: C
Each month a retailer sells 100 identical items. On each item he makes a profit of $30 that constitutes 10% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?	Choose the correct choice: A) 191 B) 213 C) 221 D) 223 E) 226

Solution: For this question, we'll need the following formula:   Sell Price = Cost + Profit   We're told that the profit on 1 item is $20 and that this represents 10% of the cost:   Sell Price = Cost + $30   Sell Price = $300 + $30   Thus, the Sell Price is $330 for each item. Selling all 100 items gives the retailer...   100($30) = $2,000 of profit   If the retailer offers a 5% discount on the sell price, then the equation changes...   5%(330) = $16.5 discount   $313.5 = $300 + $13.5   Now, the retailer makes a profit of just $13.5 per item sold.   To earn $2,000 in profit, the retailer must sell....   $13.5(X) = $2,000   X = 2,000/13.5   X = 222.222222 items   You'll notice that this is not among the answer choices.... 221 and 223 are.   Selling 221 items would get us 9(221) = $1989 which is NOT enough money. To get back to AT LEAST $2,000, we need to sell 223 items.   Final Answer:   223
Answer: D
A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss?	Pick:
A) Rs. 20  B) Rs. 15  C) Rs. 22.50  D) Rs. 7.50  E) None of these

Solution: CP of 20 dozen of bananas = 15 * 20 = Rs. 300   Number of bananas which are rotten = 1/4 * 20= 
1/4 * 20 = 5
5 dozen.   SP of two-third of remaining bananas= (2/3 * 15) * 22.5 = Rs. 225   SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75.   SP of 1 dozen bananas = 75/5 = Rs. 15.   ANSWER:Rs. 15
Answer: B
A water tank, having the shape of a rectangular prism of base 100 square centimeters, is being filled at the rate of 1 liter per minute. Find the rate at which the height of the water in the water tank increases. Express your answer in centimeters per minute. Pick:
A) 40 cm/m  B) 15 cm/m  C) 10 cm/m  D) 35 cm/m  E) 20 cm/m

Solution: The volume of a rectangular prism is given by   area of base ? height   The rate at which the tank is being filled is 1 liter per minute which we need to convert   1 liter = 1 dm3   But 1 dm = 10 cm. Hence   1 liter = (10 cm)3 = 1000 cm3   The height h of the water is related to the volume by   volume = area of base ? h   In one minute the volume increases by 1 liter or 1000 cm3 and the height increases by   h = volume / area of base = 1000 cm3 / 100 cm2 = 10 cm   correct answer 10 cm/m
Answer: C
An error 4% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is	Choose the correct choice from the following choices:
A) 8.04% B) 8.14% C) 8.23% D) 8.16% E) 8.5%

Solution: 100 cm is read as 102 cm.   A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.   (A2 - A1) = [(104)2 - (100)2]   = (104 + 100) x (104 - 100)   = 816 cm2.   Percentage error = 8.16   8.16%
Answer: D
How much 60% of 50 is greater than 30% of 30?	Choose the correct choice from the following.
A) 21  B) 91  C) 11  D) 17  E) 12

Solution: (60/100) * 50 – (30/100) * 30   30 - 9= 
30 - 9 = 21
21   21nswer: 21
Answer: A
The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Choose the correct option:
A) 10 m
B) 16 m
C) 245 m
D) 19 m
E) 235 m

Solution: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30   = 25/2 => 2(140 + x) = 750 => x   = 235 m.   Answer: 235 m
Answer: E
2a
33
+ b9
____
99
If a and b represent positive single digits in the correctly worked computation above, what is the value of a + 3b ?
Choices
A) 2 B) 7 C) 9 D) 11 E) 12

Solution: Adding the digits in unit's place , a+ 3 + 9 = 19 (Since a and b are positive single digits )   => a = 7   Now adding the digits in ten's place , 2+ 3 + b + 1= 9 (1 has been carried over from nit's place addition)   => b= 3   a+3b = 2+2*3   =11   Answer 11
Answer: D
A goat is tied to one corner of a square plot of side 12m by a rope 7m long. Find the area it can graze?	Choose the correct choice from the following options: A) 32 B) 36.5 C) 38.5 D) 39 E) 39.5

Solution: Area covered by goat = Pi*r^2/4 ( here we divide by 4 because rope is tied at the corner of the plot and only 1/4 part , the goat can graze)   where r= 7 m = length of rope   So area = (22/7)*7*7/4= 
(22/7)*7*7/4 = 77/2 = around 38.5
38.5 sq m   answer :38.5
Answer: C
Find the constant k so that : -x2 - (k + 8)x - 8 = -(x - 2)(x - 4)  Select.
A) 11  B) 12  C) 14  D) 19  E) 15

Solution: -x2 - (k + 8)x - 8 = -(x - 2)(x - 4) : given   -x2 - (k + 8)x - 8 = -x2 + 6x - 8   -(k + 8) = 6 : two polynomials are equal if their corresponding coefficients are equal.   k = -14 : solve the above for k   correct answer 14
Answer: C
Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, his gain percent is?
Choose the correct choice from the following options:	A) 5 5/11%	B) 6%	C) 7%	D) 8%	E) 9%

Solution: Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.   Selling Price (S.P.) = Rs. 5800.   Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300.   Gain % = 300/5500 x 100	%	= 5	5/11	%   5 5/11%)
Answer: A
There are two concentric circles such that the area of the outer circle is four times the area of the inner circle. Let A, B and C be three distinct points on the perimeter of the outer circle such that AB and AC are tangents to the inner circle. If the area of the outer circle is 12 square centimetres then the area (in square centimetres) of the triangle ABC would be
Choose one:
A) π√​12 B) 9/π C) 9√3/π D) 6√3/π E) None of these

Solution: Explanation :   Outer circle:   Since πR² = 12, R = √(12/π) = 2√(3/π).   Inner circle:   Since the area is 1/4 the area of the outer circle, πr² = 3 and r = √(3/π)   AO is the Radius of the outer circle and OD is the radius of the inner circle.   A line tangent to a circle and a radius drawn to the point of tangency form a right angle.   Thus, ∆AOD is a right triangle.   Hypotenuse AO is twice the length of leg OD.   A right triangle whose hypotenuse is twice the length of a leg is a 30-60-90 triangle.   Thus, ∆AOD is a 30-60-90 triangle.   In a 30-60-90 triangle, the sides are proportioned x : x√3 : 2x.   Thus, AD = √3 * √(3/π) * = 3/√π.   Using the same reasoning for ∆OCD, we can deduce that CD = 3/√π.   Thus, AC = 2 * 3/√π = 6/√π.   The formula for the area of an equilateral triangle = (s²√3)/4.   Since AC = 6/√π, the area of ∆ABC = (6/√π)² * √3/4 = 36/π * √3/4 = (9√3)/π.   Answer : 9√3/π
Answer: C
Capacity of a cylindrical vessel is 25,872 litres. If the height of the cylinder is 200% more than the radius of its base, what is the area of the base in square cms?
Choose the correct choice.
A) 336
B) 1232
C) 616
D) 926
E) cannot be determined

Solution: let r be the radius   so height,h=r+(200% of r)=r+2r=3r   volume of cylinder=pi*r^2*h   or pi*r^2*3r=25872   or 22/7 *r^3=8624   or r^3=392*7=8*7*7*7   0r r=14   so area of base=22/7 *14*14= 
22/7 *14*14 = 616
616   ANSWER:616
Answer: C
Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?  Choose the correct choice from the following options.
A) 3	B) 4	C) 5	D) 6	E) 7

Solution: 2: 5: 13   2x 5x 13x   15 7.5 2.5   30x + 37.5x + 32.5x = 100x/20x   Average 30  + 37.5  + 32.5= 
30  + 37.5  + 32.5 = 100
100x/20x   Average = 5   Answer: 5100 /20= 
100 /20 = 5
5   Answer: 5
Answer: C
A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?	Choose one:
A) 22 1/7	B) 22 1/4	C) 22 1/2	D) 22 1/1	E) 22 1/3

Solution: 100 --- 10 DS = 10   ? ---- 1   75 ---- 15 US = 5   ? ----- 1 S = (10 - 5)/2   = 22 1/2 kmp Answer: 22 1/2
Answer: C
The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $9.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of x(2^1/2) - x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat? Choices:	A) $4.50	B) $5.10	C) $9.30	D) $5.50	E) $5.60

Solution: I Tried using Time/Rate approach:-   Initial Price Difference = 9.80 - 3.20= 
9.80 - 3.20 = 6.6
6.60   Price of $9.30orn increasing by 5x   Price of Wheat decreasing by x(1.4)-x= .4x   Since both the quantities are moving towards reducing the Price Gap hence:-   Relative Increase = 5x +.4x   Let T be the Time by which GAP is filled so,   6.6 = T(5.4x) -> T= (6.6)/5.4X   Final Price = 3.20 + 5X * T -> 3.20 + 5*6.6/5.4 = 9.3   Answer $9.30.
Answer: C
Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?
Select
A) 10.27 a.m
B) 10.15 a.m
C) 10.27 a.m
D) 10.55 a.m
E) 10.25 a.m

Solution: Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4= 
80 * 9/4 = 180
180 hrs.   Time taken to cover remaining distance= (350 - 180)/60 = 17/6 hrs   = 2 5/6 = 2 hrs 50 min   Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min.   So, Anna reached city A at 10.25 a.m.   Answer: 10.25 a.m
Answer: E
The marks obtained by Vijay and Amith are in the ratio 4:7 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?  Select: A) 6:8 B) 6:1 C) 6:5 D) 6:7 E) 6:3

Solution: 4:7   3:2   -------   12:21:14   12:14   6:7   Answer: 6:7
Answer: D
If each of 4 subsidiaries of Corporation R has been granted a line of credit of $791,000 and each of the other 3 subsidiaries of Corporation R has been granted a line of credit of $112,000, what is the average (arithmetic mean) line of credit granted to a subsidiary of Corporation R?  Pick one
A) $500,000  B) $448,000  C) $406,000  D) $313,600  E) $116,000

Solution: My take is A.   (791000*4 + 112000*3)/7= 
(791000*4 + 112000*3)/7 = 500_000
500000
Answer: A
A sporting goods store sold 64 Frisbees in one week, some for $3 and the rest for $4 each. If receipts from Frisbee sales for the week totaled $200, what is the fewest number of $4 Frisbees that could have been sold?  Choose the correct choice from the following options: A) 24 B) 8 C) 12 D) 4 E) 2

Solution: In this question however, because we are told that exactly 64 Frisbees have been sold and revenue was exactly $204, there is only one possible solution for the number of $3 and $4 Frisbees sold.   To solve, we have 2 equations and 2 unknowns   Let x = number of $3 Frisbees sold   Let y = number of $4 Frisbees sold   x + y = 64   3x + 4y = 200   x = 64 - y   3(64-y) + 4y = 200   192 - 3y + 4y = 200   y = 8   Answer: 8
Answer: B
If x is an integer and 2.13 × 10^x is less than 2100, what is the greatest possible value for x?
Choose the correct answer
A) 2  B) 6  C) 5  D) 4  E) 3

Solution: If x=3   2.13 × 10^3 = 2130 > 2,100   So, x = 2   2nswer : 2
Answer: A
k = 2^n + 8, where n is an integer greater than 1. If k is divisible by 9, which of the following MUST be divisible by 9?
Answers:
A) 2^n - 8  B) 2^n - 2  C) 2^n  D) 2^n + 4  E) 2^n + 5

Solution: Given: k, M and N are integers   If k is a divisor of both N and M, then k is a divisor of N+M (and N–M and M–N)   We're told that 9 is a divisor of 2^n + 8   We also know that 9 is a divisor of9.   So, applying the above rule, 9 is a divisor of 2^n + 8 +9, and 9 is a divisor of 2^n + 8 -9=2^n -1   2^n + 4
Answer: D
How many positive integers less than 30 have no common prime factor with 30?	Select the correct option
A) 5 B) 6 C) 7 D) 8 E) 9

Solution: 30=2*3*5. So, the number must be less than 30 and not have primes 2, 3, or 5.   This means that the number could be: 1, 7, 11, 13, 17, 19, 23, or 29. Total of 8 numbers.   Answer: 8.
Answer: D
Derek throws three dice in a special game. If he knows that he needs 15 or higher in this throw to win, then find the chance of his winning the game.
Choose the correct choice from the following answers
A) 5/54
B) 13/115
C) 20/145
D) 6/54
E) 90/155

Solution: Total cases = 6*6*6= 
6*6*6 = 216
216   n(X)/n(S)=20/216 = > 5/54   5/54NSWER 5/54
Answer: A
A person travelled from his house to office at 30km/hr and office to house at 70km/hr. Then find the average speed?
Choose the correct choice from the following answers.
A) 30km/hr  B) 40km/hr  C) 42km/hr  D) 50km/hr  E) 62km/hr

Solution: Average speed = (2*30*70)/(30+70)= 
(2*30*70)/(30+70) = 42
42km/hrAnswer is 42km/hr
Answer: C
The mass of 1 cubic meter of a substance is 200 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (1 kg =1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)	Choose the correct choice from the following choices
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: 200 kg - 1 cubic meter;   200,000 g - 1 cubic meter;   200,000 g - 1,000,000 cubic centimeters;   1 g - 1,000,000/200,000 = 10/2= 
10/2 = 5
5 cubic centimeters.   Answer: 5.
Answer: E