MU-NLPC/Calc-aqua_rat huggingface dataset:
The value of a bike depreciates at the rate of 25% every year. It was purchased 2 years ago. If its present value is Rs.4500 , its purchase price was
Choose the most appropriate option
A) 8000 B) 7500 C) 7000 D) 6500 E) 6000

Solution: Explanation:   = Rs.8000   8000nswer: 8000
Answer: A
Two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 4 seconds. The length of the faster train is
Choose the correct choice from the following answers.
A) 80 m B) 100 m C) 90 m D) 180 m E) None

Solution: Solution   Relative Speed	= (36 + 45) km/hr   = (81 x 5/18) m/sec   = (45/2) m/sec   Length of the train	= (45 / 2 x 4) m   = 90 m.   Answer 90 m
Answer: C
John and Peter are among the ten players a volleyball coach can choose from to field a six-player team. If all six players are chosen at random, what is the probability of choosing a team that includes John and Peter?	Choose the correct choice from the following options
A) 1/2	B) 1/3	C) 1/4	D) 2/5	E) 3/10

Solution: The total possible ways of selecting a 6-member team is 10C6 = 210   The possible ways which include John and Peter is 8C4 = 70   The probability of choosing both John and Peter is 70/210 = 1/3   The answer is 1/3.
Answer: B
A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.675 in all. Find the share of B?
Choose the correct answer
A) 186  B) 167  C) 168  D) 140  E) 177

Solution: A+B+C = 675   A = 3B   3B+B+B-25 = 675   5B = 700   B = 140   Answer: 140
Answer: D
Let's play a game. I have all the ten digits of numbers available. I use all the digits just once to create a number of ten digits. Can you find out what number I have in mind using the following clues?
One digit is divisible by 1.
Two digits are divisible by 2.
Three digits are divisible by 3.
Four digits are divisible by 4.
Five digits are divisible by 5.
Six digits are divisible by 6.
Seven digits are divisible by 7.
Eight digits are divisible by 8.
Nine digits are divisible by 9.
Ten digits are divisible by 10.	Choose the correct choice from the following options:  A) 3816547290  B) 3816557290  C) 3816547280  D) 3813547290  E) 3816147290

Solution: 3816547290   3816547290
Answer: A
In a birthday party, every person shakes hand with every other person. If there was a total of 28 handshakes in the party, how many persons were present in the party?
Choose the correct choice from the following options:
A) 5
B) 8
C) 1
D) 9
E) 7

Solution: Suppose there are nn persons present in a party and every person shakes hand with every other person. Then, total number of handshakes   = nC2=n(n−1)/2   n(n−1)=28×2n(n−1)=56   n=8   Ans: 8
Answer: B
A fence consists of m lengths of fence that are each n feet long. A fence post separates each length of fence by its width of x feet. What is the total length H of the fence including the fence posts on each end?
Choose the correct choice from the following:  A) mn  B) m(n + x)  C) H=m(n + x) + x  D) m(n + x) + 2x  E) 2mn

Solution: Notice that since a fence post separates each length of fence, then there will be m+1 posts, for example if there are m=2 fences, then there will be 3 posts: PFPFP. Thus the total length H of the posts is (m+1)x.   The total length of the fence is mn, therefore the total length of the fence including the fence posts on each end is (m+1)x+mn=mx+x+mn=m(n+x)+x.   Answer: H=m(n + x) + x.
Answer: C
A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year? Select:
A) 59099
B) 59009
C) 590055
D) 59000
E) 59001

Solution: Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.   Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.   Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)   Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.   Income of A = Twice the income of B   (2500 + 18000 + P) = 2(P)   P = 20500   Total profit = 2P + 18000   = 2*20500 + 18000= 
2*20500 + 18000 = 59_000
59000.Answer: 59000
Answer: D
If the first day of a year (other than leap year) was Sunday, then which was the last day of that year?  Choose the correct choice from the following answers:
A) Saturday B) Sunday C) Tuesday D) Monday E) None of these

Solution: Explanation :   Given that first day of a normal year was Sunday   Odd days of the mentioned year = 1 (Since it is an ordinary year)   Hence First day of the next year = (Sunday+ 1 Odd day) = Monday   Therefore, last day of the mentioned year = Sunday. Answer : Option Sunday
Answer: B
How many halves are there in three-fourth?	Choose the most appropriate option
A) 8.1	B) 12	C) 32	D) 7.3	E) 1.5

Solution: divide 3/4 by 1/2   =3/4÷1/2   =3/4*2/1   =6/4   =1.5.   Answer is 1.5.
Answer: E
in how many possible ways you can write 3240 as product of 3 positive integers a, b, c .	Choose the correct option.
A) 450 B) 420 C) 350 D) 320 E) 300

Solution: 3240 => 2^3 * 3^4 * 5^1   a => 2^x1 * 3^y1 * 5^z1   b => 2^x2 * 3^y2 * 5^z2   c => 2^x3 * 3^y3 * 5^z3   a * b * c = 3240   x1 + x2 + x3 = 3 => 5C2   y1 + y2 + y3 = 4 => 6C2   z1 + z2 + z3 = 1 => 3C2   5C2 * 6C2 * 3C2 = 10 * 15 * 3= 
10 * 15 * 3 = 450
450   450NSWER:450
Answer: A
How long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length? Choose the correct option:
A) 28  B) 27  C) 55  D) 18  E) 12

Solution: T = (660 + 165)/54 * 18/5= 
(660 + 165)/54 * 18/5 = 55
55   Answer: 55
Answer: C
A man swims downstream 90 km and upstream 55 km taking 5 hours each time; what is the speed of the current?  Choose one:
A) 3.8
B) 3.5
C) 3.3
D) 3.2
E) 1.6

Solution: 90 --- 5 DS = 18   ? ---- 1   55 ---- 5 US = 11   ? ---- 1 S = ?   S = (18 - 11)/2= 
(18 - 11)/2 = 7/2 = around 3.5
3.5   Answer: 3.5
Answer: B
A dog takes 2 leaps for every 3 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is : Choices.
A) 1:5
B) 2:5
C) 3:5
D) 4:5
E) 6:5

Solution: Explanation:   Dog : Hare = (2*3) leaps of hare : 3 leaps of hare = 6 : 5.   Answer: 6:5) 6:5
Answer: E
If 21 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect? Choose the correct answer.
A) 150  B) 170  C) 190  D) 210  E) 230

Solution: If two lines are not parallel, then they will intersect in exactly one point. Lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel. We are also given that no three lines are concurrent. This means that no three lines intersect at the same point. So every pair of two lines we select will have a unique point of intersection which they will not share with any third line.   The number of ways to select 2 lines from 21 lines is 21C2 = 210   The answer is 210.
Answer: D
What is the greatest prime factor of 7!6! + 6!5! ?
Choices
A) 17	B) 23	C) 37	D) 43	E) 53

Solution: 7!6! + 6!5! = 6!5!(7*6+1) = 6!*5!*43   The answer is 43.
Answer: D
A list of measurements in increasing order is 2, 5, 6, 8, 15 and x. If the median of these measurements is 3/4 times their arithmetic mean, what is the value of x?  Pick one:
A) 16  B) 18  C) 20  D) 22  E) 24

Solution: The median is (6+8)/2= 
(6+8)/2 = 7
7   The mean is (2+5+6+8+15+x)/6= (36+x)/6   (36+x) /6 * 3/4 = 7   x = 56-36= 
56-36 = 20
20   The answer is 20.
Answer: C
Can you find the last number in the below sequence
3 , 7 , 10 , 11 , 12 , 17 ?
Choose the correct choice:
A) 44
B) 55
C) 60
D) 40
E) 20

Solution: 20   20(Twenty) : when you write them , these are only numbers having vowel '20'
Answer: E
A and B complete a work in 5 days. A alone can do it in 10 days. If both together can do the work in how many days? Choose the most appropriate option:
A) 3.33 days	B) 3.99 days	C) 2.99 days	D) 2.98 days	E) 2.44 days

Solution: 1/5 + 1/10 = 3/10   10/3 = 3.33 days   3.33 daysnswer: 3.33 days
Answer: A
If n is a prime number greater than 5, what is the remainder when n^2 is divided by 12 ?
Choose the correct choice from the following:
A) 0  B) 1  C) 2  D) 3  E) 5

Solution: There are several algebraic ways to solve this question, but the easiest way is as follows:since we cannot have two correct answers just pick a prime greater than 5, square it and see what would be the remainder upon division of it by 12.   n=7 --> n^2=49--> remainder upon division 49 by 12 is 1.   Answer: 1.
Answer: B
A train 2000 m long can cross an electric pole in 25 sec and then find the speed of the train?  Choose the correct choice:
A) 322
B) 324
C) 326
D) 328
E) 330

Solution: Length = Speed * time   Speed = L/T   S = 2000/25= 
2000/25 = 80
80 M/Sec   Speed= 80*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 324 Kmph   Answer: 324
Answer: B
The average (arithmetic mean) of five numbers is 5. If 2 is subtracted from each of four of the numbers, what is the new average?	Pick.
A) 3.4 B) 4.5 C) 6.2 D) 5.7 E) 6.9

Solution: Let the numbers be a , b, c , d , e ,f   So, Total of these 5 numbers must be 25   Or, a + b + c + d + e = 25   So, 12 must be subtracted from the total sum   i.e a + b + c + d + e - 8   Or, 25 - 8 = 17   Hence average of the 5 numbers now is  17/5= 
 17/5 = 17/5 = around 3.4
>3.4   So, 3.4nswer will be 3.4
Answer: A
There are 13 boys and 10 girls in a class. If three students are selected at random, in how many ways that 1 girl or 2 boys are selected ? Answers.
A) 88 B) 90 C) 92 D) 96 E) 98

Solution: n(s) = sample space = 23C3 = 1771   E = event that 1 girl and 2 boys are selected   n(E) = we have to select 2 boys from 13 or 1 girl from 10   = 13C2 + 10C1   = 88   88ns - 88
Answer: A
When the no.7y86038 is exactly divisible by 11, then the smallest whole no.in place of y?	Choose the correct choice from the following choices:	A) 1	B) 3	C) 5	D) 7	E) 9

Solution: The given number =7y86038   Sum of the odd places =8+0+8+7= 
8+0+8+7 = 23
23   Sum of the even places= 3+6+y   (Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)   23-(9+y) = divisible by 11   14 � y = divisible by 11.   Y must be 3, to make given number divisible by 11.   3
Answer: B
In the xy plane line m has the equation 4x + y = u. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?
Choose one:  A) -4/3  B) 1/4  C) -4  D) 3/4  E) 4/3

Solution: The equation of line m is y=-4x+u. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x.   Point (r, r+1) lies on line n means that (r+1)=1/4*r --> r( +1)= 
( +1) = 1
1/4*r --> r=-4/3.   -4/3nswer: -4/3.
Answer: A
A car covers a certain distance at aspeed of 60 kmph in 4 hours. To cover the same distance in 2hr, it must travel at a speed of?
Pick.
A) 567 km/hr	B) 678 km/hr	C) 782 km/hr	D) 120 km/hr	E) 720 km/hr

Solution: Distance = (60 x 4) = 240 km.   Speed = 120 km/hristance/Time   Speed = 240/2= 
240/2 = 120
120 kmph   Answer : 120 km/hr
Answer: D
If integers a and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. ab + b^2
II. (a + b)^2
III. a + b Choose the correct choice:
A) I only
B) II only
C) III only
D) I and II only
E) I, II, and III

Solution: Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.   I. ab + b^2 --> if a=1 and b=2 then ab + b^2=6, which is a factor of 30. OK;   II. (a + b)^2 --> (a + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD;   III. a + b --> if a=1 and b=2 then a + b=3, which is a factor of 30. OK.   Answer: II only.
Answer: B
In how many ways can the letters of the word ASTERIX be arranged in a row so that the vowels appear in alphabetic order? Choose the correct choice from the following answers:  A) 800  B) 820  C) 880  D) 960  E) 840

Solution: three letters can be arranged in 3! ways.   only one combination AEI is required.   7 letters can be arranged in 7! ways.   thus 7!/ 3! * 1 = 840.
Answer: E
A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?  Choose the correct option: A) 1.9 B) 1.5 C) 1.4 D) 1.1 E) 1.6

Solution: 72 --- 9 DS = 8   ? ---- 1   45 ---- 9 US = 5   ? ---- 1 S = ?   S = (8 - 5)/2= 
(8 - 5)/2 = 3/2 = around 1.5
1.5   Answer: 1.5
Answer: B
Anand and Deepak started a business investing Rs. 1000 and Rs. 5000 respectively. Out of a total profit of Rs. 2000, Deepak's share is: Options
A) 3776 B) 1284.2 C) 8400 D) 1666.6 E) 1671.8

Solution: Ratio of their shares = 1000: 5000= 1:5   Deepak's share = 2000 * 5/6 = Rs. 1666.6.   Answer: 1666.6
Answer: D
power windows: 60%
anti-lock brakes: 25%
CD player: 75%
The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes?	Choose the correct answer:
A) 25  B) 18  C) 11  D) 38  E) 0

Solution: Answer: D   Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for.   If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a C38 player is 75%, we can set up the following equation:   75=15+22+x   x=38, choice38.
Answer: D
If 3/w + 3/x = 3/y and wx = y, then the average (arithmetic mean) of w and x is	Choose the correct choice from the following.
A) 1/2 B) 1 C) 2 D) 4 E) 8

Solution: Given: 3/w + 3/x = 3/ywx=y   Find: (w+x)/2 = ?   3(1/w + 1/x) = 3(1/y) - divide both sides by 3   (1/w + 1/x) = 1/y   (x+w)/wx = 1/wx - sub'd in y=wx   x+w - 1 = 0   x+w = 1   Therefore (w+x)/2 = 1/2   1/2ns: 1/2
Answer: A
Points A, B, and C lie, in that order, on a straight railroad track. The distance from point A to point B is twice the distance from point B to point C. A train traveled from point A to point C without stopping. The train's average speed when traveling from point A to point B was 50 miles per hour and the train's average speed when traveling from point B to point C was 25 miles per hour. What was the train's average speed, in miles per hour, when traveling from point A to point C? Options
A) 20 B) 25 C) 30 D) 35 E) 15

Solution: Average speed = distance/time   Because we are looking for average speed we can pick a distance for the variable d.   Speed A-B = 50   Speed B-C = 25   Average Speed = total distance/total rate   rate = distance/time   A====================B==========C   If A-B is twice the length of B-C then let A-B = 2d and let B-C = d   Average speed = 3d/(2d/50) + (d/25)   3d/(2d/50) + (2d/50)   3d/(4d/50)   150d/10d   Average speed = 15   ANSW15R: 15150 /10= 
150 /10 = 15
15   ANSW15R: 15
Answer: E
In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points P is in the same quadrant as the fourth vertex of the square?
Choose the correct option.
A) (-5, -3) B) (-5, 3) C) (5, -3) D) (3, -5) E) (3, 5)

Solution: The question:In the xy-plane, the points P=(c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points is in the same quadrant as the fourth vertex of the square?   I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means   Vertex #1 = (c, d) is in QII (that is, negative x and positive y)   Vertex #2 = (c, -d) is in QIII (that is, both xy negative)   Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive)   That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =(3, 5).
Answer: E
A certain shirt was marked down 10% the first week and another 20% the next week. What percent of the regular price was the final cost of the shirt after the two markdowns?
Choose one
A) 30%	B) 36%	C) 40%	D) 72%	E) 80%

Solution: If the price of the shirt is 100, and it is marked down by 10% and then 20% or charged 90% of the price first and 80% of the price of reduced price, the final price is :-   100*90*80/10000= 
100*90*80/10000 = 72
72   72% is the final price of old price.   72% is the answer
Answer: D
The average of 65 numbers is 40. If two numbers, 25 and 60 are discarded, then the average of the remaining numbers is nearly	Choose the correct choice.
A) 28.32  B) 39  C) 39.92  D) 29  E) 30

Solution: Explanation :   Total sum of 63 numbers = (65 * 40) - (25 + 60) = 2600 - 85= 
2600 - 85 = 2_515
2515   Average= 2515/63 = 39.92   Answer : 39.92
Answer: C
what will be the next number in the following series??
1,4...48,100,180,294  Choose the most appropriate option:
A) 32
B) 46
C) 24
D) 18
E) 30

Solution: 1x1x1=1;   2x2x1=4;   3x3x2=18;   4x4x3=48;   5x5x4=100;   6x6x5=180;   7x7x6=294;   so answer is 18.   ANSWER:18
Answer: D
The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 675 sq m, then what is the breadth of the rectangular plot?
Choose the correct choice from the following answers
A) 16 B) 17 C) 18 D) 15 E) 14

Solution: Let the breadth of the plot be b m.   Length of the plot = 3 b m   (3b)(b) = 675   3b2 = 675   b2 = 225   b = 15 m.   Answer: Option 15
Answer: D
50% of the apartments in a certain building have windows and hardwood floors. 25% of the apartments without windows have hardwood floors. If 40% of the apartments do not have hardwood floors, what V percent of the apartments with windows have hardwood floors? Choose the correct choice from the following choices.
A) 10 B) 16 2/3 C) 40 D) 50 E) 83 1/3

Solution: yup you need to construct a matrix   X********| Windows'|No Windows'''| total   hardFl****'|50*****''|10*********'|60   Not hardFl*|10******|30*********'|40   Total*****|60******'|40*********'|100   so V percent of the apartments with windows have hardwood floors = 50/60 *100   = 83 1/3   so 83 1/3 is the answer.[/u]
Answer: E
Sandy leaves her home and walks toward Ed's house. Two hours later, Ed leaves his home and walks toward Sandy's house. The distance between their homes is 52 kilometers, Sandy's walking speed is 6 km/h, and Ed's walking speed is 4 km/h. How many kilometers will Sandy walk before she meets Ed?	Choose the correct choice from the following answers
A) 33  B) 34  C) 35  D) 36  E) 37

Solution: Sandy walks 12 km in the first two hours so there are 40 km remaining.   When Ed starts walking, they complete a total of 10 km per hour.   They will meet four hours after Ed starts walking.   Since Sandy walks for 6 hours, she walks 36 km.   The answer is 36.
Answer: D
Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?	Choose one:
A) 17 1/9 min  B) 17 1/8 min  C) 17 1/7 min  D) 17 8/7 min  E) 17 3/7 min

Solution: 1/20 + 1/30 - 1/40   = 7/120   120/7 = 17 1/7   Answer:17 1/7 min
Answer: C
How much pure alcohol should be added to 400ml of a 15% solution to make the strength of solution 30%?  Choose the correct choice from the following choices
A) 100 ml	B) 60 ml	C) 120 ml	D) 130 ml	E) 150 ml

Solution: we can also go by answer choices   Tke 100 ml for eg   400 (old)+100 (new concentr)ml     500*30/100= 
  500*30/100 = 150
150 ml (50ml is de old concentration +100 ml (newly added)   Answer 150 ml
Answer: E
The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?
Choose the correct option.
A) 1/2  B) 3/4  C) 1/5  D) 3/5  E) 4/7

Solution: Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D   1 2 3 1 =iXiX71=4;   1 3 Required probability 3/4   3/4
Answer: B
A die is tossed. Find the probability of getting a multiple of 2 ? Pick one:
A) 1/5
B) 2/3
C) 1/6
D) 1/3
E) 1/2

Solution: S = {1,2,3,4,5,6}   1/2= event of getting a multiple of 2 = {2,4,6}   P(1/2) = 3/6 = 1/2   Answer is 1/2
Answer: E
A chair is bought for Rs.300/- and sold at a loss of 20% find its selling price Choose the correct choice from the following
A) Rs.500/-
B) Rs.510/-
C) Rs.515/-
D) Rs.230/-
E) Rs.240/-

Solution: Loss = 300*20/100= 
300*20/100 = 60
60   S.P= C.P - Loss   = 300- 60   =Rs.240/-   Answer :Rs.240/-
Answer: E
Solve 7y – 5 = 3y + 11  Choose the most appropriate option:
A) 4	B) 6(1/3)	C) 7(1/3)	D) 3	E) 9(1/3)

Solution: Sol.   7y – 5 = 3y + 11   => 7y – 3y = 11 + 5   => 4y = 16 => x = 4   4nswer 4
Answer: A
There were two candidates in an election. Winner candidate received 60% of votes and won the election by 240 votes. Find the number of votes casted to the winning candidate?	Select the correct option:
A) 228  B) 720  C) 255  D) 199  E) 231

Solution: W = 60% L = 40%   60% - 40% = 20%   20% -------- 240   60% -------- ?  60  - 40= 
 60  - 40 = 20
20%   20% -------- 240   60% -------- ?=> 720   Answer:720
Answer: B
Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?	Choose the most appropriate option.
A) 10 : 5 B) 15 : 2 C) 20 : 2 D) 25 : 2 E) None of thees

Solution: Explanation:   Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number.   US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2.   Now US : Indian = 25 : 10, and Indian : British = 10 : 2   Hence the two ratios can be combined and US : British = 25 : 2   Answer: 25 : 2
Answer: D
Two spherical balls lie on the ground touching. If one of the balls has a radius of 6 cm, and the point of contact is 10 cm above the ground, what is the radius of the other ball (in centimeters)?	Choose one.
A) 12 B) 16 C) 20 D) 24 E) 30

Solution: A straight line will join the two centers and the point of contact, thus making similar triangles.   4/6 = (r-10)/r   4r = 6r - 60   r = 30   The answer is 30.
Answer: E
Car X began traveling at an average speed of 35 miles per hour. After 36 minutes, car Y began traveling at an average speed of 38 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped? Choices
A) 105
B) 140
C) 175
D) 210
E) 245

Solution: In 36 minutes, car X travels 21 miles.   Car Y gains 3 miles each hour, so it takes 7 hours to catch car X.   In 7 hours, car X travels 245 miles.   The answer is 245.
Answer: E
If n ≠ 0, which of the following must be greater than n?
I. n^4
II. 2n
III. 2 - n
Pick one
A) I only	B) II only	C) I and II only	D) II and III only	E) None

Solution: n ≠ 0 => n = negative or n = positive   if n = negative:   2n < n (n = -1 then 2n = -2 => -2 < -1)   n^2 > n (n =-1 then n^2 = 1 => n^2 > n)   2 - n > n (n = -1 then 2--1 = 2+1= 
2+1 = 3
3=> 2-n > n)   but if n = positive:   n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II   2 - n < n(n =2 then 2-2= 
2-2 = 0
0)=> only I   =>answer is I only
Answer: A