MU-NLPC/Calc-aqua_rat huggingface dataset:
When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 4 times, what is the probability that it will land on the same side each time?
Choose the correct choice from the following answers:
A) 1/8	B) 1/4	C) 1/16	D) 1/2	E) 1/32

Solution: Must be either 4 tails or 4 heads   1/2*1/2*1/2*1/2+1/2*1/2*1/2*1/2   1/16 + 1/16 = 1/8   1/8nswer: 1/8
Answer: A
The length of the longest rod that can fit in a cubical room of 4 m side is? Choose the correct choice from the following answers
A) 100%	B) 108%	C) 120%	D) 110%	E) 101%

Solution: 100%   100%nswer:100%
Answer: A
A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400?	Choose the correct choice from the following options
A) 2998	B) 1900	C) 2788	D) 2662	E) 1122

Solution: 65 * 6 : 84 * 5 : 100 * 3   26:28:20   C share = 74000 * 95/100 = 7030 * 20/74= 
7030 * 20/74 = 1_900
> 1900   Answer:1900
Answer: B
In the coordinate plane, points (x, 2) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =  Pick:
A) 4.5  B) 7  C) 9  D) 11  E) 12

Solution: Line k passes through the origin and has slope 1/2 means that its equation is y=1/2*x.   Thus: (x, 2)=(4, 2) and (10, y) = (10,5) --> 4+5=2+5=9.   Answer: 9.
Answer: C
Rani bought more apples than oranges. She sells apples at ₹23 apiece and makes 15% profit. She sells oranges at ₹10 apiece and makes 25% profit. If she gets ₹653 after selling all the apples and oranges, find her profit percentage X.
Pick one:
A) 16.8% B) 17.4% C) 17.9% D) 18.5% E) 19.1%

Solution: Given: Selling price of an Apple = 23 --> Cost price = 23/1.15= 
23/1.15 = 20
20   Selling price of an orange= 10 --> Cost price = 10/1.25= 
10/1.25 = 8
8   A > O   23*(A) + 10*(O)= 653   653 - 23*(A) has to be divisible by 10 --> Units digit has to be 0   Values of A can be 1, 11, 21, 31, .... --> 1 cannot be the value   17.4%etween 11 and 21, If A = 11, O = 30 --> Not possible   If A = 21, O = 17 --> Possible   Cost price = 20*21 + 8*17 = 420 + 136= 
420 + 136 = 556
556   Profit= 653 - 556= 
653 - 556 = 97
97   Profit% X= (97/556)*100 = 17.4%   Answer: 17.4%
Answer: B
Leo has an average price of Rs.57 on every item in his shopping cart. At the last minute he decided to get rid of apple juice worth Rs. 80 and get orange juice worth Rs. 60. If his shopping cart has 4 items, what is his new average?	Choices.
A) 48 B) 52 C) 56 D) 57 E) 60

Solution: Sum of prices of items before replacement= 57x4=228   Sum of ages of employees after replacement=(57x4)+60-80=208   The new average age=208/4= 
208/4 = 52
52   Answer: 52
Answer: B
Find the value of y from (12)^3 x 6^4 ÷ 432 = y?	Pick.
A) 2356 B) 3467 C) 4567 D) 5189 E) 5184

Solution: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184   432 12 x 62   5184
Answer: E
If in the word 'DISTURBANCE', the first letter is interchanged with the last letter, the second letter is interchanged with the tenth letter and so on, which letter would come after the letter T in the newly formed word ?
Choose the correct choice
A) S  B) C  C) T  D) R  E) U

Solution: The new letter sequence is E C N S B R U T S I D   Clearly, S comes after T   SNSWER S
Answer: A
A person travels 12 km in the southward direction and then travels 5km to the right and then travels 15km toward the right and
finally travels 5km towards the east, how far is he from his starting place?  Select.
A) 5.5 kms B) 3 km C) 13 km D) 6.4 km E) 7.4 km

Solution: 12 km south then 5km right means in west direction again he moves 15 km towards right means north direction then he moves 5 km east....In this 5km in both east &west directions will cancel with each other.Remaining is in north and south directions,as he moves 15km,12km in the respective directions.The distance  (15-12)= 
 (15-12) = 3
3km   ANSWER:3 km
Answer: B
Company A imported 10,500 widgets made of either brass or aluminum. The widgets are painted blue, red or green. If 10 percent of the widgets are made of brass and of those 20 percent are painted red and 40 percent are painted blue how many brass widgets painted green were imported?  Pick
A) 480  B) 840  C) 1050  D) 420  E) 2100

Solution: Answer A.   We are told that 10% of all imported widgets are made of brass and of those, 20% are red and 40% are blue. Since we know that there are only three colors, the remaining 40% must be green. 40% blue of 10% brass widgets leads to 4% green brass widgets out of the total 10,550 widgets.   10,500 /100 * 4 = 420.   Answer 420.
Answer: D
A farmer has a field that measures 1000 ft wide by 2000 ft long. There is an untillable strip 20 ft wide on the inside edge of the field, and a 30 ft wide untillable strip bisects the field into two squares (approximate). Approximately what percentage of the field is tillable?	Choose the correct choice.
A) 98%	B) 93%	C) 91%	D) 90%	E) 88%

Solution: Total Area = 1000*2000   Tillable Square's side horizontally = (2000-20-30-20)/2 = 1930/2= 
1930/2 = 965
965   Tillable Square's side vertically= (1000-20-20)= 
(1000-20-20) = 960
960= 960   Consider it as 960:   Why approximated to 93 and not 91 because we shortened one side from 965 to 960. Thus, in reality the squares are bigger.   Ans: "93%"
Answer: B
Rectangle ABCD is constructed in the coordinate plane parallel to the x- and y-axes. If the x- and y-coordinates of each of the points are integers which satisfy 6 ≤ x ≤ 11 and -5 ≤ y ≤ 5, how many possible ways are there to construct rectangle ABCD?
Choose the correct choice from the following answers:
A) 396
B) 1260
C) 825
D) 7920
E) 15840

Solution: As the rectangle is parallel to coordinate axes, the coordinates of the points of the rectangle would be   (X1, Y1), (X2, Y1), (X2, Y2), (X1,Y2)   given that X1, X2 lie between 6 and 11..ie., 6 possible numbers   Possible combinations for X1,X2 would be 6C2 = 15   Similarly, Possible combinations for Y1, Y2 would be 11C2 = 55   Possible ways of constructing rectangle is by selecting any of the combination of X1,X2 and Y1,Y2   = 15 * 55= 
15 * 55 = 825
825   Ans. 825
Answer: C
A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?  Choose the correct choice:
A) 110 B) 140 C) 250 D) 987 E) 165

Solution: Explanation:   Total number of persons in the committee = 5 + 6= 
5 + 6 = 11
11   Number of ways of selecting group of eight persons= 11C8 = 11C3= (11 * 10 * 9)/(3 * 2)= 
(11 * 10 * 9)/(3 * 2) = 165
165 ways.   Answer: 165
Answer: E
Two clocks were set right at noon on Sunday. One gains 2 min and the other loses 3 min in 24 hours. What will be the true time when the first clock indicates 3 pm on Wednesday?
Choose the correct choice from the following choices:
A) 2 : 38 pm
B) 2 : 54 pm
C) 2 : 23 pm
D) 2 : 48 pm
E) None of these

Solution: Time from noon on Sunday to 3 pm on Wednesday = 75 hours.   24 hours 2 minutes of the first clock = 24 hours of the correct one.   ⇒ 1 hour of the first clock = 24 × (30/721) hours of correct one.   ⇒ 75 ours of the first clock   = 24 × 30 × (75/721) hours of correct one   = 54000/721 hours = 74 hours 53.7 min.   Hence the answer is 2 : 54 pm.   Answer 2 : 54 pm
Answer: B
For each of her sales, a saleswoman receives a commission equal to 20 percent of the first $500 of the total amount of the sale, plus 25 percent of the total amount in excess of $500. If the total amount of one of her sales was $800, the saleswoman’s commission was approximately what percent of the total amount of the sale?  Options
A) 22% B) 24% C) 25% D) 27% E) 28%

Solution: Total sales =800   Comission = (20/100)*500+ (25/100)*300   =100 + 75= 
100 + 75 = 175
175   %Comission=(175/800)*100=21.8~ 22%   22%nswer is 22%
Answer: A
In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
Choose the correct answer:  A) 54000  B) 50400  C) 40500  D) 45000  E) None of them

Solution: In the word 'CORPORATION', we treat the vowels OOAIO as one letter.   Thus, we have CRPRTN (OOAIO).   This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.   Number of ways arranging these letters = 7!/2! = 2520.   Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged   in 5!/3!= 20 ways.   Required number of ways = (2520 x 20) = 50400.   Answer is 50400.
Answer: B
The diagonals of a rhombus are 12 cm and 20 cm. Find its area?  Select the correct option.
A) 176 B) 186 C) 120 D) 179 E) 172

Solution: 1/2 * 12 * 20= 
1/2 * 12 * 20 = 120
120   Answer:120
Answer: C
99,997^2 - 3^2 =
Answers:
A) 10^10 - 2
B) (10^5 – 2)^2
C) 10^4(10^5 – 2)
D) 10^5(10^5 – 6)
E) 10^5(10^5 – 2)

Solution: (99,997)^2 - (3)^2 = (100,000 -3)^2 - (3)^2 = (100,000)^2 - 2*3*100,000 + 3^2-3^2=(10^5)^2 - 2*3*(10^5) = 10^10 - 6*(10^5)=10^5(10^5 - 6) Answer 10^5(10^5 – 6)
Answer: D
The average of first 10 prime numbers is?	Options.
A) 10.11  B) 12.9  C) 12.11  D) 13.11  E) 14.11

Solution: Sum of 10 prime no. = 129   Average = 129/10= 
129/10 = 129/10 = around 12.9
12.9   Answer : 12.9
Answer: B
Set A contains four different positive odd integers and six different positive even integers. Set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even? Choose the most appropriate option: A) 3/5 B) 4/5 C) 17/25 D) 21/25 E) 43/50

Solution: There can be an odd product only if both integers are odd.   P(odd product) = 4/10*2/5 = 4/25   P(even product) = 1 - 4/25 = 21/25   The answer is 21/25.
Answer: D
A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?  Choose the correct choice:	A) 150 m	B) 165 m	C) 155 m	D) 160 m	E) 170 m

Solution: Length of the train be ‘X’   X + 150/15 = X + 250/20   4X + 600 = 3X + 750   X = 150m   150 mNSWER:150 m
Answer: A
The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 216 metres, what is its area?  Select the correct option
A) 1325 sq.metres B) 1260 sq.metres C) 2835 sq.metres D) 3380 sq.metres E) None of these

Solution: Let the length and breadth be 7x and 5x respectively.   Then, P = 2(7x + 5x) = 216 â‡’ x = 9   Area = 7 Ã— 9 Ã— 5 Ã— 9 = 2835 sq.m.   Answer 2835 sq.metres
Answer: C
A boy was asked to find 7/9 of x. But he divided the x by 7/9, Thus he got 32more thanthe answer. Find the x.	Choose one
A) 43	B) 45	C) 59	D) 63	E) 65

Solution: x/7/9 = 9x/7 = 32 + y   Actualy he should do 7x/9 = y   y = (9x/7) - 32   y = (9x - 224)/7   (9x - 224)/7 = 7x/9   81x - 2016 = 49x   81x - 49x = 2016   32x = 2016   x = 63   63
Answer: D
A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 20 inches. Find b.	Pick one:  A) 8  B) 16  C) 4  D) 32  E) 48

Solution: From the info that the maximum sides of the cubes is 4, we know that the GCF of 12 (=2^2*3) andbis 4 (=2^2), sob=2^x, where x>=2.   From the second premise, we know that the LCM of 12 (2^2*3) andbis 20 (2^2*5), sob=2^2 or 2^2*5(4 or 20).   4ombining 2 premises shows the answer is 4(4).
Answer: C
On the xy-coordinate plane, point A lies on the y-axis and point B lies on the x-axis. Points A, B, and C form a right triangle with a 90-degree angle at point C and the triangle has an area of 30. If AC is parallel to the x-axis, and BC is parallel to the y-axis, which of the following could be the coordinates of point C?  Choose the most appropriate option
A) (2, 25)  B) (4, -15)  C) (3, -24)  D) (-2, 16)  E) (-6, -12)

Solution: The area of the triangle formed will be:   1/2 * base * height =   1/2 * |(X-coordinate of point C)| * |(Y-coordinate of point C)| = 30   Thus |product of coordinates of point C| = 60   The answer is (4, -15).
Answer: B
A boat crossed a lake from North to East at the speed of 10 km/h, entered a river and covered twice as much distance going upstream at 9 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.8 km/h that day, what was its approximate downstream speed?	Choose the correct option.
A) 4	B) 5	C) 6	D) 7	E) 11

Solution: One way of solving this is:   Speed of boat on still water (lake)=10kmph   Speed upstream = 9kmph = speed in still water - speed of river => speed of river = 1kmph   =>Speed downstream = speed in still water + speed of river = 10+1= 
10+1 = 11
11kmph   Ans is 11
Answer: E
From the set of numbers x, y, t, z, p, q, r and w, how many different combinations can we have without the t,p,q and r in them? Ex:. (x,y), (x), (w,z,y,x), etc and (x,y)=(y,x)	Choose the correct choice from the following options
A) 10 B) 12 C) 15 D) 16 E) 30

Solution: Another way: Any letter (x, y, z, w) can be included or not. So, we have 2^4 combinations - 4 empty combination = 12 combinations   12
Answer: B
If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 50/r years. If Luke's parents invested $13,500 in a long term bond that pays 12 percent interest compounded annually, what will be the approximate total amount of the investment 12 years later, when Luke is ready for college?	Choose the correct choice from the following answers
A) 62,000
B) 85,500
C) 95,500
D) 100,500
E) 100,000

Solution: Answer equals D in 48 years. I thought by 50th year it would reach 100,500. Options should have been separated more widely for clarity.
Answer: D
A man can row with a speed of 25 kmph in still water. If the stream flows at 15 kmph, then the speed in downstream is?	Pick.
A) A)35 B) B)38 C) C)30 D) D)40 E) E)45

Solution: M = 25   S = 15   40S = 25 + 15= 
25 + 15 = 40
40   Answer:40
Answer: D
Starting with 0, a mathematician labels every non-negative integer as one of five types: alpha, beta, gamma, delta, or epsilon, in that repeating order as the integers increase. For instance, the integer 8 is labeled delta. What is the label on an integer that is the sum of an alpha raised to the seventh power and a beta raised to the seventh power?	Choose the correct choice:
A) alpha  B) beta  C) gamma  D) delta  E) epsilon

Solution: Let the alpha be 5k and let the beta be 5j+1.   (5k)^7 + (5j+1)^7 which has the form 5k+1, which is a beta.   The answer is beta.
Answer: B
The denominator of a fraction is 3 more than the numerator. If the numerator as well as the denominator is increased by 4, the fraction becomes 4/5. What was the original fraction ? Options.
A) 8/19  B) 8/11  C) 8/12  D) 8/99  E) 8/17

Solution: Explanation:   Let the numerator be x Then, denominator = x + 3.   Now. (x + 4)/(x + 3) +4 = 4/5 <=> 5 (x + 4) = 4(x + 7)   => x = 8.   The fraction is 8/11.   Answer: 8/11) 8/11
Answer: B
There are four inns in a town. If 3 men check into the inns in a day, then what is the probability that each checks into a different inn?
Choices.
A) 1/6	B) 2/8	C) 3/8	D) 2/3	E) 4/3

Solution: Total ways for the 3 men to check into the inns = 4³ ways.   The number of cases where 3 men are checking in different inns = 4 x 3 x 2 = 24 ways.   Therefore, the required probability = 24/4³ = 3/8.   ANSWER:3/8
Answer: C
If Finn was 18 months old one year ago, how old was he, in months, x months ago?  Choose the correct choice from the following answers
A) x − 30  B) x − 12  C) 18 − x  D) 24 − x  E) 30 − x

Solution: Age Today = 18 months + 12 months (1year) = 30 months   X months ago- Today's Age - X = 30 - X   Ans- 30 − x
Answer: E
$350 is divided among A, B, and C so that A receives half as much as B, and B receives half as much as C. How much money is C's share? Select
A) $200 B) $225 C) $250 D) $275 E) $300

Solution: Let the shares for A, B, and C be x, 2x, and 4x respectively.   7x = 350   x = 50   4x = 200   The answer is $250.
Answer: C
A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?	Choose the correct option:
A) 2400  B) 2828  C) 1208  D) 1272  E) 1292

Solution: Explanation:   1200 * 12: x * 9 = 2:3   x = 2400   2400nswer:2400
Answer: A
here's an easy question of averages, but let's try to see innovative ways of solving this.
A class has 12 boys and x girls. Average score of boys and girls is 79 and 92 respectively. the average of the whole class is 86, what is the value of x?  Choose the correct choice from the following options:	A) a) 14	B) b) 7	C) c) 8	D) d) 10	E) e) 12

Solution: 12(79)+92x/12+x=86   948+92x/12+x=86   948+92x=86(12+x)   948+92x=1032+86x   X's one side, numbers one side we get,   92x - 86x=1032-948   6x=84   hence, x=14   a) 14nswer a) 14
Answer: A
If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 5 years would be
Choose the correct choice from the following options
A) (1.5)^4
B) (1.05)^5
C) (1.05)^4
D) 1 + (0.05)^4
E) 1 + 4(0.05)

Solution: In this prompt, the answer choices show that we don't actually have to calculate anything - we just need to 'format' the calculation correctly. We're told that the interest is COMPOUNDED ANNUALLY, so we need the Compound Interest Formula, with a Principal of $1, an R of 5% (which would 'translate' as .05) and a T of . We'd have....   Answer :(1.05)^5
Answer: B
Diesel costs Rs.4 per lit and petrol costs 4.63 per litre. If the price of diesel rise by 10% a month and the price of petrol is unchanged.How many months will it take until a litre of Diesel costs more than a litre of petrol. Choose the correct choice from the following options:
A) 9 months  B) 5 months  C) 6 months  D) 3 months  E) 2 months

Solution: 2 monthsxplanation :   =>In the First Month the price of the diesel would be 4*110/100= 
4*110/100 = 22/5 = around 4.4
4.4=>In the Second Month the price of the diesel would be 4.4*110/100= 
4.4*110/100 = 4.84
4.84 which is higher than the   price of the petrol!   Answer : 2 months
Answer: E
Each child has 2 pencils and 13 Skittles. If there are 9 children, how many pencils are there in total? Answers.
A) 16
B) 12
C) 18
D) 22
E) 08

Solution: 2*9= 
2*9 = 18
18.Answer is 18.
Answer: C
Of 70 players on a football team, 49 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?  Choose the correct choice from the following options
A) 54 B) 59 C) 63 D) 71 E) 92

Solution: Total = 70   Thrower = 49   Rest = 70 - 49= 
70 - 49 = 21
21   Left Handed= 21/3= 
21/3 = 7
7   Right handed= 14   If all Thrower are right handed then total right handed is   49 + 14= 
  49 + 14 = 63
63   so C. 63 is the right answer
Answer: C
When n is divided by 13, the remainder is 6. When n is divided by 11, the quotient is equal to Z, and the remainder is equal to 6. Z must be divisible by which of the following numbers?	Choose the correct choice from the following answers:	A) 13	B) 14	C) 15	D) 16	E) 17

Solution: N = 139 q + 6   N = 11 z + 6   Equating   13Q + 6= 11z+6   11z=193   11z/13 = q   since q is an integer Z must be divisible by 19.   Hence 13
Answer: A
A woman has 4 shirts, 5 pants and 2 belts. How many different clothing combinations can she wear? Pick:
A) 11	B) 20	C) 40	D) 60	E) 4

Solution: 4 shirts x 5 pants x 2 belts = 40   Answer: 40
Answer: C
if bell rang at a difference of 6,8,12,18,45 sec. respectively.if they start ranging together at 8'o clock morning.then at what time they rang together?  Options
A) 3 minute	B) 6 minute	C) 15/2 minute	D) 1 min. 19 sec.	E) none of the above

Solution: l.c.m {6,8,12,18,45}   =360 sec=6 min   answer 6 minute
Answer: B
A certain car uses 12 gallons of gasoline in traveling 420 miles. In order for the car to travel the same distance using 10 gallons of gasoline, by how many miles per gallon must the car’s gas mileage be increased?  Choose the correct answer
A) 2
B) 4
C) 6
D) 7
E) 10

Solution: 420/10= 
420/10 = 42
42 The difference is  42 - 35= 
 42 - 35 = 7
7.   Answer 7
Answer: D
There are 18 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes?  Choose the correct choice from the following choices:	A) 21	B) 24	C) 27	D) 45	E) 54

Solution: Note that each handshake includes two people.   The total number of handshakes is  18*3/2= 
 18*3/2 = 27
27   The answer is 27.
Answer: C
We have 9 people and 6 chairs. In how many ways chairs can be occupy? Choose the correct choice from the following options.
A) 3258
B) 3215
C) 5000
D) 4200
E) 3024

Solution: no. of ways they can be occupy = 9*8*7*6= 
9*8*7*6 = 3_024
3024   Answer is 3024
Answer: E
Suppose a car can run on ethanol and gas and you have a 15 gallons tank to fill. You can buy fuel that is either 30 percent ethanol or 80 percent ethanol. How much of each type of fuel should you mix so that the mixture is 40 percent ethanol?  Choose one
A) 11	B) 12	C) 13	D) 14	E) 15

Solution: Le x represent number of gallons of gas that contain 30 percent ethanol   Let 15 - x be number of gallons of gas that contain 80 percent ethanol   Since the mixture contains 40 percent ethanol, only 40% of the 15 gallons will be ethanol   40% of 15 = (40/100) times 15 = (40/100) times 15/1 = (40 × 15) / (100 × 1) = 600 / 100= 
600 / 100 = 6
6   In order for x gallons of gas to contain 30% ethanol, we must take 30% of x or 30% times x   In order for 15 - x gallons of gas to contain 80% ethanol, we must take 80% of 15 - x or 80% times 15 - x   0.30 × x + 0.80 × (15 - x)= 6   0.30x + 0.80 × 15 - 0.80 × x = 6   0.30x + 12 - 0.80x = 6   0.30x - 0.80x + 12 = 6   -0.50x + 12 = 6   -0.50x = -6   x = 12   So 12 gallons of gass contain 30 percent ethanol and 15 - 12= 
15 - 12 = 3
3 gallons contain 80 percent ethanol   Therefore, mix 12 gallons of a 30% ethanol with 3 gallons of an 80% ethanol   Answer 12
Answer: B
A dog is tied to a tree by a long nylon cord. If the dog runs from the due North side of the tree to the due South side of the tree with the cord extended to its full length at all items, and the dog ran approximately 30 feet, what was the approximate length of the nylon cord S, in feet?	Choose the correct answer.
A) 30
B) 25
C) 15
D) 10
E) 5

Solution: Because the cord was extended to its full length at all items, the dog ran along a semi-circular path, from north to south.   The circumference of a full circle is 2*pi*r, but since we only care about the length of half the circle, the semi-circle path is pi*r.   S=pi*r = 30. Round pi = 3, then r = 10.   Chord is about 10 feet long.10
Answer: D
A person can swim in still water at 6 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 14km?  Choose one
A) 3.5
B) 4.5
C) 5
D) 9
E) 6

Solution: M = 6   S = 2   US = 6 - 2= 
6 - 2 = 4
4   D= 42   T = 14/4= 
14/4 = 7/2 = around 3.5
3.5   3.5nswer: 3.5
Answer: A
If positive integer k is divided by 10, the quotient is m and the remainder is 2, then which of the following must be true?
I. k + m is even
II. k cannot be a prime number
III. k is divisible by 4 Answers.
A) None
B) I
C) II
D) III
E) I and II only

Solution: k = 10m+2 = 2(5m+1)   I. k + m = 2(5m+1) + m => even if only m is even, however m can be odd => not always true   II. k can not be a prime: not always true:   m=0 => k=2 : a prime   III. not true if m is even   Nonens: none of the above
Answer: A