MU-NLPC/Calc-aqua_rat huggingface dataset:
If 20! × 20!/20^n is an integer, what is the largest possible value of n?  Choose the correct answer:	A) 20	B) 16	C) 8	D) 4	E) 1

Solution: 20! × 20!/20^n is an integer.   Or 20! × 20!/(2^2n*5^n)   This means we need to find the power of 5 in the numerator. We can safely say that the number of powers of 5 will be lower than the number of powers of 4 in the numerator.   Largest power of 5 in 20! = [20/5] + [20/25] = 4   Since there are 2 20!'s, power of 4 in the numerator = 2*4= 
2*4 = 8
8   Hence the largest value of b for which 20! × 20!/20^n is integer= 8   ANSWER:8
Answer: C
If a, b, and c are consecutive even positive integers, which of the following could be equal to a + b + c ?  Pick one
A) 141	B) 200	C) 624	D) 391	E) 412

Solution: The key to answering this question quickly is to realize that a+b+c is a multiple of BOTH 2 and 3. With that information, you can quickly eliminate answer choices. If you don't recognize those two Number Properties though, then you can still get to the correct answer (but it will require a bit more work).   We're told that a, b and c are CONSECUTIVE EVEN INTEGERS, so we could write them algebraically as...   A + (A+2) + (A+4) = 3A + 6   We know that 3A + 6 COULD equal one of those five answers; we just have to find it...   Could 3A + 6 = 141   3A = 135   A = 45   This is NOT an EVEN INTEGER, so 141 is NOT the answer   Could 3A + 6 = 200   3A = 194   A = 64.6666   This is NOT an EVEN INTEGER, so 200 is NOT the answer   Could 3A + 6 = 624   3A =618   A = 206   This IS an EVEN INTEGER! The numbers would be 206, 208 and 210. This IS the answer   Final Answer:   624
Answer: C
If each edge of a cube is increased by 50%, find the percentage increase in Its surface area  Choose the correct answer:
A) 125%  B) 129%  C) 185%  D) 725%  E) 145%

Solution: Let the edge = a cm   So increase by 50 % = =   Total surface 125%rea of original cube =   TS125% of new cube =   ==   Increase in area = =   Increase % = = 125%   125%nswer: a
Answer: A
Find the least number which when divided by 5,6,7, and 8 leaves a remainder 3, but when divided by 9 leaves no remainder
Choose the most appropriate option.
A) 1683  B) 1684  C) 1685  D) 1582  E) 1584

Solution: Explanation :   L.C.M. of 5,6,7,8 = 840.   Required number is of the form 840k + 3   Least value of k for which (840k + 3) is divisible by 9 is k = 2.   Required number = (840 X 2 + 3)=1683   1683NSWER IS 1683
Answer: A
A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days of 7 hours each. How long will they take to do it, working together 8 hours a day?  Choose the correct choice
A) 4 days
B) 3 days
C) 7 days
D) 2 days
E) 9 days

Solution: Sol. A can complete the work in (7 x 9) = 63 hours.   B can complete the work in (6 x 7) = 42 hours.   A’s 1 hour's work = (1/63) and B's 1 hour's work =(1/42)   (A + B)'s 1 hour's work =(1/63)+(1/42)=(5/126)   Both will finish the work in (126/5) hrs.   Number of days. of (42/5) hrs each =(126 x 5)/(5 x 42)=3 days   Ans: 3 days
Answer: B
If the perimeter of a rectangular garden is 800 m, its length when its breadth is 100 m is?
Choose the correct choice from the following options:  A) 338 m  B) 300 m  C) 200 m  D) 276 m  E) 971 m

Solution: 2(l + 100)   = 800 => l   = 300 m   Answer:300 m
Answer: B
If a child walks at the rate of 5m/min from his home, he is 6 minutes late for school, if he walks at the rate of 7m/min he reaches half an hour earlier. How far is his school from his home ? Pick one:
A) 450 min
B) 540 min
C) 630 min
D) 360 min
E) none of these

Solution: Let the distance between home and school is x.   Let actual time to reach be t.   Thus, x/5 = t + 6 ---- (1)   and x/7 = t - 30 -----(2)   Solving equation 1 and 2   x = 630 min   ANSWER:630 min
Answer: C
Which of the following must be subtracted from 2^24 so that the resulting integer will be a multiple of 3?  Pick.
A) 2	B) 3	C) 1	D) 4	E) 5

Solution: {4^1} / 3 =4/3 remainder 1   {4^2} / 3 = 16/3 remainder 1   {4^3} / 3 = 64/3 remainder 1   {4^4} / 3 = 256/3 remainder 1   Actually the same remainder keeps repeating .....   Try with a diff no, say 2   {2^1}/3 = remainder 2   {2^2}/3 = remainder 1   {2^3}/3 = remainder 2   {2^4}/3 = remainder 1   Answer : 1
Answer: C
In a class of 300 students, 150 study Spanish and 100 study French. If a student must study at least one of these two languages, what percent of the students study French but NOT Spanish? Choose the correct choice from the following answers:
A) 50%
B) 40%
C) 30%
D) 20%
E) 10%

Solution: No of students study french= 300- No of students study spanish = 300-150= 
300-150 = 150
150   % of the students study french but not spanish= (150/300)*100= 
(150/300)*100 = 50
50 %   50%nswer: 50%
Answer: A
Martin bought 5 packet milk at an average price (arithmetic mean) of 20¢. If Martin returned two packet to the retailer, and the average price of the remaining millk packet was 12¢, then what is the average price, in cents, of the two returned milk packets? Choose the most appropriate option
A) 30  B) 31  C) 32  D) 33  E) 34

Solution: Total price of 5 packet milk=5*20= 
5*20 = 100
100   Total price of 3 packet milk=3*12= 
3*12 = 36
36   Total price of 2 packet returned milk=100-36= 
100-36 = 64
64   Average price of 2 packet milk=64/2= 
64/2 = 32
32   32orrect option Answer:32
Answer: C
If log8p = 2.5, log2q = 5, then p in terms of q is? Choose the correct answer
A) 3√q B) 2q C) q D) q/2 E) None of these

Solution: log8p = 5/2   => p = 85/2 = 23(5/2) = (25)3/2   log2q = 5   => q = 25   Therefore, p = q3/2.   3√qNSWER:3√q
Answer: A
A straight line in the xy-plane has a slope of 2 and a y-intercept of 2. On this line, what is the x-coordinate of the point whose y-coordinate is 520 ?
Choose the correct choice from the following choices.
A) 259
B) 498
C) 676
D) 823
E) 1,002

Solution: slope of 2 and a y-intercept of 2   y-coordinate is 520   y = 2x + 2   518 = 2x   x = 259   Answer:   A. 259
Answer: A
At a certain high school, the senior class is twice the size of the junior class. If 3/8 of the seniors and 1/4 of the juniors study Japanese, what fraction of the students in both classes study Japanese?
Choose the correct choice: A) 1/2 B) 2/3 C) 1/4 D) 1/3 E) 3/4

Solution: Start by deciding on a number of students to represent the number of students in the senior class. For this example I will choose 200 students. That would make the number of students in the junior class 100. Then we can find out how many students are taking Japanese in each grade and add them together. (3/8)*200=75 and   (1/4)*100= 
  (1/4)*100 = 25
25. 75+25=100. There are a total of 300 students in the junior class and senior class combined (100+200=300), and there are 100 total students in Japanese, so 100 students in Japanese / 300 total students equals 1/3 of the students in both classes that study Japanese.   Answer: 1/3
Answer: D
Evaluate: |8 - 8(3 - 12)| - |5 - 11| = ?	Pick.
A) 40	B) 74	C) 60	D) 70	E) 80

Solution: According to order of operations, inner brackets first. Hence   |8 - 8(3 - 12)| - |5 - 11| = |8 - 8*(-9)| - |5 - 11|   According to order of operations, multiplication within absolute value signs (which may be considered as brackets when it comes to order of operations) next. Hence   = |8 + 72| - |5 - 11|   = |80| - |-6|   = 80 - 6= 
80 - 6 = 74
74   correct answer 74)74
Answer: B
A ship sails out to a mark at the rate of 23 kmph. and sails back at the rate of 16 kmph. The average rate of sailing is ?
Choose the correct answer.
A) 5 km/hr  B) 12 km/hr  C) 12.5 km/hr  D) 19 km/hr  E) None

Solution: Answer   Average = ( 2uv / u +v ) km/hr   = ( 2 x 23 x 16 ) / (23 +16 ) km/hr.   = 19 km/hr.   Correct Option: 19 km/hr
Answer: D
1 man or 2 women or 3 boys can do a work in 44days. Then in how many days will 1man, 1woman and 1 boy do the work?  Pick one.
A) 20days
B) 24days
C) 30days
D) 15days
E) 10days

Solution: number of days = 44*1*2*3/(1*2 + 2*3 + 1*3)= 
44*1*2*3/(1*2 + 2*3 + 1*3) = 24
24days   Answer is 24days
Answer: B
If 150!/10^n is an integer, what is the largest possible value of n?	Choices
A) 38	B) 47	C) 32	D) 36	E) 37

Solution: The question actually asks the highest power of 10 which divides 150! ( For a number to be an integer - Without any remainder all the trailing zeroe's must be divided by the denominator)   10 = 2 x 5   150 factorial will have 37 as -   150/5= 
150/5 = 30
30   30/5= 
30/5 = 6
6   6/5=1   So answer will be (37) 37
Answer: E
A car traveled 75% of the way from town A to town B at an average speed of 80 miles per hour. The car travels at an average speed of S miles per hour for the remaining part of the trip. The average speed for the entire trip was 40 miles per hour. What is S ?  Choose the correct choice from the following answers.
A) 16
B) 20
C) 25
D) 30
E) 37.5

Solution: Total distance = 100 miles (easier to work with %)   75% of the distance = 75 miles   25% of the distance = 25 miles   1st part of the trip →  75/80= 
 75/80 = 15/16 = around 0.9375
0.9375   2nd part of the trip → 25/S= t   Total trip → (75+25)/40 = 0.9375 + t » 100/40 = 0.9375 + t » 2.5 = 0.9375 + t » t = 1.5625   Back to 2nd part of the trip formula: 25/S = 1.5625 » S = 16   16ns 16
Answer: A
The average age of an adult class is 40years. 17 new students with an avg age of 32years join the class. Therefore decreasing the average by 4year. Find what was theoriginal strength of class?	Options:
A) 8
B) 12
C) 15
D) 17
E) 18

Solution: Let original strength = y   Then , 40y + 17 x 32 = ( y + 17) x 36   â‡’ 40y + 544= 36y + 612   â‡’ 4y = 68   âˆ´ y = 17   17
Answer: D
find the number
if 1 = 2
2 = 10
3 = 30
4 = 68
5 = ?  Answers
A) 110 B) 120 C) 130 D) 140 E) 150

Solution: 1^3+1=2   2^3+2=10   3^3+3=30   4^3+4=68   so 5 = 5^3+5=130   ANSWER:130
Answer: C
A tank contains 7,000 gallons of a solution that is 5 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride? Choose the correct choice from the following
A) 4.77%  B) 5.77%  C) 6.77%  D) 7.77%  E) 8.77%

Solution: We start with 7,000 gallons of a solution that is 5% sodium chloride by volume. This means that there are 0.05 x 7,000 = 350 gallons of sodium chloride.   When 2,500 gallons of water evaporate we are left with 4,500 gallons of solution. From here we can determine what percent of the 4,500 gallon solution is sodium chloride.   (sodium chloride/total solution) x 100 = ?   (350/4,500) x 100 = ?   0.077 x 100 = ?   = 7.7%   Answer is 7.77%.
Answer: D
A starts 3min after B for a place 4.5 km distant B on reaching his destination immediately returns and after walking a km meets A. If A can walk 1km in 18min, then what is B's speed?  Choices:
A) 5kmph  B) 4kmph  C) 6kmph  D) 3.5kmph  E) 4.5kmph

Solution: If speed of B is x kms/min, then   (4.5+1)/x= [3.5/(1/18)] +3   x=1/12 km/min= 5 kms/hr   5kmphNSWER:5kmph
Answer: A
In how many ways 4 Indians and 5 Englishmen can be seated in a row so that they are alternate?	Choose the correct choice from the following:
A) 1200
B) 9600
C) 3240
D) 4250
E) 2880

Solution: number of ways = 4!*5! = 2880   Answer is 2880
Answer: E
45 men can complete a work in 17 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work?	Choices:  A) 6.6  B) 10  C) 15  D) 7  E) 8

Solution: 45*17 men can complete the work in 1 day   1 man's 1 day work = 1/765   45 men 6 days work = 6*1/17 = 6/17   remaining work = 1-6/17 = 11/17   75 men's 1 day's work = 75/765 = 5/51   11/17 work is done by them in  51/5 * 11/17= 
 51/5 * 11/17 = 33/5 = around 6.6
6.6 days   6.6nswer is 6.6
Answer: A
Johnny borrows $30,000 from Tony at 3% daily interest compounded daily. How much does Johnny owe Tony after 4 weeks?	Choose the correct option
A) 30000*0.02^56 B) 30000*1.12 C) 30000*2.12 D) 30000*1.03^28 E) (30000*1.02)^56

Solution: A=A= P(1+r100)^n   So, A=30000(1+3/100)^7âˆ—4   So, A=A= 30000(1.03)^28   Hence answer will be (30000*1.03^28)
Answer: D
A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 22 sec. What is the length of the goods train?	Pick one:
A) 299
B) 190
C) 276
D) 270
E) 281

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Time= 22 sec.   Let the length of the train be x meters.   Then, (x + 250)/22 = 20   x = 190 m.   Answer: 190
Answer: B
A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.20000, find their shares?	Answers
A) s.8000, Rs.12000	B) s.8000, Rs.12700	C) s.10000, Rs.12090	D) s.8000, Rs.12003	E) s.10000, Rs.12200

Solution: The ratio of their profits s.8000, Rs.12000:B   = 8:12 = 2:3   Share of s.8000, Rs.12000 in the total profit   = 2/5 * 20000   = Rs.8000 Share of s.8000, Rs.12000 in the total profit = 3/5 * 20000   = Rs.12000   s.8000, Rs.12000nswer: s.8000, Rs.12000
Answer: A
Let y = 2g + x^2 and g = 4x + 1.
If g^2 = 625, then which of the following can be a value of 2y + 3g?	Choose the correct choice from the following choices
A) 100
B) 130
C) 141
D) 142
E) 247

Solution: 800score Official Solution:   First note that g can either be 25 or -25. We are going to have to use both to find all solutions before we can choose a final answer. We begin by substituting g = 25 and then g = -25. If g = 25, then x = 6. If g = -25, then x = -26/4. Since all of our solutions are whole numbers, we can dismiss -26/4. We use g = 25 and x = 6 to determine the value of y: y = 2(25) + 36 = 86. Finally, we substitute the values for y and g into the last expression to determine its value : 2(86) + 3(25) = 172 + 75= 
172 + 75 = 247
247;the correct answer is (247).
Answer: E
For what value(s) of x is the following equation satisfied: 5x-9-4x = -4x+6+5x  Choose the correct option: A) a. -5 B) b. 0 only C) c. 5/2 only D) d. No value E) e. Any value

Solution: 5x-9-4x = -4x+6+5x   k - 9 = k + 6   -9 = 6, which is false.   So, no k satisfies given equation.   Answer: d. No value.
Answer: D
A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
Select:
A) 18:11	B) 22:13	C) 23:12	D) 11:9	E) 11:10

Solution: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.   18:11 : B   8000*18 : (8000*4) + (4000*14)   14400 : 88000   18:11:B = 18:11   18:11NSWER:18:11
Answer: A
An bus covers a certain distance at a speed of 240 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?	Choose the correct choice.
A) 700 km/hr B) 720 km/hr C) 780 km/hr D) 800 km/hr E) 890 km/hr

Solution: Distance = (240 x 5) = 1200 km.   Speed = Distance/Time   Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]   Required speed = 1200 x 3 km/hr = 720 km/hr.   720 km/hr
Answer: B
Certain stocks in April were 10% less than they were in May and 20% Lesser than they were in June. What was the percentage decrease in the stocks from May to June?	Options:	A) 5%	B) 10%	C) 20%	D) 28%	E) 50%

Solution: Let stocks value in Feb = 100 => In Jan = 90 and March = 90 * 80/100= 
90 * 80/100 = 72
72   Thus, percent decrease in stocks from Feb to March= 100 - 72= 
100 - 72 = 28
28%   Hence Answer is 28%
Answer: D
Lottery balls numbered consecutively from one through one hundred are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 1 on it?  Choose the correct choice from the following:
A) 9/100
B) 1/10
C) 11/100
D) 19/100
E) 1/5

Solution: Probability = No of balls with 1 / total number of balls   = {1,10,11,12 to 19, 21,31,41,51,61,71,81,91,100}/100   = 20/100=1/5   Answer is 1/5
Answer: E
find the remainder (32)^33^34 when divided by 11?
Pick one.
A) 9 B) 10 C) 11 D) 12 E) 13

Solution: unit digit of 33^34 = 9 i.e odd no.   (32)^33^34 / 11   = (11*3-1)^(-------9) / 11   = (-1)^(odd) / 11   = -1/10   => rem = -1+11= 
-1+11 = 10
10   ANSWER:10
Answer: B
4 + 4 + 4 + 4 + 3 x 4^2 + 3 x 4^3 + 3 x 4^4 + 3 x 4^5 + 3 x 4^6 =  Choices:
A) 4^24 B) 4^20 C) 4^16 D) 4^12 E) 4^7

Solution: Let's see that 4 + 4 + 4 +4 is 4^2, then: 4^2 + 3 x 4^2 becomes 4 x 4^2 that is 4^3. You follow with the next element: 4^3 + 3 x 4^3 is equal to 4 x 4^3 that is 4^4. Then is assumed right before 3 x 4^6: 4^6 + 3 x 4^6 becomes 4 x 4^6 that is 4^7. Thus, the correct answer is the option 4^7, 4^7.
Answer: E
Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.961. Find the cost of each ice-cream cup?
Choose the correct choice from the following answers:	A) 25	B) 66	C) 77	D) 99	E) 91

Solution: Let the cost of each ice-cream cup be Rs.x   16(6) + 5(45) + 7(70) + 6(x) = 961   96 + 225 + 490 + 6x = 961   6x = 150 => x = 25.   25nswer: 25
Answer: A
In Town X, 64 percent of the population are employed, and 40 percent of the population are employed males. What percent of the employed people in Town X are females?  Pick:
A) 16% B) 24% C) 38% D) 40% E) 52%

Solution: We are asked to find the percentage of females in employed people.   Total employed people 64%, out of which 40 are employed males,hence 24% are employed females.   (employed females)/(total employed people)=24/64=38%   Answer: 38%.
Answer: C
A boat can move upstream at 35 kmph and downstream at 75 kmph, then the speed of the current is?
A. 5 kmph Select
A) 15	B) 12	C) 17	D) 13	E) 20

Solution: US = 35   DS = 75   M = (75- 35)/2= 
(75- 35)/2 = 20
20   Answer:20
Answer: E
What is the sum of all 3 digit positive integers that can be formed using the digits 1, 5, and 8, if the digits are allowed to repeat within a number?  Select the correct option:	A) 126	B) 1386	C) 3108	D) 308	E) 13986

Solution: There can be 27 numbers. Every digit has three possibilities because question permits repetition. So it becomes a very good summation problem.   If there are 27 digits. There are 27 hundred digits, 27 tens digit and 27 ones digit to be summed. Of 27 hundred digits, 9 of them are 1, 9 of them are 5 and the last 9 are 8. Same is true for the other two digits.   Thus the sum is:   9x100+9x500+9x800+9x10+9x50+9x80+9x1+9x5+9x8=   999x(1+5+8)=999x14=13986   13986
Answer: E
Sunil invested $ 1800 fir 4 years and $ 1300 for 2 years at the same rate of Simple Interest. If the total interest from these investments is $ 1900, what is the rate of interest? Choose the correct choice from the following choices:
A) 18 3/4%	B) 5 1/3%	C) 19 1/4%	D) 16%	E) 18 2/4%

Solution: (1800x4xR)/100+(1300x2xR)/100=1900   98R=1900   R= 19 1/4%   Answer is 19 1/4%
Answer: C
Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2178?	Choose the correct choice from the following
A) 2277	B) 2669	C) 2200	D) 2766	E) 2998

Solution: Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2178.   => (90%) of (110%) of x = Rs. 2178.   => (90/100)(110/100)x = 2178   => x = (2178 * 100)/(9 * 11)   => x = Rs. 2200   Answer: 2200
Answer: C
Pipe A fills a tank in 42 minutes. Pipe B can fill the same tank 6 times as fast as pipe A. If both the pipes are kept open when the tank is empty, how many minutes will it take to fill the tank?
Choose one:	A) 3	B) 4	C) 5	D) 6	E) 7

Solution: A's rate is 1/42 and B's rate is 1/7.   The combined rate is 1/42 + 1/7 = 1/6   The pipes will fill the tank in 6 minutes.   The answer is 6.
Answer: D
A large box contains 18 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box?	Choose the correct option
A) 230  B) 320  C) 450  D) 540  E) 110

Solution: The number of chocolate bars is equal to   18 *25= 
18 *25 = 450
450   correct answer 450
Answer: C
A small water pump would take 3 hours to fill an empty tank. A larger pump would take 1/4 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time? Choose the correct choice from the following choices:
A) 3/13
B) 1/5
C) 1/10
D) 1/3
E) 1/7

Solution: Rate of the small pump is 1/3 tank/hour   Rate of the larger pump is 1/(1/4) or 4 tank/hour;   Combined rate of the two pumps is 1/3+4=13/3 tank/hour, together they will fill the empty tank in 1/(13/3)= 3/13 hours (time=job/rate).   3/13nswer: 3/13
Answer: A
Susan, John, Tim, Matt and Kim need to be seated in 5 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
Choose the correct choice from the following
A) A)60	B) B)120	C) C)80	D) D)240	E) E)60

Solution: Total number of arrangements = 5! = 120   In exactly half, Susan will be to the left of Tim, which gives us 60 arrangements   Option (60)
Answer: A
On the xy co-ordinate plane, point C is (4,-2) and point D is (-1,2.5). The point on line segment CD that is twice as far from C as from D is:  Choices:
A) (1,-1) B) (1,1) C) (2,0.25) D) (3,0.5) E) (3,1)

Solution: We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.   *It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:   Taking the x-coordinate first, the distance between C and D is |(x-coordinate of C) - (x-coordinate of D)|= |5 - (-1)= 
5 - (-1) = 6
6   The x-coordinate that is twice as far from C as it is from D (and in between C and D) will be 4 units from C and 2 units from D. So the x coordinate of the point we're looking for is  5-4= 
 5-4 = 1
1, or  (-1)+2= 
 (-1)+2 = 1
1.   Now looking at the y-coordinate, we do the same thing. The distance between C and D is |(-2) - 2.5|= 4.5   The y-coordinate that is twice as far from C as it is from D (and in between C and D) will be 3 units from C and 1.5 units from D. So the y coordinate of the point we're looking for is  (-2)+3= 
 (-2)+3 = 1
1, or  2.5-1.5= 
 2.5-1.5 = 1
1.   So now we have our coordinates of the point on the line that is twice as far from C as it is from D: (3,1)   Answer: (3,1)
Answer: E
A man two flats for $675958 each. On one he gains 14% while on the other he loses 14%. How much does he gain or lose in the whole transaction?
Select the correct option
A) 1.96% B) 2.56% C) 3.12% D) 4.65% E) 5.12%

Solution: In such a case there is always a loss   Loss% = (14/10)^2 = 49/25= 
49/25 = 49/25 = around 1.96
1.96%   1.96%nswer is 1.96%
Answer: A
James can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?
Select
A) 365/784 B) 415/784 C) 175/256 D) 256/175 E) 263/541

Solution: James will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.   So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.   The event of not hitting the target even once is the complement of the event of hitting the target at least once.   The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾   Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256   The probability that he will hit the target at least in one of the four shots=1-81/256   =175/256   Ans: 175/256
Answer: C
If 10 people contributed a total of $30.00 toward a gift and each of them contributed at least $2.00, then the maximum possible amount any one person could have contributed is	Choose the correct choice from the following options:
A) $1.00 B) $1.25 C) $12.00 D) $6.00 E) $20.00

Solution: $12.00 for me   9 people with 2$ each -> maximum = 12
Answer: C