MU-NLPC/Calc-aqua_rat huggingface dataset:
If the complement of a certain angle is one time the measure of that certain angle, then what is the measure of that certain angle? Choose the correct answer:
A) 45°
B) 30°
C) 22.5°
D) 18°
E) 15°

Solution: Thecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example.   The original angle is x, so the complement is x, and together, these add up to 90 degrees.   x + x = 90   2x = 90   x =45°   45°nswer = (45°)
Answer: A
A train , having a length of 165 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train	Select.
A) 9 sec	B) 8 sec	C) 6 sec	D) 4 sec	E) 2 sec

Solution: Explanation:   Distance = 165 m   Relative speed = 60+6= 
60+6 = 66
66 kmph (Since both the train and the man are in moving in opposite direction)= 66×10/36 mps = 110/6 mps   Time = distance/speed = 165/(110/6)= 
165/(110/6) = 9
9 s   9 secnswer: Option 9 sec
Answer: A
A sum of Rs. 1360 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B's share is:	Pick:	A) 240	B) 120	C) 190	D) 200	E) 250

Solution: Let C's share = Rs. x   Then, B's share = Rs. x/4, A's share = Rs. (2/3 x (x/4))= Rs. x/6   Therefore, x/6 + x/4 + x = 1360   =17x/12 = 1360   x = 1360 x 12/17= Rs. 960   Hence, B's share = Rs. (960/4)= Rs. 240.   240nswer is 240.
Answer: A
Mazy bought shares for a total value of $1000. Next day, the price of shares is reduced by 10%. With the same $1000, he could now buy 10 more shares. Which of the following is closest to the original price per share?  Pick one
A) $10  B) $11  C) $12  D) $13  E) $14

Solution: From the given information,we can conclude that Mazy bought x number of shares for $1000. With a 10% reduction in price, he could buy the same x number of shares for  1000*.90= 
 1000*.90 = 900
$900 . With the remaining money ($1000 - $900= $100), he can buy 10 more shares. So, the reduced price per share = $100/10= 
100/10 = 10
$10.   Therefore, if the reduced price of $10 equals the original price * 9/10, then the original price is approximately $11=$11
Answer: B
A bag contains 5 white marbles and 5 red marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?	Pick one:
A) 1/6 B) 1/35 C) 1/3 D) 1/462 E) 1/126

Solution: first, total ways to select for all boys and girls, i.e 10!/(5!*5!) = 252   then there are one two way girls can have all same colors, either white or red.   The number of ways in which 5 girls can select 5 white balls = 5C5 = 1   The number of ways in which 5 girls can select 5 red balls = 5C5 = 1   Therefore, total favorable outcomes/total outcomes = 2/252= 1/126   1/126
Answer: E
If xy not equal 0 and x^2*y^2 -xy = 6, which of the following could be y in terms of x?
I. 1/2x
II. -2/x
III. 3/x Choices.
A) I only
B) II only
C) I and II
D) I and III
E) II and III

Solution: (xy)^2-xy-6=0   (xy-3)(xy+2)=0   so either xy=3 i.e. y=3/x   or xy=-2 i.e. y=-2/x   so II and III is the ans
Answer: E
During the break of a football match, the coach will make 3 substitutions. If the team consists of 14 players among which there are 2 forwards, what is the probability that none of the forwards will be substituted? Choose the correct choice from the following answers
A) 21/55  B) 18/44  C) 21/99  D) 28/44  E) 36/55

Solution: Required probability = no. of favorable outcome/ total no. of outcomes   out of 14 players any 3 can be selected in 1421/993 ways   after removing 2 forwards any 3 players can be selected from the remaining 9 players in 921/993 ways   thus required probability = 921/993/1421/993 =21/99
Answer: C
In the equation 2x – cy = 18, c is a constant. If the value of y is 2 when x is 6, what is the value of x when y is 3 ? Options
A) −9/2
B) -4
C) -3
D) 4
E) 9/2

Solution: 2x - cy = 18   x=6, y=2;   12-2c=18   c=-3   2x-cy=18   when y=3, c=-3, x=   x=9/2   ANSW9/2R:9/2
Answer: E
Population of a city in 20004 was 1000000. If in 2005 there isan increment of 25% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
Select the correct option
A) 976374 B) 979923 C) 980241 D) 1178125 E) 1083875

Solution: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)   = P (1 + 25/100)(1 - 35/100)(1 + 45/100)   = 1178125   1178125
Answer: D
A sum fetched a total simple interest of Rs. 929.20 at the rate of 8 p.c.p.a. in 5 years. What is the sum?	Choose the correct choice from the following choices
A) 2323	B) 1223	C) 2563	D) 1853	E) 2353

Solution: Explanation :   SI = Rs.929.20   P = ?   T = 5 years   R = 8%   P = 100×SI/RT   =100×929.20/8×5   = Rs.2323   2323nswer : Option 2323
Answer: A
A toy store regularly sells all stock at a discount of 20 percent to 40 percent. If an additional 25 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $16 before any discount? Choose the correct choice from the following: A) $5.60 B) $7.20 C) $8.80 D) $9.60 E) $15.20

Solution: Cost price is $16. Lowest possible price is when max discount is applied.   So Discount of 40% first and then 25%.   Final price = 16 * (1-40/100) * (1- 25/100) = 16 * 60/100 * 75/100= 
16 * 60/100 * 75/100 = 36/5 = around 7.2
7.2   Ans $7.20
Answer: B
Joe is painting a rectangular room whose dimensions are given by a, b and c meters. Joe takes 8 hours to paint a wall with dimensions a and c. He takes 4 hours to paint a wall with dimensions b and c and 12 hours to paint the ceiling with dimensions a and b. If Joe works at a constant rate and a = 12, then what is the volume of the room?	Choose the correct choice from the following.
A) 218 cubic meters
B) 224 cubic meters
C) 230 cubic meters
D) 288 cubic meters
E) It can’t be determined.

Solution: Time to paint each wall as given in problem:   AC = 8 hours   BC = 4 hours   AB = 12 hours   Since he works at constant rate and it takes him twice as long to paint AC compared to BC   AC=2BC   Plug in 6 for A and you find that B=6   Since painting AB takes 3 times as long compared to BC,   AB=3BC   Plug in 6 for A and 3 for B and you find that C=4   A*B*C=12*6*4= 
12*6*4 = 288
288 cubic meters   Answer: 288 cubic meters
Answer: D
The time it took car P to travel 150 miles was 2 hours less than the time it took car R to travel the same distance. If car P’s average speed was 10 miles per hour greater than that of car R, what was car R’s average speed, in miles per hour?
Choose the correct answer
A) 23 B) 50 C) 60 D) 70 E) 80

Solution: Let speed of car R be=x   Then speed of car P= x+10   A/Q,   (150/x)-(150/(x+10))=2   Solving for x=23 miles\hr.   23
Answer: A
What sum of money will produce Rs.70 as simple interest in 3 years at 3 1/2 percent?
Choose one:
A) 667 B) 500 C) 266 D) 288 E) 211

Solution: 70 = (P*3*7/2)/100   P = 667   667nswer: 667
Answer: A
In a group of 100 adults, 80 percent of the women are left-handed. If there are 12 right-handed women in the group, how many men are in the group?
Choose the correct choice from the following answers:  A) 48  B) 52  C) 54  D) 60  E) 40

Solution: 12 left-haded women compose   100-80= 
  100-80 = 20
20% (or 1/5) of all women, so there are total of   5*12= 
  5*12 = 60
60 women --> 100-60=40men.   Answer: 40. --  100-60= 
 --  100-60 = 40
40men.   Answer: 40.
Answer: E
For what values of k will the pair of equations (3x + 4y)/2 = 6 and kx + 12y = 30 does not have a unique solution?	Choices:
A) 12
B) 9
C) 3
D) 7.5
E) 2.5

Solution: we have 2 equations   1. (3x + 4y)/2 = 6 --> 3x + 4y = 12 -- > 9x + 12y = 36   2. kx + 12y = 30   substract 1-2, we get (9-K)x = 6   i.e. x = 6/(9-k)   then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is 9
Answer: B
A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6p.a for 2 years. Find his gain in the transaction per year. Choose the correct choice from the following:
A) Rs. 112.50	B) Rs. 125	C) Rs. 150	D) Rs. 167.50	E) Rs. 175

Solution: Gain in 2 years   = Rs.[(5000 x (25/4)	x(2/100))-((5000 x 4 x 2)/100)]   = Rs. (625 - 400)   = Rs. 225.   Gain in 1 year = Rs.(225/2)   = Rs. 112.50   Rs. 112.50NSWER :Rs. 112.50
Answer: A
After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6600. Find the actual price of the good.	Choose one:  A) s. 6000  B) s. 9000  C) s. 10800  D) s. 9649  E) s. 9980

Solution: Let actual price was 100.   After three successive discount this will become,   100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4   Now Compare,   68.4 = 6600   1 = 6600/68.4   100 = (6600*100)/68.4 = Rs. 9649.   Answer: Option s. 9649
Answer: D
Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?  Choices.
A) 22  B) 12  C) 88  D) 99  E) 27

Solution: 1/8 + 1/24 = 1/6   6 * 2= 
6 * 2 = 12
12   Answer:12
Answer: B
A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.	Choose the correct choice from the following answers.
A) 29,000 square meters
B) 16,000 square meters
C) 20,000 square meters
D) 32,000 square meters
E) 45,000 square meters

Solution: Let us first find the distance d jogged   distance = rate ? time = (12 km / hr) ? 30 minutes   = (12 km/hr) ? 0.5 hr = 6 km   The distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to   6 km / 10 = 0.6 km = 0.6 ? 1000 meters = 600 meters   Let L and W be the length and width of the field. The length is twice the width. Hence   L = 2 W   The perimeter is 600 meters and is given by   2 (L + W) = 600   Substitute L by 2 W   2 (2 W + W) = 600   Simplify and solve for W   4 W + 2 W = 600   6 W = 600   W = 100   Find L   L = 2 W = 200   Find the area A of the rectangle   A = L * W = 200 * 100 = 20,000 square meters   correct answer 20,000 square meters
Answer: C
Hillary and Eddy are climbing to the summit of Mt. Everest from a base camp 5,000 ft from the summit. When they depart for the summit at 06:00, Hillary climbs at a rate of 800 ft/hr with Eddy lagging behind at a slower rate of 500 ft/hr. If Hillary stops 1000 ft short of the summit and then descends at a rate of 1,000 ft/hr, at what time do Hillary and Eddy pass each other on her return trip?	Choose the correct choice from the following answers.
A) 11.0 B) 12.0 C) 13.0 D) 14.0 E) 15.0

Solution: Solution:H stopped 1000 ft before reaching the final point, time taken to reach 4000 ft= 4000/800= 
4000/800 = 5
5hrs.   this means she reached there at 11:00.   speed difference between them is 800-500= 
800-500 = 300
300 ft/hr   so by the time H stops they have 1500 ft of distance   so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft/hr and distance bwn them is 1500 ft so time taken to meet= 1 hr from 11:00   means 12:00 is the answer.   12.0
Answer: B
Two cars, Car1 and Car2 move towards each other from R and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach R starting from Y? Choose the correct answer:
A) 15.5 sec B) 8.4 sec C) 33.6 sec D) 31.11 sec E) 16.8 sec

Solution: R--------------------------------------|----------------------------Y   Car A(20mps)------------------------->P<---------------Car B(15mps)   Let 2 cars meet each other at point P in t seconds.   Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance RY= 35t.   From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further.   so, 15t/20 = 10   So t=40/3 sec and total distance = (35*40)/3   Hence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx.   Answer 31.11 sec
Answer: D
An aeroplane covers a certain distance at a speed of 100 kmph in 2 hours. To cover the same distance in 1 hours, it must travel at a speed of? Choose the correct choice from the following:	A) 100km/hr	B) 150km/hr	C) 200km/hr	D) 250km/hr	E) 300km/hr

Solution: Distance = 100*2= 
100*2 = 200
200 km   Required speed= 200 *1= 
200 *1 = 200
200km/hr   Answer is 200km/hr
Answer: C
If the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is?  Select the correct option.
A) 22 B) 29 C) 23 D) 12 E) 13

Solution: 2 * 22/7 * 14 * x = 1056 => x   = 12   Answer:12
Answer: D
A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 12 seconds. What is the length of the train in meters?	Select the correct option.
A) 400 meters	B) 120 meters	C) 1777 meters	D) 60 meters	E) None of these

Solution: Train overtakes a bike means that we are talking about total length of the train. (train's head is close to bike when it started and its tail crosses the bike when it overtakes the bike)   Relative speed= 100-64= 
100-64 = 36
36Km/h= 36000 m/h   time= 12 seconds   Distance= speed*time    36000* 12/3600= 
 36000* 12/3600 = 120
120 meters.   120 meters is the answer.
Answer: B
A can have a piece of work done in 4 days, B can work two times faster than the A, C can work three times faster than A. How many days will they take to do the work together ?  Choices: A) 3/4 days B) 6/7 days C) 1/4 days D) can't say E) none

Solution: A's 1 day work is 1/6   6/7 days's 1 day work is 2/6   C's 1 day work is 3/6   (A+6/7 days+C)'s 1 day work(1/6+2/6+3/6) is 7/6   so, they can finish the work in 6/7 days   ANSWER:6/7 days
Answer: B
A company has two types of machines, type R and type S. Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 2 hours. If the company used the same number of each type of machine to do job in 12 hours,how many machine R were used? Select:
A) 3/4 B) 4 C) 18/19 D) 9 E) 12

Solution: yes there is a typo in the question, I got the same ques on my GMAT PREP last week, and the questions goes as:   A company has two types of machines,type R and type S.Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 2 hours .If the company used the same number of each type of machine to do job in2 hours,how many machine R were used?   So for a job to be done in 2 hours R = 1/2   R_a(Rate of Machine R) = 1/36   R_s(Rate of Machine S) = 1/2   Lets say x machines are used to attain the desired rate, thus   x/36+x/2 = 1/2 (Desired R =1/2 i.e. to complete the job in 2 hours)   (x+18x)/36 = 1/2   19x/36 = 1/2   x = 18/19.   QA = 18/19 (ANSWER 18/19)
Answer: C
Last year, Company M made q dollars in profit. Half of the profit went to the company’s founder. The rest was split evenly among his Three other partners. In terms of q, how much did each of the other partners receive?  Choose the correct choice from the following answers.
A) q/4 B) q/5 C) q/6 D) q/7 E) q/8

Solution: Profit = q   Profit to company founder = q/2   Profit to other partners = q/2   Number of other partners = 3   Profit to each partner = (q/2)/3 = q/6   Answer: q/6
Answer: C
Barbata invests $2600 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?	Pick one: A) 1200 B) 3000 C) 1300 D) 3600 E) 2400

Solution: Let the additional invested amount for 8% interest be x;   Equation will be;   2600+0.05*2600+x+0.08x = 2600+x+0.06(2600+x)   0.05*2600+0.08x = 0.06x+0.06*2600   0.02x = 2600(0.06-0.05)   x = 2600*0.01/0.02= 
2600*0.01/0.02 = 1_300
1300   Ans: "1300"
Answer: C
An agent, gets a commission of 2.5% on the sales of cloth. If on a certain day, he gets Rs. 12.50 as commission, the cloth sold through him on that day is worth	Pick:
A) 333	B) 500	C) 887	D) 299	E) 132

Solution: Explanation:   Let the total sale be Rs. x.   Then, 2.5%. of x = 12.50 <=> (25/100 * 1/100 * x) = 125/10 <=> x = 500.   Answer: 500) 500
Answer: B
The slant height of a cone is 10 cm and radius of the base is 5cm, find the curved surface of the cone? Choose the correct answer:
A) 150
B) 155
C) 158
D) 157
E) 190

Solution: π * 10 * 5   = 157   Answer:157
Answer: D
If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $76, how much does one shirt cost? Pick:
A) $10
B) $12
C) $13.20
D) $15
E) $18

Solution: 3J + 2S = 69   2J + 3S = 76   ----------------   5J + 5S = 145 ----(divide by 5)---> J + S = 29   3J + 2S = J + 2(J + S) = J + 58 = 69 ---> J = 11   3*11 + 2S = 69   33 + 2S = 69   2S = 36   S = 18   Answer: $18
Answer: E
In a certain company, the ratio of male to female employees is 7:8. If 3 more men were hired, this ratio would increase to 8:9. How many male employees are there in the company? Choose one:
A) 6  B) 21  C) 27  D) 189  E) 192

Solution: Another approach is to use TWO variables.   Let M = present number of males   Let F = present number of females   The ratio of male to female employees is 7:8   So, M/F = 7/8   Cross multiply to get 7F = 8M   If 3 more men were hired, this ratio would increase to 8:9   So, (M+3)/F = 8/9   Cross multiply to get 9(M+3) = 8F   Expand: 9M + 27 = 8F   We now have a system of two equations and two variables:   7F = 8M   9M + 27 = 8F   Solve to get: M = 189 and F = 216   ANSWER:189
Answer: D
How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 150 m in length?  Choose the correct choice from the following options:
A) sec  B) sec  C) sec  D) sec  E) sec

Solution: sec = 110 + 150= 
110 + 150 = 260
260 m   S= 60 * 5/18 = 50/3   T = 260 * 3/50= 
260 * 3/50 = 78/5 = around 15.6
15.6 sec   Answer: sec
Answer: D
In the city of San Durango, 90 people own cats, dogs, or rabbits. If 60 people owned cats, 20 owned dogs, 40 owned rabbits, and 18 owned exactly two of the three types of pet, how many people owned all three?	Pick one: A) 1 B) 3 C) 6 D) 11 E) 12

Solution: Total = 6 + D + R - (6D + DR + 6R) - 26DR   90 = 60 + 20 + 40 - (18) - 2x   x = 6   So, answer will be 6
Answer: C
For any number s, s* is defined as the greatest positive even integer less than or equal to s. What is the value of 5.2 – 5.2*? Choose the correct choice from the following answers.
A) 0.2 B) 1.2 C) 1.8 D) 2.2 E) 4.0

Solution: Since s* is defined as the greatest positive even integer less than or equal to s, then 5.2* = 4 (the greatest positive even integer less than or equal to 5.2 is 4).   Hence, 5.2 – 5.2* = 5.2 - 4= 
5.2 - 4 = 1.2
1.2   Answer: 1.2.
Answer: B
If the volume of two cubes are in the ratio 8:1, the ratio of their edges is: Select:
A) 2:1	B) 3:2	C) 3:5	D) 3:7	E) None of these

Solution: Explanation:   Let the edges be a and b of two cubes, then   a3/b3=8/1   =>(a/b)3=(2/1)3   a/b=2/1   =>a:b=2:1   Option 2:1
Answer: A
The simple interest accrued on an amount Rs.10,000 at the end of two years is same as the compound interest on Rs.8,000 at the end of two years. The rate of interest is same in both the cases. What is the rate of interest?	Choose the most appropriate option
A) 58%  B) 90%  C) 80%  D) 50%  E) 54%

Solution: Given that Rs.10,000 is invested in S.I for two years and Rs.8,000 in C.I for two years   => C.I - S.I   => 8,000 { [1 + r/100]2 - 1} = (10,000)2r /100   => 8{ 1 + 2r/100 + r2 / (100)2 - 1} = r/5   => 16r/100 + 8r2/(100)2 = 20r/100   => 4r/10 = 8r2/(100)2   => 8[r/100]2 - 4r/100 = 0   => r/100 {8r/100 -4} = 0   => r = 0% of 50%   Since r!= 0%, r =50%   Answer: 50%
Answer: D
3 candidates in an election and received 1000, 2000 and 4000 votes respectively. What % of the total votes did the winning candidate got in that election? Select:	A) 45%	B) 50%	C) 57.14%	D) 60%	E) 65.12%

Solution: Total number of votes polled = (1000 + 2000 + 4000)= 
(1000 + 2000 + 4000) = 7_000
7000   So, Required percentage= 4000/7000 * 100 = 57.14%   57.14%
Answer: C
1/(3-2√2)=?
Choose one:
A) 9+4√5	B) 9-4√5	C) 3+2√2	D) 9-2√5	E) 4+9√5

Solution: This question requires us to rationalize (fix) the denominator.   For more on this technique, seehttps://www.gmatprepnow.com/module/gmat ... video/1044   Given: 1/(3-2√2)   Multiply top and bottom by the 3+2√2ONJUGATE of 3-2√2, which is 3+2√2   So, 1/(3-2√2) = (1)(3+2√2)/(3-2√2)(3+2√2)   = (3+2√2)/(1)   = 3+2√2   =   3+2√2
Answer: C
I flew my tiny seaplane to visit my mother. On the flight up, I flew at 110 mph. On the way home, I flew 72 mph. What was my average speed for the trip?  Options: A) 198 mph B) 91 mph C) 88 mph D) 100 mph E) 99 mph

Solution: (110 mph +72 mph)/2= 91 mph   Correct answer is: 91 mph
Answer: B
A retailer buys a radio for Rs 225. His overhead expenses are Rs 20. He sellis the radio for Rs 300. The profit percent of the retailer is Choose the correct choice from the following choices:
A) 22.4%  B) 50%  C) 25%  D) 52%  E) None of these

Solution: Explanation:   cost price = (225 + 20)= 
(225 + 20) = 245
245 sell price= 300   gain = (55/245)*100 = 22.4%. 22.4%nswer: 22.4%
Answer: A
John invested Rs. 3500 in a scheme for 3 years at compound interest rate 4% p.a. How much amount will John get on maturity of the fixed deposit?  Choose the correct choice from the following answers:
A) s.4000 B) s.3578 C) s.3258 D) s.3990 E) s.3937.02

Solution: Amount = [3500 * (1 + 4/100)3]   = 3500 * 26/25 * 26/25 * 26/25   = Rs.3937.02   Answer:s.3937.02
Answer: E
Martins made a part payment of $650 toward buying a brand new washing machine, which represents 15% of the total cost of the washing machine, how much remains to be paid? Pick:	A) $1116.3	B) $3583.3	C) $3283.3	D) $3683.3	E) $2683.3

Solution: Explanation:   Let's start with what the total price of the washing machine would be. If 15% is equal to $650 then 100% equals $x. We just have to multiply $650 by 6.67 to get total amount=$4333.3. Out of this amount we then need to deduct the amount already paid which was $650 so we have $4333.3-$650=$3683.3   Answer: Option $3683.3 4333.3- 650= 
 4333.3- 650 = 3_683.3
$3683.3   Answer: Option $3683.3
Answer: D
In a particular 100 meter race, 7 athletes are participating that are numbered 1-7. In how many ways can athlete #4 finish ahead of #2 provided there's no tie among the athletes?  Choose the correct choice from the following answers: A) 1240 B) 1860 C) 2520 D) 3220 E) 4180

Solution: The total number of ways for the athletes to finish is 7! = 5040.   #4 will be ahead of #2 in exactly half of these possibilities.   5040/2= 
5040/2 = 2_520
2520   The answer is 2520.
Answer: C
A zinc-copper alloy with 6 kg of pure zinc would contain 90% of zinc. The alloy with 4 kg of 90% zinc alloy contains 84% of zinc. Calculate the weight and percentage of zinc in the zinc-copper alloy.
Choices:
A) 2.4 kg or 80%  B) 4.8 kg or 80%  C) 3.4 kg or 60%  D) 7.4 kg or 18%  E) 1.4 kg or 60%

Solution: Right Answer Explanation:   x : 6   y : 100   90   10 : 90 – y   (90-y)/6 = 10/x = ………..(1)   In the second case,   x 4   y 90   84   6 84-y   Therefore (84-y)/4 = 6/x ………..(2)   Dividing (1) and (2)   =   540 – 6y = 1260 – 15y   9y = 720   y = 80   x = 60/(90-80) = 60/10= 
60/10 = 6
6 kg   Quantity of zinc in x= 80% of x   = 0.8 6   = 4.8 kg   Weight and percentage of zinc is 4.8 kg or 80%   4.8 kg or 80%
Answer: B
The average (arithmetic mean) of 14, 32, and 53 is 3 more than the average of 21, 47, and x. What is x?
Choose the correct choice from the following options:
A) 20	B) 21	C) 22	D) 23	E) 24

Solution: The average of 14, 32, and 53 is 33.   The average of 21, 47 and x is 30.   Then 21 + 47 + x = 90.   x = 22.   The answer is 22.
Answer: C