MU-NLPC/Calc-aqua_rat huggingface dataset:
A man covers a distance on scooter. Had he moved 3kmph faster he would have taken 40 min less. If he had moved 2kmph slower, he would have taken 40min more. The distance is.
Choose the correct choice from the following answers.
A) 30 km
B) 60 km
C) 80 km
D) 20 km
E) 40 km

Solution: 40 km   40 km   Let distance = x m   Usual rate = y kmph   x/y – x/y+3 = 40/60 hr   2y(y+3) = 9x ---------------------------------(1)   x/y-2 – x/y = 40/60 hr y(y-2) = 3x -----------(2)   divide 1 & 2 equations   by solving we get x = 40 km
Answer: E
12 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 1 cm height. What is the diameter of each sphere?
Choose the correct choice from the following answers:	A) 2 cm	B) 4 cm	C) 8 cm	D) 10 cm	E) 12 cm

Solution: Volume of cylinder = pi*r^2*h   Volume of a sphere = 4*pi*R^3 / 3   12*4*pi*R^3 / 3 = pi*r^2*h   R^3 = r^2*h / 16 = 1 cm^3   R = 1 cm   D = 2 cm   The answer is 2 cm.
Answer: A
A small company is planning to rent either computer A or computer B to print customer mailing lists. Both computer A and computer B must be rented on an hourly basis. The rental fee is based only on the amount of time the computer is turned on. It will cost 40 percent more per hour to rent computer A than to rent computer B. Computer B would, however, require 20 hours more than computer A to do the job. If either computer A, or computer B were rented the total cost to rent the computer would be $850.00. What would be the approximate hourly charge to rent computer B?	Select:
A) $9.40  B) $11.30  C) $12.14  D) $17.80  E) $22.10

Solution: Pa = price of A   Pb = price of B   Ta = time for A to complete the job   Tb = time for B to complete the job   Given   Pa = 1.4 Pb   Ta+20 = Tb   Pa*Ta = Pb*Tb=850   1.4Pb * (Tb-20) = Pb*Tb   1.4 Pb Tb - Pb Tb = 1.4 Pb * 20   0.4PbTb = 28Pb   Tb = 28/0.4= 
28/0.4 = 70
70   Pb=850/70 ~ 12.14   $12.14
Answer: C
The owner of a furniture shop charges his customer 60% more than the cost price. If a customer paid Rs. 2000 for a computer table, then what was the cost price of the computer table?	Options:
A) 2789	B) 2772	C) 1250	D) 6725	E) 2099

Solution: CP = SP * (100/(100 + profit%))   = 1250(100/160) = Rs. 1250.   Answer: 1250
Answer: C
Tom spent six lucky days in Las Vegas. On his first day he won a net amount of only $20, but on each of the following days, the daily net amount he won grew by d dollars. If Tom won a total net amount of $1620 during his stay in Las Vegas, how much did he win on the last day?
Choose the correct choice from the following choices:
A) 330 B) 500 C) 520 D) 540 E) 620

Solution: I drew a diagram:   1 - $20   2 -   3 -   4 - $320   5 -   6 -   Total: $1,620   Between 1 and 6 are 5 days where he won $1,600. This means he averaged $320 per day (1600/5). You can put $320 by 4 because it's the middle number. Now you just find the two points betwenn $20 and $320 (320-20 = 300 / 3= 
300 / 3 = 100
100). So each day, he earned $100 more. This means on day 6, tom earned$520. Answer choice 520.
Answer: C
The average of first nine prime numbers which are odd is?  Choose the correct choice from the following answers:
A) 16.1 B) 15.1 C) 14.1 D) 17.1 E) 13.1

Solution: Explanation:   Sum of first 9 prime no. which are odd = 158   Average = 127/9 = 14.1   Answer:14.1
Answer: C
If two sides of a triangle are 12 and 6, which of the following could be the area of triangle?
1. 35
2. 48
3. 56	Choose the most appropriate option:
A) a) 1 only
B) b) 1 and 2 only
C) c) 1 and 3 only
D) d) 2 and 3 only
E) e) 1, 2 and 3 only

Solution: when two sides of a triangle are known , the maximum area occurs when the angle between those two sides is 90.   lets say base = 12 , height =8 (angle = 90)   maximum area = (1/2)*12*8= 
(1/2)*12*8 = 48
48 ( this is the same maximum area even when base is 8 and height is 12).   if we fix the base and keep lowering the angle, it will result in a lower height . hence the resulting area will always be < 48.   C,D and E are ruled out.   3 and 2 are possible areas as their areas are less than 48.   Hence the answer is d) 2 and 3 only.
Answer: D
An error 2% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square? Choices
A) 4.05%  B) 4.02%  C) 4%  D) 3%  E) 2%

Solution: Percentage error in calculated area   =(2+2+(2×2)/100)%   =4.04%   4.05%NSWER:4.05%
Answer: A
Joan and Karl each bought a bicycle and the sum of their purchases was $800. If twice of what Joan paid was $40 more than what Karl paid, what did Joan pay for her bicycle?  Choose the correct option.
A) $280  B) $300  C) $320  D) $340  E) $360

Solution: J+K=800 so K=800-J   2J=K+40   2J=(800-J)+40   3J=840   J=280   The answer is $280.
Answer: A
When positive integer n is divided by 3, the remainder is 1. When n is divided by 7, the remainder is 5. What is the smallest positive integer k such that k+n is a multiple of 21? Select
A) 2	B) 4	C) 6	D) 8	E) 10

Solution: n = 3p + 1 = 7q + 5   n+2 = 3p + 3 = 7q + 7   n+2 is a multiple of 3 and 7, so it is a multiple of 21.   The answer is 2.
Answer: A
Find the principle on a certain sum of money at 9% per annum for 2 2/5 years if the amount being Rs.1120?	Select.
A) 1000 B) 912.88 C) 927.78 D) 926.82 E) 921.05

Solution: 1120 = P [1 + (9*12/5)/100]   P= 921.05   Answer: 921.05
Answer: E
In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was : Choose the correct choice from the following choices.
A) 2500  B) 2600  C) 2700  D) 2900  E) 3200

Solution: Total number of votes = 7500   Given that 20% of Percentage votes were invalid   Valid votes = 80%   Total valid votes = 7500x (80/100)   1st candidate got 55% of the total valid votes.   Hence the 2nd candidate should have got 45% of the total valid votes   Valid votes that 2nd candidate got = total valid votes x 45/100   7500x (80/100)x45/100= 2700   answer :2700
Answer: C
Which of the following equivalent to (1/125)^2?	Choose the correct choice from the following choices
A) (0.03)^5  B) (0.04)^3  C) (0.05)^6  D) (0.06)^3  E) (0.07)^2

Solution: (1/125)^2 = (1/5^3)^2 = (1/5)^6 = (1/25)^3 = (0.04)^3   Answer: Option (0.04)^3
Answer: B
In how many ways can 5 boysand 2 girls be arranged at a table if 2 girls are never together?  Select:	A) 230	B) 240	C) 254	D) 260	E) 480

Solution: Total ways of arranging 7 person in a circle = 6! = 720 ways   If we consider two women as one, then we have   5+1= 
  5+1 = 6
6 persons. Arranging these six persons in circle will take= 5! = 120 ways   And two women can arrange themselves in 2! ways   Total ways in which two women sit together in circle = 5!*2! = 240 ways   Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240= 
720 - 240 = 480
480 ways   480
Answer: E
There are 7 magazines lying on a table; 3 are fashion magazines and the other 4 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?  Choose the correct choice from the following:	A) 1/2	B) 7/8	C) 32/35	D) 11/12	E) 13/14

Solution: answer is7/8   Total probability=7C3=48   4C3 +4C2*4C1+4C1*4C2=4+24+24=42   therefore the probability that at least one of the fashion magazines will be selected= 42/48=7/8   7/8
Answer: B
if x/4-x-3/6=1,then find the value of x. Choose the correct choice from the following:
A) 6	B) 4	C) 5	D) 1	E) 2

Solution: (x /4)-((x-3)/6)=1=> (3x-2(x-3) )/12 = 1 => 3x-2x+6=12 => x=6.   6nswer is 6
Answer: A
Triathlete Dan runs along a 2-mile stretch of river and then swims back along the same route. If Dan runs at a rate of 8 miles per hour and swims at a rate of 6 miles per hour, what is his average rate for the entire trip in miles per minute?
Select the correct option.
A) 1/9  B) 2/15  C) 3/15  D) 1/4  E) 3/8

Solution: Dan travels 4 miles round trip.   Running part: (2/8 = 1/4*60= 
1/4*60 = 15
15 minutes)   Swimming Part: (2/6= 1/3*60= 
1/3*60 = 20
20 minutes)   4 miles in (15+20) minutes   4/35= 1/9 mile per minute   1/9nswer: 1/9 mile per minute
Answer: A
A man has only 20-paise and 25-paise coins in a bag. If he has 50 coins in all totaling to Rs.11.25, then the number of 20-paise coins is Pick
A) 28
B) 27
C) 26
D) 25
E) 24

Solution: x=20p;y=25p;   x+y=50;   0.20x+0.25y=11.25;   25x+25y=1250;   20x+25y=1125;   =>x=25;   ANSWER:25
Answer: D
A takes twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2days. B can do the work alone in?  Select:
A) 8
B) 10
C) 12
D) 15
E) 20

Solution: Suppose A,B,12 takes x,x/2,x/3 hours to finish the work   Then, 1/x + 2/x + 3/x = 1/2   6/x = 1/2   x = 12   Answer is 12
Answer: C
The cost of 2 books and 2 magazines is $26. The cost of 1 book and 3 magazines is $27. How much does 1 magazine cost? Choose the correct choice.
A) 8	B) 5	C) 7	D) 4	E) 6

Solution: Let the cost of 1 book = x, let the cost of 1 magazine = y   2x + 2y = 26   x = (26 - 2y)/2   x = 13 - y   Again,   (13 - y) + 3y = 27   13 + 2y = 27   2y = 14   y = 7   Answer: 7
Answer: C
If 45-[28-{37-(15-*)}]= 57, then * is equal to:  Pick:
A) -29  B) -19  C) 18  D) 29  E) 39

Solution: 45-[28-{37-(15-*)}]= 57 => 45-[28-{37-15+*}]=57   45-[28-37+15-*]=57 => 45[43-37-*]=57   45-[6-*]=57 => 45-6+*=57   39+*=57 => *=57-39= 
57-39 = 18
18   ANSWER:18
Answer: C
Five different books (A, B, C, D and E) are to be arranged on a shelf. Books C,D and E are to be arranged first and second starting from the right of the shelf. The number of different orders in which books A, B and may be arranged is	Select:	A) 1!	B) 2!	C) 5!	D) 15!	E) 24!

Solution: Solution   Since books C,D and E are arranged first and second, only books A and B will change order. Therefore it an arrangement problem involving 2 items and the number of different order is given by   2!   Answer 2!
Answer: B
A line has a slope of 3/4 and intersects the point R (-12, -39). At which point does this line intersect the x-axis?
Pick
A) (40,0)
B) (30,0)
C) (0,40)
D) (40,30)
E) (0,30)

Solution: Assume that the equation of the line is y=mx+c, where m and c are the slope and y-intercept.   You are also given that the line crosses the point (-12,-39), this means that this point will also lie on the line above.   Thus you get -39=m*(-12)+c , with m=3/4 as the slope is given to be 3/4.   After substituting the above values, you get c = -30.   Thus the equation of the line is y=0.75*x-30 and the point where it will intersect the x-axis will be with y coordinate = 0.   Put y=0 in the above equation of the line and you will get, x=40.   Thus, the point R of intersection is (40,0).   (40,0) is the correct answer.
Answer: A
A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used? Choose the correct answer:
A) 8	B) 4	C) 5	D) 7	E) 6

Solution: 7 * 8 : 9 * x = 8:9 => x= 7   Answer:7
Answer: D
A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 28 minutes. When both pipes are opened, find when the cistern will be full?	Answers: A) 27 B) 76 C) 70 D) 21 E) 28

Solution: 1/20 - 1/28 = 1/70   70 minutes.Answer: 70
Answer: C
A certain city with a population of 60,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?  Select:	A) a) 10,700	B) b) 10,800	C) c) 10,900	D) d) 11,000	E) e) 5,000

Solution: Let x = number of people in smallest district   x*1.1 = number of people in largest district   x will be minimised when the number of people in largest district is maximised   10*x*1.1 = 11x = total number of people in other districts   So we have 11x + x = 60k   x = 5,000   Answer : e) 5,000
Answer: E
A and B start a business with Rs.2000 and Rs.8000 respectively. How should they share their profits at the end of one year?  Choose the correct option:
A) 3:5 B) 1:4 C) 3:1 D) 3:2 E) 3:9

Solution: They should share the profits in the ratio of their investments.   The ratio of the investments made by A and 1:4 =   2000 : 8000 => 1:4   Answer:1:4
Answer: B
Find the sum to 200 terms of the series 1 + 4 + 6 + 5 + 11 + 6 + ....	Select the correct option:
A) 30,200 B) 29,800 C) 30,400 D) 40,400 E) None of these

Solution: Spot the above series is a combination of two APs.   The 1st AP is (1 + 6 + 11 + ....) and the 2nd AP is (4 + 5 + 6 + ...)   Since the terms of the two series alternate   S =(1 + 6 + 11 + .... to 100 terms) + (4 + 5 + 6 + .... to 100 terms)   => 100[2 x 1 + 99 x 5]/2 + 100[2 x 4 + 99 x 1]/2 --->(Using the formula for the sum of an AP)   =>50[497 + 107] =50[604] = 30200   Alternatively, we can treat every two consecutive terms as one.   So, we will have a total of 100 terms of the nature:   (1 + 4) + (6 + 5) + (11 + 6).... -> 5, 11, 17,....   Now, a= 5, d=6 and n=100   Hence the sum of the given series is   S= 100/2 x[2 x 5 + 99 x 6]   => 50[604]   => 30200   30,200NSWER:30,200
Answer: A
The average of first six prime numbers which are between 60 and 90 is
Select the correct option:
A) 35.4 B) 42 C) 45.7 D) 57 E) 72.33

Solution: 72.33xplanation :   first six prime numbers which are between 60 and 90 = 61, 67, 71, 73, 79, 83   average = (61 + 67 + 71 + 73 + 79 + 83)/6   = 72.33   Answer : 72.33
Answer: E
P is five times as old as Q, and Q is seven years older than R. If R is z years old, what is P’s age in terms of z?	Choose the correct answer: A) 5z + 7 B) 5z − 35 C) 5z + 35 D) (z + 7)/5 E) (z − 7)/5

Solution: P = 5Q   Q = R+7 = z+7   P = 5(z+7) = 5z + 35   The answer is 5z + 35.
Answer: C
A certain roller coaster ride has between 29 and 150 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on. Which of the following is the sum of the greatest possible number of people in the line and the least possible number of people in the line?  Pick.
A) 269 B) 184 C) 174 D) 169 E) 142

Solution: Let x be the number of people   x=5m+2   x=6n   x=30p+12   Least = 30+12= 
30+12 = 42
42   Highest= 30*4+12= 
30*4+12 = 132
132   Total= 174   ANSWER:174
Answer: C
If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 54/r years. If Joe's parents invested $5,000 in a long-term bond that pays 6 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Joe is ready for college?	Choose one.
A) $20000	B) $15000	C) $12000	D) $10000	E) $9000

Solution: Since investment doubles in 54/r years, then for r=6 it'll double in   54/6= 
  54/6 = 9
~9 years (we are not asked about the exact amount so such an approximation will do). Thus after 18 years investment will become $5,000*2=$10,000 .   Answer: $10000.
Answer: D
A pair of articles was bought for $50 at a discount of 60%. What must be the marked price of each of the article? Choose the correct choice from the following.
A) $25	B) $10	C) $29.65	D) $35.95	E) $45.62

Solution: S.P. of each of the article = 50/2= 
50/2 = 25
$25   Let M.P= $x   40% of x = 25   x = 25*.4= 
25*.4 = 10
$10   Answer is $10
Answer: B
If APPLE is coded as 0 and FLOWER is coded as 63, then BASKET is coded as Select
A) 2	B) 19	C) 35	D) 40	E) None

Solution: APPLE = 1+16+16+12+5= 
1+16+16+12+5 = 50
50 i.e 5*0=0   FLOWER = 6+12+15+23+5+18= 
6+12+15+23+5+18 = 79
79 i.e 7*9=63   BASKET =2+1+19+11+5+20= 
2+1+19+11+5+20 = 58
58 5*8=40   ANSWER:40
Answer: D
Annie will be half as old as Larry in 3 years. Annie will also be one-third as old as Jerome in 5 years. If Jerome is 12 years older than Larry, how old is Annie? Choose the correct option: A) 5 B) 8 C) 19 D) 26 E) 34

Solution: J = L+12   (1) 2(5+3) = L+3   (2) 3(5+5) = J+5 = L+17   Let's subtract equation (1) from equation (2)   5+9= 
5+9 = 14
14   5= 5   The answer is 5.
Answer: A
Barbara has 8 shirts and 9 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants?  Select
A) 41	B) 66	C) 36	D) 70	E) 56

Solution: 8 shirts   9 pants   we can combine 2 shirts with (9-3) pants   2*6= 
2*6 = 12
12   we can combine the other shirts (6) with any pants (9)   6*9= 
6*9 = 54
54   Thus total :12+54= 
12+54 = 66
66	ANS:66
Answer: B
When 1/10 percent of 4,000 is subtracted from 1/10 of 4,000, the difference is	Choose the correct choice from the following:  A) 396  B) 36  C) 3996  D) 40  E) 400

Solution: (1/10)*4000 - (1/10)%*4000 =   400 - (1/1000)*4000 =   400 - 4= 
400 - 4 = 396
396   The answer is 396.
Answer: A
A river 3m deep and 36 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is? Choose the correct choice from the following options: A) 4500 B) 2678 C) 3600 D) 3400 E) 2500

Solution: (2000 * 3 * 36)/60= 
(2000 * 3 * 36)/60 = 3_600
3600 M3   Answer:3600
Answer: C
Rates for having a manuscript typed at a certain typing service are $6 per page for the first time a page is typed and $4 per page each time a page is revised. If a certain manuscript has 100 pages, of which 35 were revised only once, 15 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?
Select:
A) $860	B) $850	C) $840	D) $830	E) $820

Solution: 50 pages typed 1x   35 pages typed 2x (original + one revision)   15 pages typed 3x (original + two revisions)   50(6)+35(6+4)+15(6+4+4)=300+350+210= 
300+350+210 = 860
860   $860nswer - $860
Answer: A
A can do a piece of work in 20 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?  Pick:
A) 10 2/5  B) 10 2/0  C) 12 2/3  D) 10 2/1  E) 10 2/3

Solution: 2/20 + 4/15 + x/20 = 1   x = 38/3 = 12 2/3 Answer: 12 2/3
Answer: C
At the start of an experiment, a certain population consisted of 3 animals. At the end of each month after the start of the experiment, the population size was double its size at the beginning of that month. Which of the following represents the population size at the end of 6 months?	Pick one.
A) 2^3
B) 3^2
C) 2(3^10)
D) 3(2^6)
E) 3(10^2)

Solution: 3*2^n where n is the #of month --> 3*2^6 Answer (3(2^6))
Answer: D
In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.42, the number of 25 paisa coins is?  Pick.
A) 16	B) 42	C) 16	D) 84	E) 26

Solution: 5x 6x 2x   50 25 100   250x + 150x + 200x = 4200   600x = 4200   x = 7 => 6x = 42   Answer: 42
Answer: B
The HCF of two numbers is 42 and the other two factors of their LCM are 11 and 12. What is the largest number.	Pick one:	A) 462	B) 450	C) 480	D) 504	E) 555

Solution: Explanation:   HCF of the two numbers = 42   HCF will be always a factor of LCM   42 is factor of LCM   other two factors are 11 & 12   Then the numbers are (42 11) and (42 x 12)   = 462 and 504   Answer: Option 504
Answer: D
What will be the percentage increase in the area of the cube's surface if each of the cube's edges grows by 20%?  Choose the most appropriate option:	A) 33%	B) 44%	C) 55%	D) 56%	E) 73%

Solution: The question is very easy. My logic is the following:   A surface = 6*a^2   After 20% increase A surface = 6* ((1.2a)^2) = 6*1.44*a^2   The increase in the surface area = (6*1.44*a^2 - 6*a^2)/6*a^2 = (6*a^2(1.44-1))/(6*a^2) = 1.44-1= 
1.44-1 = 0.44
0.44= 44%   ANSWER:44%
Answer: B
there are 3 girls and 6 boys. how many kids are there? Choose the correct choice from the following answers:
A) 10
B) 19
C) 20
D) 9
E) 12

Solution: 9
Answer: D
In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?	Choose the correct choice from the following choices:
A) 30 B) 10 C) 18 D) 28 E) 32

Solution: Answer   Let A be the set of students who have enrolled for English and B be the set of students who have enrolled for German.   Then, (A U B) is the set of students who have enrolled at least one of the two subjects. As the students of the class have enrolled for at least one of the two subjects, A U B = 40   We know A U B = A + B - (A n B)   i.e, 40 = A + 22 - 12   or A = 30 which is the set of students who have enrolled for English and includes those who have enrolled for both the subjects.   However, we need to find out the number of students who have enrolled for only English = Students enrolled for English - Students enrolled for both German and English   = 30 - 12= 
30 - 12 = 18
18.   choice is (18)
Answer: C
There are 10 points in a plane out of which 4 are collinear. Find the number of triangles formed by the points as vertices.  Choose one:
A) 102  B) 116  C) 103  D) 512  E) 105

Solution: The number of triangle can be formed by 10 points = 10C3.   Similarly, the number of triangle can be formed by 4 points when no one is collinear=4C3.   In the question, given 4 points are collinear, Thus, required number of triangle can be formed,   = 10C3-4C3 = 120-4= 
120-4 = 116
116.   Ans: 116
Answer: B
If 99<x<199 and 10<y<100, then the product xy CANNOT be equal to: Choose the correct choice from the following answers:
A) 19,104 B) 19,903 C) 19,356.732 D) 19,502 E) 19,880

Solution: Correct Answer: (B)   Determine the range of xy by multiplying the two extremes of each individual range together. The smallest value of xy must be greater than 99 * 10. The largest value must be less than 199 * 100. This means that 990 < xy < 19,900. (19,903) is outside of this range, so it is not a possible product of xy.
Answer: B
Three numbers are in the ratio 4 : 5 : 6 and their average is 25. The largest number is :	Choose the correct option:
A) 30 B) 98 C) 27 D) 21 E) 22

Solution: Explanation:   Let the numbers be 4x, 5x and 6x, Then, (4x + 5x + 6x ) / 3 = 25   => 5x = 25   => x = 5.   Largest number 6x = 30.'   30nswer: 30) 30
Answer: A
If x and y are integers such that x^2= 2y and xy = 256, then x – y = ? Options: A) -30 B) -24 C) -5 D) 5 E) 20

Solution: here x and y are integers .   x^2=2y,xy =256.   substitute (x^2)/2=y in xy => x^3=256*2=>x^3=512.   here x^3 is positive ,   x is also positive.   x=8 then y=32.   x-y=-24   so option -24 is correct
Answer: B
The entire contents of a full sack of flour can be used to make 15 cupcakes and 8 pizzas. The same full sack of flour can be used to make 5 cupcakes and 14 pizzas. If a full sack of flour is used to make only pizzas, how many pizzas can be made?	Select:
A) 18 1/4 B) 18 1/2 C) 18 3/4 D) 17 E) 19 1/4

Solution: 15x+8y=5x+14y   x=3/5y. Answer 17
Answer: D
If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?  Choose the correct choice from the following answers
A) Rs.1520  B) Rs.1570  C) Rs.1500  D) Rs.1550  E) Rs.1700

Solution: Let the cost price of an article be Rs. x.   (19% of x) - (12% of x) = 105   19x/100 - 12x/100 = 105 => 7x = 105 * 100   => x = 1500   Rs.1500ost price = Rs.1500   Answer:Rs.1500
Answer: C
A manufacturer is using glass as the surface for the multi-touch screen of its smartphone. The glass on the manufactured phone has a 7% probability of not passing quality control tests. The quality control manager bundles the smartphone in groups of 10. If that bundle has any smartphone that does not pass the quality control test, the entire bundle of 10 is rejected.
What is the probability that a smartphone bundle that will be rejected by quality control?
Choose the correct answer: A) 0.25 B) 1-0.93^10 C) 1-0.95^10 D) 1-0.05^10 E) 0.95^10

Solution: Find the probability of the opposite event and subtract from 1.   The opposite event is that bundle will NOT be rejected by quality control, which will happen if all 10 phones pass the test, so P(all 10 phones pass test)=0.93^10.   P(at least one phone do not pass the test)=1- P(all 10 phones pass test)=1-0.93^10.   Answer: 1-0.93^10.
Answer: B