MU-NLPC/Calc-aqua_rat huggingface dataset:
In ten years, David will be four times as old as Aaron. Twenty years ago, David was twice as old as Ellen. If David is five years older than Ellen, how old is Aaron? Choose the correct choice from the following choices
A) 0.5–5  B) 6–10  C) 11–15  D) 16–20  E) 21–25

Solution: Let David's present age be 'd', 0.5–5aron's present age be 'a' and Ellen's present age be 'e'   In ten years, David will be four times as old as 0.5–5aron --> d+10 = 4(a+10)   Twenty years ago, David was twice as old as Ellen --> d-20 = 2(e-20)   David is seven years older than Ellen --> d = e + 5   e+5-20 = 2e-40   e-15 = 2e-40   e = 25   d = 32   42 = 4a + 40   a = 0.5   0.5–5nswer: 0.5–5
Answer: A
If x = √11 + √20, y = √15 + √17 and z = √14 + √18, then which of the following holds true? Choose the correct choice from the following options:  A) x < y < z  B) Y< z < x  C) y < x < z  D) x < z < y  E) None of these

Solution: By squaring and simplifying,   x2 = 31 + 2√220   y2 = 32 + 2√255   z2 = 32 + 2√252   x2 < z2 < y2 => x < z < y.   Answer:x < z < y
Answer: D
a metallic cuboid of dimensions 27x18x12 m is melted.find the minimum amount of the volume of molten metal which should be added to mould it into a cube whose edge is 'a' cm where a is an integer.  Choose the correct choice from the following answers:	A) 16 m	B) 17 m	C) 18 m	D) 19 m	E) 15 m

Solution: volume of cuboid = 27*18*12 = (27*27*8)= (3*3*2)^3= 18^3   so no amount of the volume of molten metal should be added to mould it into a cube whose edge is 'a' cm where a is 18 m.   ANSWER:18 m
Answer: C
Gasoline varies in cost from $0.95 to $1.15 per gallon. If a car’s mileage varies from 16 to 24 miles per gallon, what is the difference between the most and least that the gasoline for a 480-mile trip will cost?
Select the correct option.
A) $15.50
B) $15.72
C) $16.10
D) $16.50
E) $17.01

Solution: Solution:   We know that the per gallon cost of gasoline varies from $0.95 - $1.15.   Now we want to find the MAXIMUM difference between the least amount of money spent on gasoline and the largest amount of money spent i.e. to calculate max. trip cost - min. trip cost.   Mileage is given to be 16 to 24 miles per gallon, thus to travel 480 miles you will need gasoline in the range 480/24 to 480/16 which is 20 to 30 gallons.   So, for these 20 gallons and 30 gallons of gasoline the cost is as follows: (divide this task into 2 parts, 1 for 30 gallons and 2nd one for 20 gallons).   Case 1: for 30 gallons the cost is 30*0.95 to 30*1.15 which is $28.50 to $34.50   Case 2: for 20 gallons the cost is 20*0.95 to 20*1.15 which is $19.00 to $23.00   Thus, the maximum cost of the 480 mile trip is $34.50 and minimum is $19.00   so the difference is $34.50 - $19.00 = $15.50   $15.50nswer: $15.50 34.50 -  19.00= 
 34.50 -  19.00 = 15.5
$15.50   $15.50nswer: $15.50
Answer: A
Mitchell took a box of pushpins and counted how many there were of each colour. There was 1 red pushpin, 5 blue pushpins, and 2 yellow pushpins. How many pushpins were there in all?  Pick:
A) 02 B) 04 C) 03 D) 05 E) 08

Solution: Add the numbers of pushpins.   1 + 5 + 2= 
1 + 5 + 2 = 8
8.   Answer is 08.
Answer: E
Robert spent $120 in buying raw materials, $195 in buying machinery and 10% of the total amount he had as cash with him. What was the total amount? Choose the correct choice:	A) A)$150	B) B)$210	C) C)$350	D) D)$160	E) E)$200

Solution: Let the total amount be x   then, (100-10)% of x = 120+195   90% of x = 315   90x/100 = 315   x = $350   Answer is $350
Answer: C
Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 115. If the ratio of his marks in English and Maths is 5:1, find his marks in Science?  Select the correct option:
A) 18
B) 77
C) 25
D) 55
E) 31

Solution: S:E = 1:3   E:M = 5:1   ------------   S:E:M = 5:15:3   5/23 * 115= 
5/23 * 115 = 25
25   Answer: 25
Answer: C
In an election, candidate A got 85% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate. Choose the correct option
A) 330000  B) 340000  C) 347000  D) 356000  E) 404600

Solution: Total number of invalid votes = 15 % of 560000   = 15/100 × 560000   = 8400000/100= 
8400000/100 = 84_000
84000   Total number of valid votes 560000 – 84000= 476000   Percentage of votes polled in favour of candidate A = 85 %   Therefore, the number of valid votes polled in favour of candidate A = 85 % of 476000   = 85/100 × 476000   = 40460000/100= 
40460000/100 = 404_600
404600   404600)
Answer: E
A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 26 m * 2 m * 0.75 m?
Choose the correct choice from the following options:
A) 29798	B) 27908	C) 78902	D) 26000	E) 27991

Solution: 26 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x   26 = 1/1000 * x => x   = 26000   Answer: 26000
Answer: D
Helen went to the stationers and bought things worth Euro 23, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?  Choose the correct option:
A) uro 16.70
B) uro 15.70
C) uro 13.70
D) uro 18.70
E) uro 17.70

Solution: E   Euro 17.70   Let the amount taxable purchases be Euro x.   Then, 6% of x = 30/100   x = (30/100 x 100/6) = 5.   Cost of tax free items = uro 17.70uro [  23 - (5 + 0.30)= 
  23 - (5 + 0.30) = 17.7
uro 17.70uro 17.70
Answer: E
In the coordinate plane, the points F (-1,1), G (1,2), and H (2,1) lie on a circle with center P. What are the coordinates of point P ? Pick:  A) (0.5,0.5)  B) (1,1)  C) (1,2)  D) (1,-2)  E) (2.5, -2.5)

Solution: I thought I need to find the 4th point that would lie on the circle   Hence my answer was D (1,-1)   But the the center of the circle will lie on (0.5,0.5)   (0.5,0.5)
Answer: A
How many meters of carpet 50cm, wide will be required to cover the floor of a room 30m * 20m?  Select:	A) 1600	B) 450	C) 300	D) 1200	E) 600

Solution: 50/100 * x = 30 * 20 => x = 1200   Answer: 1200
Answer: D
The market value of a certain machine decreased by 15 percent of its purchase price each year. If the machine was purchased in 1982 for its market value of $8,000, what was its market value two years later?  Choose the correct choice from the following:  A) $8,000  B) $5,600  C) $3,200  D) $4,400  E) $800

Solution: B.   Market value in 1982= $ 8000   Market value in 1983 = $ 8000- ($ 8000 x 15/100) = 8000-1200= 
8000-1200 = 6_800
$ 6800   Market value in 1984= Market value in 1983 - (15 % of $8000)= 6800-1200= 
6800-1200 = 5_600
$5600
Answer: B
The water level in a rectangular swimming pool measuring 60 feet by 10 feet is to be lowered by 6 inches. How many gallons of water must be removed? (1 cu ft = 7.5 gallons)	Choose the correct option: A) 100 B) 2250 C) 750 D) 1200 E) 5625

Solution: 6 inches = 1/2 feet (there are 12 inches in a foot.), so  60*10*1/2= 
 60*10*1/2 = 300
300 feet^3 of water must be removed, which equals to   300*7.5= 
  300*7.5 = 2_250
2250 gallons.   Answer: 2250
Answer: B
A vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. How much of the
mixture must be drawn off and replaced with water so that the mixture may be half water and half
syrup?
Choose the correct choice from the following answers
A) 13
B) 14
C) 15
D) 16
E) 17

Solution: Explanation :   Let the quantity of the initial liquid in the vessel = 8 litre and quantity of water in the initial liquid = 3   litre andquantity of syrup in the initial liquid = 5 litreLet x litre of the mixture is drawn off and replaced   with waterQuantity of water in the new mixture = 3−3x8+xQuantity of syrup in the new mixture =   5−5x8Given that in the new mixture, quantity of water = quantity of   syrup⇒3−3x8+x=5−5x8⇒10x8=2⇒5x4=2⇒x=85⇒85litre   Initially we assumed that the quantity of the initial liquid in the vessel = 8 litre for   the ease of calculations. For that 8/5 litre of the mixture to be drawn off and replaced   with water so that the mixture may be half water and half syrup   Now, if the initial liquid in the vessel = 1 litre, quantity of the mixture to be drawn off   and replaced with water so that the mixture may be half water and half syrup   =85×18=15   It means 1/5 of the mixture has to be drawn off and replaced with water so that the mixture   may be half water and half syrup   Answer : Option 15
Answer: C
If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability W that a number picked up in first 90 positive integers will have the result of # as an odd digit ?	Choices:  A) (a) 4/10  B) (b) 4/9  C) (c) 1/2  D) (d) 6/10  E) (e) 5/9

Solution: Here is how I did it. Probably there may be better way to do it.   First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90.   That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment.   So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17)   Number of integers, whose digits add to 1: 1 and 10 = 2   Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4   Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6   Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8   Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10   Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8   Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6   Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4   Number of integers, whose digits add to 16: 79, 88 = 2   So in total there are  2+4+6+8+10+8+6+4+2= 
 2+4+6+8+10+8+6+4+2 = 50
50 such numbers   Probability W= 50/90 = 5/9   Correct answer (e) 5/9
Answer: E
Suresh borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next two years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of 11 years is Rs.8160, how much money did he borrow?	Select:
A) s.8500
B) s.6000
C) s.10880
D) s.9000
E) s.7000

Solution: using the formula S.I=P*T*R/100   (x*6*3/100)+(x*9*2/100)+(x*13*3/100)=8160   x=10880   ANSWER:s.10880
Answer: C
a three digit number, sum of the digit is 17, the sum of square of digits is 109, if it is subtracted wit 495 the number gets reversed, find the three digit number.  Choose one:
A) 683	B) 863	C) 368	D) 686	E) 786

Solution: from the given options   863-495= 
863-495 = 368
368   therfore ans is 863   ANSWER:863
Answer: B
Mohan purchased 12 kgs of rice at the rate of Rs.26 per kg and 8 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper?
Select:
A) A)Rs.598	B) B)Rs.594	C) C)Rs.596	D) D)Rs.595	E) E)Rs.520

Solution: Explanation:   Price of 12 kgs of rice at Rs.26/kg = 12x26 = Rs.312   Price of 8 kgs of pulses at Rs.26/kg = 8x26 = Rs.208   Therefore, Total amount = Rs.312+Rs.208 = Rs.520.   Answer: Option Rs.520
Answer: E
A can do a piece of work in 5 days and B can do it in 6 days how long will they both work together to complete the work?	Pick one
A) 2 6/11
B) 2 8/11
C) 2 7/11
D) 2 9/11
E) 2 10/11

Solution: Explanation:   A’s one day work = 1/5   2 8/11’s one day work = 1/6   (A+2 8/11)’s one day work = 1/5 + 1/6 = 11/30 => time = 30/11 = 2 8/11 days   Answer: Option 2 8/11
Answer: B
What is the sum of the numbers between 1 and 20, inclusive?  Choose the correct choice from the following
A) 310	B) 200	C) 215	D) 285	E) 210

Solution: Sol. 1+2+3...17+18+19+20   answer. 210
Answer: E
The length of the shorter side of a rectangle is 2 units. The length of each
diagonal is 4 units. What is the acute angle between the diagonals?
Pick:  A) 15o  B) 22.5o  C) 45o  D) 60o  E) 75o

Solution: Suppose the vertices of the rectangle are labeled A, B, C, and D in such a way   that AB is the shorter side. Let O be the intersection point of the two diagonals. Then   4AOB is equilateral   correct answer 60o
Answer: D
Sixty five percent of a number is 21 less than four fifth of that number. What is the number ? Choose the correct choice.
A) 240 B) 180 C) 120 D) 220 E) 140

Solution: Let the number be x.   Then, 4*x/5 –(65% of x) = 21   4x/5 –65x/100 = 21   5 x = 2100   x = 140.   Answer is 140.
Answer: E
For every order, a certain mail-order company charges a shipping fee of $3 plus an additional $2 if the value of the order is over $50 but not over $100 or an additional $3 if the value of the order is over $100. How much greater are the total shipping fees for 2 orders of $75 each than the total shipping fee for 2 order of $250 ?	Select:  A) $1  B) $2  C) $3  D) $4  E) $5

Solution: Total cost involved for each 75 $ shipment:  3+2= 
 3+2 = 5
5 $. Thus, for two such orders= 10$   Total cost involved for a 250$ shipment: 3+3= 
3+3 = 6
6$. Thus, for two such orders= 12$   The difference = 2$.   $2
Answer: B
A watch was sold at a loss of 10%. If the watch was sold for $24 more, there would have been a gain of 6%. What is the cost price?	Choose the correct choice from the following answers:
A) $120
B) $150
C) $180
D) $210
E) $240

Solution: 0.9x + 24 = 1.06x   0.16x = 24   x = 150   The answer is $150.
Answer: B
What is the absolute value of twice the difference of the roots of the equation D=5y^2 − 20y + 15 = 0 ?	Choose the correct choice from the following options: A) 0 B) 1 C) 2 D) 3 E) 4

Solution: D=5y^2 − 20y + 15 = 0 --> y^2 − 4y + 3 = 0 --> y=1 or y=3. The difference is 2, twice the difference is 4.   Answer: 4.
Answer: E
If (2x + 2)(x + 3) = 2x^2 + x, what is a possible value of x?	Choose the correct answer
A) -6/7  B) -6/8  C) -5/7  D) 8/7  E) 6/8

Solution: Rearranging the given expression:   (2x + 2)(x + 3) = 2x^2 + x   i.e. 2x^2 + 8x + 6 = 2x^2 + x   i.e. 7x = -6   i.e. x = -6/7   -6/7nswer: Option -6/7   Had it been a difficult expression to solve further, then we could have used options to check which one satisfies the expression after solving it as further as possible.
Answer: A
The water from one outlet, flowing at a constant rate, can fill a swimming pool in 12 hours. The water from a second outlet, flowing at a constant rate, can fill the same pool in 8 hours. If both outlets are used at the same time, approximately what is the number of hours required to fill the pool?  Choose the correct answer
A) 0.22	B) 0.31	C) 2.50	D) 3.21	E) 4.8

Solution: Always remember RT=W i.e Rate*Time = Work   Also remember that rate can be added or subtracted. For e.g if A do a work in 2 day and B do a work in 2 day.   They both of them together will do a work in 1 day.   So now your question first determine both outlets rate.   1st outlet rate = 1/12 (R=W/T here W=1 work, T = 12hrs)   2nd outlet rate = 1/8 (R=W/T here W=1 work, T = 8hrs)   Both of them working together rate = 1st outlet rate + 2nd outlet rate = 1/12+1/8 = 5/24   again apply the formula RT=W   T = W/R = 1/5/24 = 24/5= 
24/5 = 24/5 = around 4.8
4.8   Answer is 4.8.
Answer: E
If (2a + 3b)/(5a - 3b) = 23/5 , then the value of b : a is ?  Select
A) 4 : 1 B) 1 : 4 C) 4 : 5 D) 5 : 4 E) 1 : 2

Solution: (2a + 3b)/(5a - 3b) = 23/5   => 10a + 15b = 115a - 69b   => 105a = 84b => 5a = 4b   a/b = 4/5   ANSWER:5 : 4
Answer: D
Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?	Select.
A) 3 sec	B) 5 sec	C) 6 ½ sec	D) 7 ½ sec	E) 5 ½ sec

Solution: 7 ½ sec   7 ½ sec   70 + 50= 
70 + 50 = 120
120 * 5/18= 100/3 mps   7 ½ sec = 150 + 100= 
150 + 100 = 250
250 m   T= 250 * 3/100 = 15/2 = 7 ½ sec
Answer: D
Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 14000, then find his savings? Select
A) 3600 B) 2800 C) 3608 D) 3602 E) 3603

Solution: Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively.   Income, 5x = 14000 => x = 2800   Savings = Income - expenditure = 5x - 4x = x   So, savings = Rs. 2800.   Answer:2800
Answer: B
In how many ways can the letters of the word ARRANGED be arranged in a row so that the vowels appear in alphabetic order?  Choose one
A) 6720 B) 5280 C) 6240 D) 5202 E) 4020

Solution: three letters can be arranged in 3! ways.   only one combination AEI is required.   8 letters can be arranged in 8! ways.   thus 8!/ 3! * 1 = 6720.   6720
Answer: A
Two numbers are respectively 71% and 80% more than a third number. The percentage that is first of the second is?  Answers.
A) 4%
B) 5%
C) 6%
D) 7%
E) 8%

Solution: I II III   171 180 100   180----------171   100-----------? => 5%   Answer:5%
Answer: B
A wire can be bent in the form of a circle of radius 56cm. If it is bent in the form of a square, then its area will be
Pick:
A) 7744
B) 8844
C) 5544
D) 4444
E) 3444

Solution: length of wire = 2 PieR= 2 *(22/7 )*56= 
2 *(22/7 )*56 = 352
352 cm   side of the square= 352/4= 
352/4 = 88
88cm   area of the square= 88*88= 
88*88 = 7_744
7744 sq cm 7744nswer: 7744
Answer: A
Machine M, N, O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 1/3 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N? Choose the correct answer:  A) 1/2  B) 1/3  C) 4/13  D) 8/29  E) 6/33

Solution: Now ultimately the speed of every machine is given with respect to Mach O.   So lets assume the speed of O, say 12 hrs to make x units (assuming 6 because we can see we will need to divide by 3 and 4   Mach O makes x units in 12 hrs   So, Mach N = 1/3 of O = 1/3*12= 
1/3*12 = 4
4 hrs to make x units   and Mach M= 3/4 of N = 3/4*4 = 6 hrs to make x units   No they are running simultaneously. Lets see how much each mach makes in 1 hr   Mach O = x/12 units   Mach N = x/4 units   Mach M = x/6 units   In 1 hr, together they make - x/12+x/4+x/6 = x/2   So what ratio of this has Mach N made?   (x/4) / (x/2) = 1/2   1/2ns:1/2=1/2
Answer: A
What is the area of a square field whose diagonal of length 40 m? Answers.
A) 287
B) 269
C) 750
D) 200
E) 800

Solution: d2/2 = (40 * 40)/2= 
(40 * 40)/2 = 800
800   Answer:800
Answer: E
A circular mat with radius 10 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat? Choose one
A) 5/12
B) 2/5
C) 0.5451
D) 3/4
E) 5/6

Solution: C.   It is a circle inscribed in a square.   Square side=24---> square(table) area=24^2   0.5451ircle diameter=20---> 0.5451ircle area=PiR^2=100Pi (where Pi=~3.14)   covered fraction=100*3.14/24*24= 
100*3.14/24*24 = 314
~314/24*24=0.5451   0.5451
Answer: C
A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?	Choose the correct choice from the following:  A) 3.75 days  B) 3.78 days  C) 3.25 days  D) 3.15 days  E) 2.75 days

Solution: 1/6 + 1/10 = 8/30 = 4/15   15/4= 
15/4 = 15/4 = around 3.75
3.75 days   3.75 daysnswer: 3.75 days
Answer: A
In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 128 of the workers of that company are men, how many of the workers are women?
Choose one:
A) 80 B) 95 C) 105 D) 112 E) 210

Solution: Set up equation:   x = total number of workers   128 = 0,4 * 2/3 * x + 0,8 * 1/3 * x   128 = 16/30 x   x = 240   240 - 128= 
240 - 128 = 112
112   Answer 112
Answer: D
Excluding stoppages, the speed of a bus is 82 kmph and including stoppages, it is 75 kmph. For how many minutes does the bus stop per hour? Answers
A) 5.12 B) 4.13 C) 6.15 D) 7.5 E) None of these

Solution: Due to stoppages, it covers 7 km less.   Time taken to cover 7 km = ((7/82)Ã—60) = 5.12 min.   Option(5.12) is correct
Answer: A
A man can row his boat with the stream at 26 km/h and against the stream in 12 km/h. The man's rate is?
Choose the correct choice from the following answers:
A) 1 kmph
B) 4 kmph
C) 5 kmph
D) 7 kmph
E) 8 kmph

Solution: 7 kmphS = 26   US = 12   S = ?   S = (26 - 12)/2= 
(26 - 12)/2 = 7
7 kmph   Answer: 7 kmph
Answer: D
A car takes 6 hours to cover a distance of 504 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?  Choose the most appropriate option.
A) 48 Kmph
B) 50 Kmph
C) 52 Kmph
D) 56 Kmph
E) 60 Kmph

Solution: Time = 6   56 Kmphistence = 504   3/2 of 6 hours = 6 * 3/2= 
6 * 3/2 = 9
9 Hours   Required speed= 504/9= 
504/9 = 56
56 Kmph   56 Kmph
Answer: D
A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 4 cm. What is the length of the wire?  Options:
A) 116 cm B) 144 cm C) 168 cm D) 173 cm E) 189 cm

Solution: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.   π(4)^2 * h = (4/3)π (12)^3 => h   = 144 cm   Answer:144 cm
Answer: B
A man can row a distance of 5 km in 60 min with the help of the tide. The direction of the tide reverses with the same speed. Now he travels a further 40 km in 10 hours. How much time he would have saved if the direction of tide has not changed? Choose the correct choice from the following options: A) 2 B) 8 C) 1 D) 6 E) 5

Solution: Explanation:   He covered 5 km in 1 hour , so he might cover 40 km in 8 hours.   But he took 10 hours.   He would have saved 10 â€“ 8 = 2 hours.   2nswer: 2
Answer: A
Given positive even integer y, which of the following CAN be evenly divisible by y?	Pick one:
A) y + 1	B) 2y - 2	C) 2y + 1	D) 3y - 1	E) y + 1⁄2

Solution: This can be easily solved by substituting values:   Assume y to be 2   A. y + 1: 3 is not evenly divisible by 2   B. 2y - 2: 2 is evenly divisible by 2   C. 2y + 1: 5 is not evenly divisible by 2   D. 3y − 1: 5 is not evenly divisible by 2   E. y + 1⁄2: 5/2 is not evenly divisible by 2   Option 2y - 2
Answer: B
Given that there are 6 basketball players per team, how many ways can you select 2 basketball players from 3 teams if no more than one player can be selected from each team?	Choose the correct option
A) 15	B) 30	C) 60	D) 108	E) 90

Solution: 2 teams can be selected from 3 teams in 3C2 ways = 3 ways   as the condition is that the 2 players should be from different teams   one player can be chosen from 1st team in 6 ways   similarly another player can be chosen from 2nd team in 5 ways   Total number of ways to choose the player = 6 * 6 * 3= 
6 * 6 * 3 = 108
108 ways   Correct Answer - 108
Answer: D
A and B together can do a piece of work in 6 days and A alone can do it in 14 days. In how many days can B alone can do it?  Choose the correct choice from the following choices.
A) 12 days B) 15 days C) 21/2 days D) 21 days E) 22 days

Solution: Explanation:   A and B can do work 1/6 in 1 day   A alone can do 1/14 work in 1 day   B alone can do (1/6 -1/14) =2/21 work in 1 day   => complete work can be done in 21/2 days by B   Answer: Option 21/2 days
Answer: C
A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is 0, what is the value of x?
Answers.
A) -4 and 0	B) -2	C) 2	D) 4	E) Cannot be determined.

Solution: A number x is multiplied with itself --> X^2   added to the product of 4 and x --> X^2+4X   If the result of these two operations is 0 --> X^2+4X=0   i.e X^2+4X=0 is the Quadratic equation which needs to be solved.   X(X+4) = 0   Hence X=0. X=-4   IMO -4 and 0
Answer: A
Working individually, Amy can hang picture frames for 5 hours and John can hang picture frames in 4 hours. If Amy and John work together but independently at the task for 1 hour, at which point John leaves, how many remaining hours will it take Amy to complete the task alone?
Pick:
A) 11/20	B) 55/20	C) 5/2	D) 30/10	E) 3/22

Solution: 55/20
Answer: B
In a games hour 4 different types of players came to the ground? cricket 16, hokey 12, football 18, softball 13. How many players are present in the ground?	Select
A) 70  B) 52  C) 62  D) 59  E) 50

Solution: total number of players= 16+12+18+13= 
16+12+18+13 = 59
59   Answer is 59
Answer: D