MU-NLPC/Calc-aqua_rat huggingface dataset:
In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?	Choose the correct choice.
A) 6  B) 6.25  C) 6.5  D) 6.75  E) 7

Solution: Run rate is calculated by dividing runs scored by the number of overs.   in the first 10 overs there were 32 runs (10*3.2)   282-32= 
282-32 = 250
250   250/40= 
250/40 = 25/4 = around 6.25
6.25 run rate for the remaining 40 overs   ANSWER : 6.25
Answer: B
A batch of cookies was divided among three tins: 2/3 of all the cookies were placed in either the blue tin or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction T of the cookies that were placed in the other tins were placed in the green tin?	Options
A) 15/2	B) 9/4	C) 5/9	D) 7/5	E) 9/7

Solution: Blue tin or red tin: 2/3 (N)   Red tin: (1/3)N   Blue tin: (1/4)N   What the last statment meant, is it wants this fraction: (# of cookies in green tin)/(# of cookies in red and green tin)   # of cookies in green tin = 2N/3 - N/4 = 8N- 3N/12 = 5N/12   # of cookies in red and green tin = N/3 + 5N/12 = 9N/12   Fraction T= 5N/12 * 12/9N = 5/9 (5/9)
Answer: C
If 0 < a < b and k = (2a + 5b)/b , which of the following must be true?
Choose the correct choice from the following choices:
A) k < 2	B) k < 7	C) k < 9	D) k > 9	E) k > 11

Solution: Here's another approach:   k = (2a + 5b)/b   = 2a/b + 5b/b   = 2(a/b) + 5   Since 0 < a < b, we know that a/b is less than 1, which means that 2(a/b) is some number less than 2.   So, we get k = (some number less than 2) + 5   From here, we can see that k must be less than 7   Answer: k < 7
Answer: B
what rate percentage is 1 minute 48 seconds to an hour? Choose the correct choice from the following answers: A) 1% B) 2% C) 3% D) 4% E) 5%

Solution: 1m48s =108s   1hr=60m=3600s   % = 108*100/3600= 
108*100/3600 = 3
3%   ANSWER:3%
Answer: C
A cube has two of its faces painted half red and half blue. The other faces are completely painted white. What is the ratio between the red painted areas and the white painted areas of the cube?  Choose the correct choice from the following options:
A) 1:9	B) 2:3	C) 2:5	D) 1:6	E) 1:4

Solution: Let x be the area of each face of the cube.   The area painted red is 2(x/2) = x   The area painted white is 4x   The ratio of red to white is x:4x which is 1:4.   The answer is 1:4.
Answer: E
A dealer sold two of his cattle for Rs. 500 each. On one of them he lost 10% on the other, he gained 10%. His gain or loss percent in the entire transaction was:	Select:
A) 10% loss
B) 1% loss
C) 1% gain
D) Neither loss nor profit
E) 2% gain

Solution: Explanation:   Loss%= (common gain or loss % / 10)2 = (10/10)= 
(10/10) = 1
1%. Answer: 1% gain
Answer: C
A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 8 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank?	Choose the most appropriate option:  A) 0.008  B) 0.08  C) 0.064  D) 0.64  E) 6.4

Solution: The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder.   pi*64*10 = pi*h*100*100 (h is distance that the oil level dropped)   h = 640/10,000 = 64/1000= 
64/1000 = 8/125 = around 0.064
0.064 ft   The answer is 0.064.
Answer: C
A man with his bike travels to a place 150 km away at an average speed of 50 km per hour and returns at 30 km per hour. His average speed for the whole journey in km per hour is	Select
A) 35 B) 37 C) 37.5 D) 40 E) 39

Solution: Explanation :   Average speed = 2xy/(x + y) km/hr   = 2*50*30/(50 + 30)= 
2*50*30/(50 + 30) = 75/2 = around 37.5
37.5 km/hr   Answer : 37.5
Answer: C
Rates for having a manuscript typed at a certain typing service are $5 per page for the first time a page is typed and $2 per page each time a page is revised. If a certain manuscript has 100 pages, of which 40 were revised only once, 10 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?
Choose the correct choice from the following choices:
A) $430
B) $620
C) $650
D) $680
E) $770

Solution: For 100-40-10= 
100-40-10 = 50
50 pages only cost is 5$ per page for the first time page is typed - 50*5=250$;   For 40 pages the cost is: first time 5$ + 2$ of the first revision - 40*(5+2)=280$;   For 10 pages the cost is: first time 5$ + 2$ of the first revision + 2$ of the second revision - 10(5+2+2)=90$;   Total: 250+280+90= 
250+280+90 = 620
620$.   Answer: $620.
Answer: B
The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 20 terms of the arithmetic progression?
Choose the correct choice:  A) 300  B) 120  C) 150  D) 170  E) 200

Solution: n th term of A.P. is given by a+(n-1)d   4 th term = a+3d   12 th term = a+11d   Given a+3d+a+11d=20 --> 2a+14d=20 --> a+7d = 10   Sum of n term of A.P = n/2[2a+(n-1)d]   subsitiuing n = 20 ...we get 20/2[ 2a + 14d] = 20 [a+7d] = 20*10 = 200...   Answer is 200...
Answer: E
The value of x + x(xx) when x = 5 is:
Options:
A) A)36	B) B)16	C) C)18	D) D)130	E) E)10

Solution: x + x(xx)   Put the value of x = 2 in the above expression we get,   5 + 5(55)   = 5+ 5(5 × 5)   = 5 + 5(25)   =5 + 125= 
5 + 125 = 130
130   130
Answer: D
A train 400 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is? Choose the correct choice from the following answers:	A) 32	B) 56	C) 29	D) 27	E) 21

Solution: S = (400 + 300)/45 = 700/45 * 18/5= 
700/45 * 18/5 = 56
56   Answer: 56
Answer: B
A woman has three blouses of different colors, four skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?	Options:
A) 8
B) 12
C) 16
D) 17
E) 22

Solution: total ways = 3*4*2=24..   now its better to find the ways in which the pink blose and green skirty are together and subtract from total to get the answer..   the ways in which the pink blose and green skirty are together=1*1*2=2..   total ways =24-2=22..   22
Answer: E
I bought two stocks, for Rs. 500. I sold one at a loss of 20% and other at a gain of 25% and then I found each stick was sold at the same price. Find the cost of the stock sold at a loss?	Choose the correct choice from the following answers:
A) A)657
B) B)280
C) C)438
D) D)306
E) E)427

Solution: x*(80/100)   = (500 - x)125/100   x = 306.4   Answer: 306
Answer: D
The maximum number of student amoung them 1080 pens and 920 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :  Options.
A) 91
B) 40
C) 80
D) 90
E) None of these

Solution: Solution   Required number of student = H.C.F of 1080 and 920 = 40. Answer 40
Answer: B
A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 30,000, B receives:  Choose the correct choice from the following options
A) s. 10,000	B) s. 10,200	C) s. 10,400	D) s. 10,700	E) s. 10,800

Solution: Let C = x.   Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.   So, x + x + 5000 + x + 9000 = 50000   3x = 36000   x = 12000   A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.   B's share = Rs. (30000 x 17/50) = Rs. 10,200.   s. 10,200
Answer: B
A person travels equal distances with speeds of 6km/hr, 12km/hr,18km/hr. and takes a total time of 11minutes. Find the total distance ?  Choices
A) 1km  B) 1500mts  C) 1800mts  D) 2km  E) 1250mts

Solution: Let the each distance be x km   total distance = 3x   then total time,   (x/6)+(x/12)+(x/18) = 11/60   x=0.6   total distance = 3*0.6= 
3*0.6 = 1.8
1.8km= 1800 meters   correct option is 1800mts
Answer: C
If x and y are both odd prime numbers and x < y, how many distinct positive integer factors does 2xy have?	Pick one:
A) 3  B) 4  C) 6  D) 8  E) 12

Solution: The solution should be the same for all numbers that fulfill the condition above. As x and y are odd prime numbers, they must be > 2. Also, they must be distinct as x<y.   I choose x=3 and y=5:   How many factors does 2x3x5=30 have:   1, 2, 3, 5, 6, 10, 15, 30 = 8 distinct positive integer factors.   Hence, the correct answer is 8.
Answer: D
At a meeting, 6 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group? Choose the correct answer
A) 12 B) 72 C) 120 D) 144 E) 720

Solution: The number of arrangements of n distinct objects in a row is given by n!n!.   The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.   From Gmat Club Math Book (combinatorics chapter):   "The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:   R=n!n=(n−1)!R=n!n=(n−1)!"   (n−1)!=(6−1)!=120(n−1)!=(6−1)!=120   Answer: 120
Answer: C
The average weight of a group of boys is 20 kg. After a boy of weight 34 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?  Select the correct option
A) 12	B) 14	C) 18	D) 13	E) 10

Solution: Let the number off boys in the group originally be x.   Total weight of the boys = 20x   After the boy weighing 34 kg joins the group, total weight of boys = 20x + 34   So 20x + 34 = 21(x + 1) = > x = 13.   ANSWER:13
Answer: D
Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?  Choose the correct choice from the following answers:	A) 1261	B) 1262	C) 2686	D) 2687	E) 2676

Solution: 1261 = 8000(21/20)3   = 9261   = 8000   ---------   1261   1261nswer:1261
Answer: A
Two pipes A and B can fill a tank in 12 and 24 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
Choose one:
A) 9 B) 8 C) 6 D) 4 E) 10

Solution: Part filled by pipe A in 1 minute =1/12   =1/12   Part filled by pipe 8 in 1 minute =1/24   =1/24   Part filled by pipe A and pipe 8 in 1 minute=   1/12 + 1/24 =1/8   =1/12+1/24=1/8   i.e., both the pipe together can fill the tank in 8 minutes.
Answer: B
A thief steals a car at 4.05 P.M. and drives it at 55 km/hr. The theft is discovered at 4.20 P.M. and the owner sets off in another car at 70 km/hr. when will he overtake the thief ? Pick one:
A) 4.50 P.M.  B) 5 P.M.  C) 5.10 P.M.  D) 5.15 P.M.  E) None of these

Solution: Explanation :   Solution: Suppose the thief is overtaken x hrs after 4.05 P.M.   Then, distance covered by the thief in x hrs. = distance covered by owner in (x - 1/4) hrs.   .'. 55x = 70(x - 1/4)   => 15x = 70/4   => x = 70/(15*4) hr = 14/12 hr   => x = (14/12 * 60)= 
(14/12 * 60) = 70
70 min.   So, the thief is overtaken at 5.15 pm.   Answer : 5.15 P.M.
Answer: D
A trained covered x km at 70 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.	Choose the most appropriate option
A) 22.25  B) 99  C) 26.25  D) 66  E) 887

Solution: Total time taken = x/70 + 2x/20 hours   = 4x/35 hours   Average speed = 3x/(4x/35) = 26.25 kmph   Answer: 26.253 /(4 /35)= 
3 /(4 /35) = 105/4 = around 26.25
26.25 kmph   Answer: 26.25
Answer: C
If r and s are positive integers and r-s=6, which of the following has the greatest value R?	Options.
A) 2r B) 2s C) r +s D) 2r-s E) 2s-r

Solution: The simplest way to do this is to assume values.   We are told that r and s are positive integers R.   Also, r-s = 6 => r = 6+s   Hence r is 6 more than s.   Let s be 10. Hence r = 16.   Option 2r: 2r = 2*16= 
2*16 = 32
32   Option B: 2s= 2 * 10= 
2 * 10 = 20
20   Option C: r + s= 16 + 10= 
16 + 10 = 26
26   Option D: 2r - s= 2(16) - 10 = 32 - 10= 
32 - 10 = 22
22   Option E: 2s - r= 2(10) - 16 = 20 - 16= 
20 - 16 = 4
4   Hence option 2r is the greatest.
Answer: A
Each shelf of a bookcase contains 24 books. If the librarian took out 40 books and rearranged the remaining books so that all shelves but the last one contained 20 books and the last shelf contained 20 books, how many shelves does the bookcase have?  Choose the correct choice from the following answers:	A) A)4	B) B)5	C) C)6	D) D)8	E) E)10

Solution: Denoting x the number of the shelves,   we can build an equation: 24x=20(x−1)+20+40   Solving the equation, we get x=10   Answer: 10
Answer: E
The sum of money will be triple itself in 20years and simple interest find rate of interest?  Select
A) A)5% B) B)10% C) C)15% D) D)20% E) E)25%

Solution: T = 20 years   P= principle amount = x   A = total amount = 3x   SI = simple interest = A-P = 3x-x = 2x   R = 100SI/PT = 100.2x/20x =10%   Answer is 10%
Answer: B
66 out of 100 the how much out of 75	Options:
A) 49.5 B) 48.5 C) 47.5 D) 46.5 E) 45.5

Solution: out of 100 -- its 66   out of 75 -- x   x= 75/100 * 66= 
75/100 * 66 = 99/2 = around 49.5
49.5   49.5NSWER:49.5
Answer: A
Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?  Choose the correct choice from the following answers
A) 226 B) Rs.992 C) 665 D) 771 E) 211

Solution: (800*3*3)/ 100= 
(800*3*3)/ 100 = 72
72   920 + 72= 
920 + 72 = 992
992   Answer: Rs.992
Answer: B
A trader bought a car at 20% discount on its original price. He sold it at a 100% increase on the price he bought it. What percent of profit did he make on the original price? Choose the most appropriate option
A) 18% B) 13% C) 60% D) 40% E) 15%

Solution: Original price = 100   60%P = 80   S = 80*(200/100)= 
80*(200/100) = 160
160   100 - 160= 60%   Answer: 60%
Answer: C
A shopkeeper sells an item at Rs 36 and incurs a loss of 10 %. At what price should the shopkeeper sell it to gain 30 % ? (in Rs)  Choose the correct choice:
A) 37	B) 26	C) 28	D) 269	E) 52

Solution: 52xplanation:   No explanation is available for this question!   ANSW52R: 52
Answer: E
In june a baseball team that played 60 games had won 30% of its game played. After a phenomenal winning streak this team raised its average to 50% .How many games must the team have won in a row to attain this average?
Choose the most appropriate option:
A) 20  B) 30  C) 34  D) 24  E) 12

Solution: Number of matches won by the team in June: 30% of 60 = 18   After a phenomenal winning streak the average is 50%   Let the team played x matches continuously and won all of them to achieve an average winning percentage of 50%.   So total matches played by the team = (60+x)   Total matches won by the team = (18+x)   Total matches won = 50% of Total matches played   (18+x) = 50% of (60+x)   18+x = (50/100)*(60+x)   18+x = (1/2)*(60+x)   36+2x = 60+x   x = 24 ANSWER 24
Answer: D
How many 4-digit Q numbers (ABCD) can be formed such that |A – D| = 2?
Choose the correct choice from the following answers
A) 2,000	B) 1,900	C) 1,800	D) 1,600	E) 1,500

Solution: 1) A=0 and D-8   2) A and D as 1 and 9..so 3*100= 
3*100 = 300
300 extra ways ans  1800-300= 
 1800-300 = 1_500
1500.   we are looking for |A-D|=2 so any of the two can be bigger..   these two can have values (1,3) ; (2,4) so on till (7,9) so total 7*2 = 14..   another arrangement could be A as 2 and D as 0... D as 2 and A as 0 is not possible as number will become 3 digits..   so the ways A and D can be placed = 14+1= 
14+1 = 15
15 ways..   B and C can be placed in 10*10 ways..   Total Q= 15*10*10=1500.1,500
Answer: E
The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 36 kmph, find the speed of the stream?	Choose the correct choice from the following answers: A) 12 kmph B) 13 kmph C) 14 kmph D) 15 kmph E) 16 kmph

Solution: The ratio of the times taken is 2:1.   The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1)= 
(2+1)/(2-1) = 3
3/1= 
3/1 = 3
3:1   Speed of the stream= 36/3= 
36/3 = 12
12 kmph.   12 kmphnswer: 12 kmph
Answer: A
The speed of a boat in still water is 20 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 18 minutes is: Select:
A) 9.5	B) 5.5	C) 7.5	D) 6.5	E) 5.1

Solution: Explanation:   Speed downstream = (20+5)= 
(20+5) = 25
25 kmph   Distance travelled= (25*(18/60))= 
(25*(18/60)) = 15/2 = around 7.5
7.5 km.   ANSWER:7.5
Answer: C
A mixture has milk and water in the ratio 5:1. 20 liters of water is added and the ratio now becomes 5:6. How much milk was present in original mixture?	Choose the correct choice from the following options:
A) 20 liters
B) 22 liters
C) 24 liters
D) 26 liters
E) 28 liters

Solution: If milk and water in original mixture is 5x and x respectively, then   5x/(x+20) = 5/6, x=4   So milk in original mixture=5*4= 
5*4 = 20
20 liters   20 litersNSWER:20 liters
Answer: A
Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 4x boxes?  Choose the correct choice from the following answers: A) 3 minutes B) 4 minutes C) 8 minutes D) 6 minutes E) 12 minutes

Solution: Rate = Work / Time   Given Rate of Machine A = X / 10 min   Machine B Produces 2x boxes in 5 min hence , Machine B produces 4x boxes in 10 min .   Rate of Machine B = 4x / 10   we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates   let's first find the combined Rate of Machine A and B   Rate of Machine A = X / 10 min + Rate of Machine B = 4x / 10 = 5X/10   Now combine Time = combine work needs to be done / 8 minutesombine Rate = 4x/5x * 10 = 8 Min   Ans: 8 minutes4 /5  * 10= 
4 /5  * 10 = 8
8 Min   Ans: 8 minutes
Answer: C
A dog is tied to a tree by a long nylon cord. If the dog runs from the due North side of the tree to the due South side of the tree with the cord extended to its full length at all items, and the dog ran approximately 30 feet, what was the approximate length of the nylon cord Q, in feet?	Pick:
A) 30
B) 25
C) 15
D) 10
E) 5

Solution: Because the cord was extended to its full length at all items, the dog ran along a semi-circular path, from north to south.   The circumference of a full circle is 2*pi*r, but since we only care about the length of half the circle, the semi-circle path is pi*r.   Q=pi*r = 30. Round pi = 3, then r = 10.   Chord is about 10 feet long.10
Answer: D
A rectangular garden is to be twice as long as it is wide. If 240 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards? Choose one
A) 40 B) 50 C) 60 D) 80 E) 100

Solution: ALTERNATE APPROACH   Backsolving ( Using answer options to reach the correct answer ) can work wonders here if one is fast in calculations.   Given Perimeter is 240   So, 2 ( L + B ) = 240   Or, L + B = 120   Now use the answer options ( Given Length ; Breath will be half the length)   (A) 40   L = 40 ; B = 20   L + b = 60   (B) 50   L = 50 ; B = 25   L + b = 75   (C) 60   L = 60; B = 30   L + b = 90   (80) 80   L = 80; B = 40   L + b = 120   (E) 100   L = 100; B = 50   L + b = 150   Thus you see no, need of any calculations, U can reach the correct option only by checking options ; correct answer will be (80)
Answer: D
A car is traveling 55 kilometers per hour. How many meters does the car travel in one minute?  Pick one.
A) 1250m/min	B) 1360m/min	C) 2560m/min	D) 916.67m/min	E) 1890m/min

Solution: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify   55 kilometers per hour = 55 km/hr   = (55 × 1000 meters) / (60 minutes) = 916.67 meters / minute   correct answer is 916.67m/min)916.67m/min
Answer: D
The bus that travels from St. Louis to Chicago and back comes to St. Louis every 2 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 6 hours. If at 12:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?
Choose the correct choice from the following answers.
A) 16:00.  B) 18:00  C) 20:00  D) 22:00.  E) 24:00.

Solution: Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 2 hours   Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 6 hours   Time taken by both buses to meet again in St. Louis will be LCM of 2 and 6 = 12   If the buses start at 12:00 o'clock from St. Louis , they will meet again in St. Louis at 18:00 hours   Answer 18:00
Answer: B
The value of a machine depreciates at 20% per annum. If its present value is $1,50,000, at what price should it be sold after two years such that a profit of $24,000 is made?
Choose one:
A) $250000
B) $430000
C) $120000
D) $170000
E) $150000

Solution: $120000   $1,20,000   The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = $96,000   SP such that a profit of $24,000 is made = 96,000 + 24,000 = $1,20,000
Answer: C
consider the sequence 1,-2,3,-4,5,-6........what is the average of first 200 terms of sequence? Choose the correct choice from the following answers:
A) -1
B) -0.5
C) 0
D) 0.5
E) 1

Solution: 1-2+3-4+5-6....................+199-200   = (1-2)+(3-4)+(5-6)....................+(199-200)   = -1-1-1......................(100 terms)   = -100   so, average= (-100)/200= -0.5   ANSWER:-0.5
Answer: B
How many factors of 270 are odd numbers greater than 1? Choose the correct choice from the following.
A) 3  B) 4  C) 5  D) 6  E) 9

Solution: prime factors of 810 are 2^1,3^4,5^1   total divisors = (power if a prime factor+1)   total no. of odd factors(3,5,) = (4+1)(1+1) =10   since we need odd divisors other than 1 =>10-1= 
10-1 = 9
9 odd divisors   9 is the answer
Answer: E
If 28% of a number exceeds 18% of it by 7.2, then find the number?  Choose the correct choice:
A) 50
B) 34
C) 55
D) 60
E) 90

Solution: Use the elimination method to find the correct option.   Of all the options only 90 fits   28% of 90 = 25.2   18% of 90 = 16.2   25.2 - 16.2 = 7.2   Required number is 90.   ANSW90R:90
Answer: E
If z = 4p, where p is a prime number greater than 2, how many different positive even divisors does z have, including z ?
Select
A) Two
B) Three
C) Four
D) Six
E) Eight

Solution: z=4p   since z = 4p thenevendivisors are:   4p/4p= 1   4p/2p  4 /4= 
  4 /4 = 1
1   4p/2p= 2   4p/44 /2= 
4 /2 = 2
2   4p/4= p   4p/2= 2p   so the answer is (Four)4 /2= 
4 /2 = 2
2p   so the answer is (Four)
Answer: C
A and B undertake to do a piece of work for Rs 600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they can finish it in 3 days, Find the share of each? Answers.
A) 300, 225, 75  B) 200, 225, 80  C) 400, 300, 100  D) 500, 300, 100  E) None of these

Solution: C’s one day’s work = (1/3) - (1/6 + 1/8) = 1/24   Therefore, A : B : C = Ratio of their one day’s work = 1/6 : 1/8 : 1/24 = 4 : 3 : 1.   300, 225, 75’s share = Rs (600 x 4/8) = 300   B’s share = Rs (600 x 3/8) = 225   C’s share = Rs[600 - (300 + 225)= 
600 - (300 + 225) = 75
Rs 75   300, 225, 75NSWER:300, 225, 75
Answer: A
The cash realised on selling a 14% stock is Rs.109.25, brokerage being 1/4% is?  Choose the correct choice from the following.
A) 366  B) 106  C) 102  D) 109  E) 122

Solution: Cash realised= Rs. (109.25 - 0.25)   = Rs. 109.   Answer: 109
Answer: D
When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following?	Select the correct option
A) 13	B) 31	C) 49	D) 55	E) 67

Solution: If a number is divisible by 9, the sum of its digits must be divisible by 9. --> If a number leaves a remainder 4 when divided by 9 the sum of its digits must be 4.   55   Answer: 55
Answer: D
Zaya purchase 13 jars in a store then she returned 10 jars to store .Now how many jars she had? Choose one.
A) A)5  B) B)11  C) C)19  D) D)3  E) E)4

Solution: 13-10= 
13-10 = 3
3. Answer is 3
Answer: D