MU-NLPC/Calc-aqua_rat huggingface dataset:
Gasoline varies in cost from $0.93 to $1.13 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? Choose the correct choice from the following choices
A) $15.13	B) $15.30	C) $15.72	D) $16.01	E) $16.23

Solution: Solution:   We know that the per gallon cost of gasoline varies from $0.93 - $1.13.   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*0.93 to 30*1.13 which is $27.90 to $33.90   Case 2: for 20 gallons the cost is 20*0.93 to 20*1.13 which is $18.60 to $22.60   Thus, the maximum cost of the 480 mile trip is $33.90 and minimum is $18.60   so the difference is $33.90 - $18.60 = $15.30   Answer: $15.30 33.90 -  18.60= 
 33.90 -  18.60 = 15.3
$15.30   Answer: $15.30
Answer: B
Ramesh purchased a refrigerator for Rs. 14500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?  Choose one
A) 34778 B) 26888 C) 20350 D) 17600 E) 12778

Solution: Price at which the TV set is bought = Rs. 14,500   Discount offered = 20%   Marked Price = 12500 * 100/80 = Rs. 18125   The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 18125 + 375 = Rs. 18500   The price at which the TV should be sold to get a profit of 10% if no discount was offered = 18500 * 110/100   = Rs. 20350   Answer: 20350
Answer: C
A man starts walking at 3 pm . ha walks at a speed of 4 km/hr on level ground and at a speed of 3 km/hr on uphill , 6 km/hr downhill and then 4 km/hr on level ground to reach home at 9 pm. What is the distance covered on one way  Pick one:
A) 10km  B) 12km  C) 14km  D) 16km  E) 18km

Solution: avg speed=2*3*6/(3+6)= 
2*3*6/(3+6) = 4
4   so speed of man=4km/hr   distance=4*6= 
4*6 = 24
24km   since we want one way distance it will be    24/2= 
 24/2 = 12
12km   ANSWER:12km
Answer: B
If 3 people a,b,c can do a work simultaneously in 6 days. a and b can do work in 10 days. b and c can do work in 15 days. c and a can do the same work in 20 days.In how many days that a can complete the same work alone?  Select the correct option:
A) 20
B) 25
C) 30
D) 24
E) 19

Solution: a+b+c=1/6(one day work)   a+b=1/10;b+c=1/15;c+a+1/20   b=1/15-c;c=1/20-a;---------(2)   substitute equation 2 in a+b=1/10   a=1/10-b;a=1/10-1/15+c;   a=1/10-1/15+1/20-a;   2a=1/10-1/15+1/20;   a=1/24(one day work)   That is the no of days that a can work alone is 24 days   The option 24 is answer
Answer: D
How many prime numbers exist between 200 and 220?	Choose the correct answer:
A) None
B) 1
C) 2
D) 3
E) 4

Solution: All the even numbers goes out of the window.   201,207,213,219 - Sum of digits = 3 so divisible by 3   All the numbers ending with 5 is obviously not prime   ANSWER:1
Answer: B
An airline passenger is planning a trip that involves three connecting flights that leave from airports A, B and C, respectively. The First flight leaves Airport A every Hour, beginning at 8:00 a.m., and arrives at Airport B 2nd a half hours later. The second flight leaves Airport B every 20minutes, beginning at 8:00a.m, and arrives at Airport C 1h 10 minutes later. The third flight leaves Airport C every hour, beginning at 8.45 a.m. What is the least total amount of time the passenger must spend between flights if all flights keep to their schedules?
Choose the correct option
A) 25min  B) 1hr 5min  C) 1hr 15min  D) 2hr 20min  E) 3hr 40min

Solution: Following way may not be a pure mathematical approach to solve it but it got me the result within a minute.   A: Flight leaves every hour; 8,9,10,11,12,1,2,3   1hr 5min: Flight leaves every 20min; 8:20,8:40,9,9:20,9:40,10,10:20,10:40,11   C: Flight leaves every hour: 8:45,9:45,10:45,11:45,12:45   Passenger leaves at 8:00AM from A; reaches 1hr 5min@ 10:30am - he will catch 10:40am flight from 1hr 5min{10 minutes spent at airport 1hr 5min}; reaches c after 1hour10minutes @11:50AM;his next flight at C is at 12:45 - he waits another 55minutes;   Total wait = 10+55= 
10+55 = 65
65 minutes= 1hour 5 mins   Ans:1hr 5min
Answer: B
Divide Rs.118000 among three persons A, B and C such that the ratio of the shares of A and B is 3:4 and that of B:C is 5:6?  Choose the correct choice:
A) A = 30000 B = 40000 C = 48000
B) A = 30000 B = 40000 C = 48030
C) A = 30000 B = 40070 C = 48000
D) A = 30000 B = 40000 C = 48300
E) A = 30200 B = 40000 C = 48000

Solution: Compound ratio of A:B:C   A:B = 3:4   B:C = 5:6   ----------   A:B:C = 15:20:24   We can divide Rs.118000 in this ratio.   Share of A = 30000 B = 40000 C = 48000 = 15/59 * 118000= 
15/59 * 118000 = 30_000
30000   Share of B= 20/59 * 118000= 
20/59 * 118000 = 40_000
40000   Share of C= 24/59 * 118000= 
24/59 * 118000 = 48_000
48000   A= 30000 B = 40000 C = 48000nswer: A = 30000 B = 40000 C = 48000
Answer: A
If 0 < x ≤ 2, then which one of the following is the maximum value of (x – 1)^2 + x ? Choose one:  A) –2  B) –1  C) 0  D) 2  E) 3

Solution: If you cannot spot that the maximum value of (x – 1)^2 + x for 0 < x ≤ 2 is when x=2 --> (x – 1)^2 + x = 2 you can do the following:   Since 0 < x ≤ 2, then (x – 1)^2 + x is positive --> discard A, B and C.   For the same reason: (x – 1)^2 is a non-negative fraction less than 1.   Thus (x – 1)^2 + x = (non-negative fraction less than 1) + (0 < x ≤ 2) < 3. Discard E.   Only D is left.   Answer: 2.
Answer: D
Find the odd man out
2, 5, 14, 41, 122, 365, 1125	Choose the correct choice from the following options
A) 2	B) 14	C) 41	D) 365	E) 1125

Solution: 1*3-1= 
1*3-1 = 2
2   2*3-1= 
2*3-1 = 5
5   5*3-1= 
5*3-1 = 14
14   14*3-1= 
14*3-1 = 41
41   41*3-1= 
41*3-1 = 122
122   122*3-1= 
122*3-1 = 365
365   365*3-1= 
365*3-1 = 1_094
1094   ANSW1125R:1125
Answer: E
A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business? Choose the correct choice from the following options.
A) Rs.7500  B) Rs.7502  C) Rs.7529  D) Rs.7596  E) Rs.7506

Solution: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18)   = 4:3:3   B's share = 25000 * 3/10   = Rs.7500.   Rs.7500nswer:Rs.7500
Answer: A
How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest? Options:
A) 8 years
B) 4 years
C) 7 years
D) 6 years
E) 2 years

Solution: Explanation:   Time = (100 x 81)/(450 x 4.5) years   = 4 years.   Answer: 4 years
Answer: B
You add x ml of a 25% alcohol solution to a 200 ml of a 10% alcohol solution to obtain another solution. Find the amount of alcohol in the final solution in terms of x. Find the ratio, in terms of x, of the alcohol in the final solution to the total amount of the solution. What do you think will happen if x is very large? Find x so that the final solution has a percentage of 15%.
Choose the correct option.
A) 100 ml B) 200 ml C) 300 ml D) 400 ml E) 500 ml

Solution: Let us first find the amount of alcohol in the 10% solution of 200 ml.   200 * 10% = 20 ml   The amount of alcohol in the x ml of 25% solution is given by   25% x = 0.25 x   The total amount of alcohol in the final solution is given by   20 + 0.25 x   The ratio of alcohol in the final solution to the total amount of the solution is given by   [ ( 20 + 0.25 x ) / (x + 200)]   If x becomes very large in the above formula for the ratio, then the ratio becomes close to 0.25 or 25% (The above function is a rational function and 0.25 is its horizontal asymptote). This means that if you increase the amount x of the 25% solution, this will dominate and the final solution will be very close to a 25% solution.   To have a percentage of 15%, we need to have   [ ( 20 + 0.25 x ) / (x + 200)] = 15% = 0.15   Solve the above equation for x   20 + 0.25 x = 0.15 * (x + 200)   x = 100 ml   100 mlnswer 100 ml
Answer: A
Find the third proportional to 2 and 10?	Choose the correct option.
A) 10	B) 12	C) 16	D) 19	E) 50

Solution: Formula = Third proportional = (b × b)/a   A = 2 and B = 10   (10 × 10)/ 2 = 100/2= 
100/2 = 50
50   50
Answer: E
John has 10 pairs of matched socks. If he loses 3 individual socks, what is the greatest number of pairs of matched socks he can have left?	Answers
A) 7	B) 8	C) 5	D) 4	E) 3

Solution: Because we have to maximize the pair of matched socks, we will remove 1 pairs(2 socks) out of 10 pairs 1 sock from the 2th pair.   Thus the no of matching socks pair remaining = 10 - 2= 
10 - 2 = 8
8   Answer 8
Answer: B
16384, 8192, 2048, 256, 16, ?
Choose one:
A) 0.3 B) 9.0 C) 0.5 D) 1.0 E) 2.0

Solution: 16384   16384 ÷ 2 = 8192   8192 ÷ 4 = 2048   2048 ÷ 8 = 256   256 ÷ 16 = 16   16 ÷ 32 = 0.5   Answer is 0.5
Answer: C
An advertising agency finds that, of its 170 clients, 115 use Television, 110 use Radio and 130 use Magazines. Also, 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines. How many use all the three?
Choose the correct choice from the following:	A) 56	B) 70	C) 90	D) 98	E) 95

Solution: Total=170   Television=115   Radio=110   Magazine=130   All the three =170-115-110-130+85+75+95= 
170-115-110-130+85+75+95 = 70
70   ANSWER 70
Answer: B
The average height of 50 pupils in a class is 150 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is? Answers.
A) 718 cm  B) 151 cm  C) 627 cm  D) 282 cm  E) 636 cm

Solution: Total height = 150 * 50= 
150 * 50 = 7_500
7500 cm.   New average= [7500 - 5 * 146 + 5 * 156 ] / 50 = 151 cm.   Answer:151 cm
Answer: B
A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? Pick one:
A) 76 sec	B) 67 sec	C) 98 sec	D) 36 sec	E) 23 sec

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 240 + 120= 
240 + 120 = 360
360 m.   Time taken= 360/10= 
360/10 = 36
36 sec.   Answer:98 sec
Answer: C
If p is an odd integer and q is an even integer, which of the following must be an odd integer?	Pick one:
A) 2q+2p  B) 3(2p-q)  C) p^2+q^2  D) p+q+3  E) 5p-2q+1

Solution: p is odd; for this assume p=1   q is even; for this assume q = 2   (2*1)+(2*2)= 
(2*1)+(2*2) = 6
6 Even   3((2*1)-2)= 0 Even   1^2+2^2 = 5 Odd    1+2+3= 
 1+2+3 = 6
6 Even     (5*1)-(2*2)+1= 
  (5*1)-(2*2)+1 = 2
2 Even   Answer:p^2+q^2
Answer: C
Suresh borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five 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?
Choose one
A) Rs.8500	B) Rs.6000	C) Rs.8000	D) Rs.9000	E) Rs.7000

Solution: using the formula S.I=P*T*R/100   (x*6*3/100)+(x*9*5/100)+(x*13*3/100)=8160   x=8000   i.e money borrowed is Rs.8000   ANSWER:Rs.8000
Answer: C
If xy not equal 0 and x^2*y^2 -xy = 12, which of the following could be y in terms of x?
I. 1/2x
II. -4/x
III. 3/x
Choose the correct choice from the following answers:
A) II and III	B) II	C) III	D) IV	E) I &II

Solution: x2y2 - xy = 12   x2y2-xy-12 = 0   (xy-3)(xy+4)=0   xy = 3 or xy=-4   y = 3/x or y = -4/x   II and III only   II and III
Answer: A
A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.300, find the original price per kg?	Choose the correct answer: A) s.7.7 B) s.7.4 C) s.7.5 D) s.7.1 E) s.7.9

Solution: 100*(20/100)= 
100*(20/100) = 20
20 --- 10   ? --- 1=> Rs.2   300 --- 80   ? --- 2 => Rs.7.5   Answer:s.7.5
Answer: C
One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 18 cm2. Find the lengths of all sides.	Choose the correct choice from the following choices:
A) 4
B) 56
C) 6
D) 7
E) 9

Solution: Let xx be the length of the longer side x>3x>3, then the other side's length is x−3x−3 cm. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1)(x+1) and (x−3+1)=(x−2)(x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be A2=(x+1)⋅(x−2)A2=(x+1)⋅(x−2) cm2, which is 18 cm2 more than the first area. Therefore   A1+18=A2A1+18=A2   x(x−3)+18=(x+1)(x−2)x(x−3)+18=(x+1)(x−2)   x2−3x+18=x2+x−2x−2x2−3x+18=x2+x−2x−2   2x=202x=20   x=10x=10. So, the sides of the rectangle are 1010 cm and (10−3)=7(10−3)=7 cm long.   Answer:	9
Answer: E
A bottle is 80% full. The liquid in the bottle consists of 60% guava juice and 40% pineapple juice. The remainder of the bottle is then filled with 70 lm of rum. How much guava is in the bottle?	Options:
A) 155 ml	B) 158 ml	C) 165 ml	D) 168 ml	E) 175 ml

Solution: if the Bottle is 100ml:   we have 48% Guava, 32% Pineapple, and 20% Rum.   Now, is the bottle 20% of rum is represented by 70 ml. So, we have to find for the same bottle 48% guava is what ml?   therefore, Guava= (70*48)/20= 
(70*48)/20 = 168
168 ml   ANSWER:165 ml
Answer: C
The cost of 16 pens and 8 pencils is Rs.352 and the cost of 4 pens and 4 pencils is Rs.96. Find the cost of each pen?  Options:
A) 33
B) 88
C) 66
D) 88
E) 20

Solution: Let the cost of each pen and pencil be 'p' and 'q' respectively.   16p + 8q = 352 --- (1)   4p + 4q = 96   8p + 8q = 192 --- (2)   (1) - (2) => 8p = 160   => p = 20   Answer: 20
Answer: E
Which of the following will divide evenly into 607,406,520?
Choose the correct answer:	A) 13	B) 21	C) 11	D) 3	E) none of these

Solution: Rule:   3: Sum of the digits should be divisible by 3   Given number : 6+7+4+6+5+2= 
6+7+4+6+5+2 = 30
30   Answer : 3
Answer: D
Find the mode of the given set of number
2, 2, 3, 5, 4, 3, 2, 3, 3, 5 Choose the correct choice from the following answers: A) 1 B) 2 C) 3 D) 4 E) 5

Solution: Arranging the number with same values together, we get   2, 2, 2, 3, 3, 3, 3, 4, 5, 5   We observe that 3 occurs maximum number of times, i.e., four.   Therefore, mode of this data is 3. ANSWER :3
Answer: C
The cash difference between the selling prices of an article at a profit of 4% and 8% is Rs. 3. The ratio of the two selling prices is?	Choose the correct choice
A) 52:56 B) 52:53 C) 52:54 D) 22:56 E) 52:51

Solution: Let C.P. of the article be Rs. x.   Then, required ratio = 104% of x / 108% of x   = 104/108 = 52/54 = 52:54   Answer: 52:54
Answer: C
What is the unit’s digit of 7^7 Choices:
A) 9
B) 5
C) 3
D) 7
E) 1

Solution: 7^1=7   7^2=49   7^3=343   7^4=1(last digit)   7^5=7(last digit) and the cycle repeats after every 4 powers   Therefore, last digit of 7^7=3   Answer 3
Answer: C
Ravi and sunil are partners in a business. Ravi invests Rs.15,000 for 8 months and Sunil invested Rs.8000 for 10 months then after one year ratio of their profits will be  Pick one:
A) 1:3
B) 2:3
C) 3:2
D) 3:1
E) 3:4

Solution: =(15000*8):(8000*10)   =120000:80000   =3:2   ANSWER:3:2
Answer: C
Three walls have wallpaper covering a combined area of 280 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 36 square meters. What is the area that is covered with three layers of wallpaper?  Pick one: A) 5 Square Meters B) 32 Square Meters C) 42 Square Meters D) 83.3 Square Meters E) 120 Square Meters

Solution: 280 - 180= 
280 - 180 = 100
100 sq m of the wallpaper overlaps (in either two layers or three layers)   If 36 sq m has two layers, 100 - 36= 64 sq m of the wallpaper overlaps in three layers. 64 sq m makes two extra layers hence the area over which it makes two extra layers is 32 sq m.   Answer (32 Square Meters).
Answer: B
Which number should replace both the asterisks in (* /20) x (*/180) = 1 ? Choose the correct choice:  A) 20  B) 40  C) 60  D) 90  E) 120

Solution: Let (y/20) x (y/180) = 1   y^2 = 20 x 180 = 20 x 20 x 9   y = (20 x 3) = 60   The answer is 60.
Answer: C
A rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?	Choose the correct choice from the following answers
A) 88 Feet
B) 66 Feet
C) 77 Feet
D) 99 Feet
E) 55 Feet

Solution: A   88 Feet   Area of the field =680 sq. feet.   Length of the adjacent sides are   20 feet and  680/20= 
 680/20 = 34
34 feet.   Required length of the fencing=20+34+34= 
20+34+34 = 88
88 feet
Answer: A
Which of the following equations represents a line that is perpendicular to y=1/2*x+1?
Choose the correct choice from the following answers
A) y−2x=8	B) 2x+4y=10	C) 3y+6x=12	D) 4y−8x=16	E) 5x−10y=20

Solution: For two lines to be perpendicular, the product of slopes should be equal to -1.   Slope of line 1 = 1/2   Slope of the line perpendicular to line 1 must be -2. Option C can be rewritten as y = -2x + 4 --> Slope = -2   y−2x=8nswer: y−2x=8
Answer: A
Find the circumference and area of radius 6 cm.	Answers.
A) 113 cm² B) 144 cm² C) 154 cm² D) 184 cm² E) 194 cm²

Solution: 113 cm²rea of circle = πr²   = 22/7 × 6 × 6 cm²   = 113 cm²   113 cm²NSWER:113 cm²
Answer: A
How many cubes of 4 cm edge can be put in a cubical box of 1 m edge.  Choices: A) 17725 cm B) 15625 cm C) 12786 cm D) 12617 cm E) 12187 cm

Solution: Number of cubes =100âˆ—100âˆ—100/4*4*4=15625   Note: 1 m = 100 cm   Answer:15625 cm
Answer: B
Rita and Sam play the following game with n sticks on a table. Each must remove 1,2,3,4, or 5 sticks at a time on alternate turns, and no stick that is removed is put back on the table. Tha one who removes the last stick (or sticks) from the table wins. If Rita goes first, which of the following is a value of n such that Sam can always win no matter how Rita plays?	Choose the correct choice from the following: A) 7 B) 10 C) 11 D) 12 E) 16

Solution: If the number of sticks on a table is a multiple of 6, then the second player will win in any case (well if the player is smart enough).   Consider n=6, no matter how many sticks will be removed by the first player (1, 2, 3 ,4 or 5), the rest (5, 4, 3, 2, or 1) can be removed by the second one.   The same for n=12: no matter how many sticks will be removed by the first player 1, 2, 3 ,4 or 5, the second one can remove 5, 4, 3, 2, or 1 so that to leave 6 sticks on the table and we are back to the case we discussed above.   Answer: 12.
Answer: D
Aparna cuts a cake into two halves and cuts one-half into smaller pieces of equal size. Each of the small pieces is twenty grams in weight. If she has seven pieces of the cake in all with her, how heavy was the original cake?	Choose the correct choice from the following answers.
A) 140 grams  B) 280 grams  C) 240 grams  D) 120 grams  E) None of these

Solution: one cake =1/2 + 1/2   1/2------6 pieces   total pieces = (1/2)cake +(6 pieces of 1/2) = 7 pieces   then 6 small picese weight = half piece cake   So 2*(6*20)= 
2*(6*20) = 240
240   ANSWER:240 grams
Answer: C
How many Books each of Volume 200 meter cube can be packed into a crate of volume 4000 meter cube? Select the correct option:
A) 20
B) 40
C) 60
D) 80
E) cannot be determined

Solution: Gud question with a simple concept.   In geo if we want to insert one shape into another we need to know the dimensions of the two shapes.   In above with volume given , we can come up with different shapes, so we cant know the answer   For ex :4000 m3 can be 400*10 or 40*100 or just 4000*1 we don't know , so we cant calculate   Answer : cannot be determined
Answer: E
Steve traveled the first 2 hours of his journey at 50 mph and the last 3 hours of his journey at 80 mph. What is his average speed of travel for the entire journey?
Select the correct option.
A) 60 mph	B) 68 mph	C) 53.33 mph	D) 64 mph	E) 66.67 mph

Solution: Answer   Average speed of travel = Total distance travelled/Total time taken   Total distance traveled by Steve = Distance covered in the first 2 hours + distance covered in the next 3 hours.   Distance covered in the first 2 hours = speed * time = 50 * 2= 
50 * 2 = 100
100 miles.   Distance covered in the next 3 hours= speed * time = 80 * 3= 
80 * 3 = 240
240 miles.   Therefore, total distance covered= 100 + 240= 
100 + 240 = 340
340 miles.   Total time taken= 2 + 3= 
2 + 3 = 5
5 hours.   Hence, average speed= Total distance travelled/Total time taken=340/5= 
340/5 = 68
68 miles per hour.   Choice 68 mph
Answer: B
In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (10, 0), (0, -3.5), (-10, 0)? Choose the correct choice from the following options
A) 56  B) 88  C) 70  D) 116  E) 120

Solution: Area of rhombus= 1/2* D1 *D2   Length of 1st diagonal = 10+10= 
10+10 = 20
20   Length of 2nd diagonal= 3.5+3.5= 
3.5+3.5 = 7
7   Area= 1/2*20*7= 
1/2*20*7 = 70
70   70 is the answer
Answer: C
Two painters 'P1' & 'P2' paint the bungalow in 3 days. If P1 alone can paint the bungalow in 12 days, in how many days can 'P2'' alone complete the same paint work?
Choose the correct choice from the following choices:
A) 4 days  B) 6 days  C) 9 days  D) 12 days  E) 15 days

Solution: EXPLANATION:   Hint:   If a person can do a part of work in 'n' days, then person's work in 1 day =	1/n   As painters P1 & P2 paint the bungalows in 3 days, then work done by both painters =	1/3   As P1 paint it alone in 12 days, then work done by painter P1 =	1/12   Work done by painter P2 =	1/3	–	1/12	=	4 – 1/12	=	3/12	=	1/4   Therefore, same work will be completed by painter P2 in 4 days.   4 daysNSWER IS 4 days
Answer: A
Let q represent the integer length of a side of a triangle. If r represents the number of distinct values for q such that we can create a triangle with lengths q, 12, and 16, what is the value of r?
Choose the correct option
A) 18
B) 20
C) 22
D) 23
E) 24

Solution: From the triangle inequality rule, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, the three inequalities are:   1. q + 12 > 16   2. 12 + 16 > q   3. q + 16 > 12   Equation 3 is true for any positive value of q.   From equation 1, q > 4   From equation 2, 28 > q   Then 28 > q > 4 so q can be any value from 5 to 27 inclusive.   The number of possible values is 23.   The answer is 23.
Answer: D
A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders Q when the order of the divisors is reversed.  Choose the correct choice from the following:
A) 8,5,3  B) 4,2,1  C) Q=3,2,1  D) Q=6,4,2  E) None of above

Solution: My approach would be   Three Divisors: 3, 5, 8   Three Remain: 1, 4, 7   Start from the bottom of the last column i.e. from the third remainder:   Go up diagonally and multiply by the second divisor:  5*7= 
 5*7 = 35
35   Go down and add the second remainder:   35 + 4= 
  35 + 4 = 39
39   Go up diagonally and multiply by the first divisor:  39* 3= 
 39* 3 = 117
117   Go down and add the first remainder:  117 + 1= 
 117 + 1 = 118
118   Divide 118 by 8, 5, 3   118/8 gives quotient= 14 and remainder = 6   14/5 gives quotient = 2 and remainder = 4   2/3 gives quotient = 0 and remainder = 2   Ans is D i.e. 6,4,2
Answer: D
If the numerator of a fraction is increased by 50% and denominator by 20%, the fraction become 9/15. What was the original fraction ?	Select the correct option
A) 12/25  B) 13/25  C) 3/5  D) 6/7  E) 7/8

Solution: Explanation :   Let the fraction be x/y   We have 150x/120y = 9/15   = x/y = 12/25   12/25nswer : Option 12/25
Answer: A