MU-NLPC/Calc-aqua_rat huggingface dataset:
An bus covers a certain distance at aspeed of 240 kmph in 5 hours. To cover the same distance in 1hr, it must travel at a speed of?
Choose the correct option:
A) 560 km/h B) 567 km/h C) 779 km/h D) 723 km/h E) 720 km/h

Solution: Distance = (240 x 5) = 1200 km.   Speed = Distance/Time   Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]   Required speed = 1200 x 3 km/hr = 720 km/hr.   5   720 km/h
Answer: E
A rectangular photograph is surrounded by a border that is 2 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 4 inches wide on each side, the total area would have been (M + 94) square inches. What is the perimeter of the photograph, in inches?	Options.
A) 34	B) 36	C) 23	D) 40	E) 42

Solution: Let Length and Breadth of photograph be L and B respectively.   Perimeter is given by 2*(L+b) -----(1)   According to the question:   (L+4)(B+4) = m ----(2)   and   (L+8)(B+8) = m + 94 ---------> (L+8)(B+8) - 94 = m ------(3)   Equating (2) and (3)   (L+4)(B+4) = (L+8)(B+8) - 94   LB + 4L + 4B + 16 = LB + 8L + 8B + 64 -94   Simplify   4L + 4B = 46 ------> 2(L+B) =23 (23heck eq (1))   Answer is 23
Answer: C
How many integerskgreater than 100 and less than 1100 are there such that if the hundreds and the units digits ofkare reversed, the resulting integer is k+99?  Choose the correct choice:	A) 50	B) 60	C) 70	D) 80	E) 90

Solution: Numbers will be like 102 => 201 = 102 + 99   203 => 302 = 103 + 99   so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit.   There will be ninet pairs of such numbers   for every pair there will 10 numbers like for 12 => 102, 112,132,142,152, 162,172,182,192.   Total = 9 *10= 
9 *10 = 90
90 hence 90.
Answer: E
A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?	Choose the correct choice from the following:
A) 288  B) 180  C) 1288  D) 1771  E) 231

Solution: Length of the train be ‘X’   X + 120/15 = X + 180/18   6X + 720 = 5X + 900   X = 180m   Answer: 180
Answer: B
A pyramid has a square base of 6 cm, and the four lateral faces are four congruent equilateral triangles. What is the total surface area of the pyramid in square cm?	Answers: A) 36 + 18*sqrt(3) B) 36 + 36*sqrt(3) C) 72 D) 72 + 36*sqrt(3) E) 72 + 72*sqrt(3)

Solution: First of all, of course, the base has an area of 36. For the lateral surfaces, it would be helpful to remember the formula for the area of an equilateral triangle.   The area of one equilateral triangle is A = (s^2*sqrt{3})/4. We know the side of the equilateral triangle must be the same as the square: s = 6. Thus, one of these equilateral triangles has an area of A = (6^2*sqrt{3})/4 = 9*sqrt{3}. There are four identical triangles, so their combined area is A = 36*sqrt{3}. Now, add the square base, for a total surface area of A = 36 + 36*sqrt{3}. Answer = 36 + 36*sqrt(3)
Answer: B
Jim wishes to buy 3 gifts that cost 15 dollars, 9 dollars, and 12 dollars. He has 1/4 of the money
he needs. How much more money must he earn in order to buy the gifts?	Choose the correct answer
A) $57  B) $47  C) $7  D) $17  E) $27

Solution: $15 + $9 + $12 = $36 needed   1/4 x $36 15 +  9 +  12= 
15 +  9 +  12 = 36
$36 needed   1/4 x $36= $9 on hand   $36 - $9 = $27 to earn   correct answer $2736 -  9= 
36 -  9 = 27
$27 to earn   correct answer $27
Answer: E
The commuter rail between Scottsdale and Sherbourne is 200 km of track, and one train makes a round trip in 5 hours. If Harsha boards the train at the Forest Grove station, which is located one fifth of the track's length out from Scottsdale, how long will it take her to get to Sherbourne?
Answers.
A) .5 hours	B) 1 hour	C) 1.5 hours	D) 2 hours	E) 2.5 hours

Solution: 2 hoursistance between Scottsdale and Sherbourne = 200 km   Time for a one-way trip between Scottsdale and Sherbourne:   5/2= 
  5/2 = 5/2 = around 2.5
2.5 hours   2 hoursistance between Forest Grove and Scottsdale: 200/5= 
200/5 = 40
40 km   2 hoursistance between Forest Grove and Sherbourne: 40 x 4= 160 km   Time between Scottsdale and Forest Grove: 2.5/5= 
2.5/5 = 0.5
.5 hours   Time between Forest Grove and Sherborne: .5 x 4= 2 hours.
Answer: D
Find the odd man out. 4, 9, 16, 25, 49, 20 Pick:  A) 12  B) 9  C) 1  D) 20  E) 19

Solution: 20 is an square. All other given numbers are square   Answer : Option 20
Answer: D
When x is divided by y, the quotient is s with remainder r. What is x in terms of r, y, and s?	Choose one:
A) y + r + s
B) ys + r
C) x/y+r
D) y/s+r
E) rs + y

Solution: (x/y) = s + r   solve for x   x=(s*y)+r   Ans ys + r.
Answer: B
John went to a shop and bought things worth Rs. 25, 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?
Pick one:
A) 19.7
B) 19.9
C) 21.5
D) 22
E) 23.7

Solution: Total cost of the items he purchased = Rs.25   Given that out of this Rs.25, 30 Paise is given as tax   => Total tax incurred = 30 Paise = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (25−30/100−x)6/100 = 30/100   ⇒ 6(25 −0.3 −x) = 30   ⇒ (25 − 0.3 − x) = 5   ⇒ x = 25 − 0.3 − 5 = 19.7   19.7)
Answer: A
10women can complete a work in 7days&10children take 14days to complete the work. How many days will 5women and 10children take to complete the work?
Answers
A) 5 days	B) 7 days	C) 8 days	D) 9 days	E) 11 days

Solution: 1 woman's 1 day's work = 1/70   1 Child's 1 day's work = 1/140   5 Women and 10 children 1 day work =   (5/70+10/140)=1/7   So 5 women and 10 children will finish the work in 7 days.   7 days)
Answer: B
The ratio between x and y is 8/5; x and y are decreased by 5, what is the ratio between the new values of x and y?
Choose the correct choice from the following choices
A) 8/5 B) 5/8 C) 4 D) 5 E) It Cannot Be Determined

Solution: Ratio = 8k/5k = 8/5, 16/10, etc.   x and y are decreased by 5 --> (8k - 5)/(5k - 5)   New ratio can be 3/0, 11/5, etc.   Answer: It Cannot Be Determined
Answer: E
The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $20,000?	Select: A) $38,796. B) $40,000. C) $19,488. D) $39,679. E) $36,796.

Solution: 20,000 *1.16*.84= Unit and tens digit of the expression is 6 and 7 respectively.   Only option $19,488. fulfills the condition and hence is the answer
Answer: C
A pet store has 4 birds, 6 cats and 5 dogs available. In how many ways can 2 birds, 2 cats and 3 dogs be selected from the store?
Pick:  A) 987 ways  B) 960 ways  C) 900 ways  D) 157 ways  E) 134 ways

Solution: The number of ways of selecting three birds, two cats and three dogs is:   = ⁴C₂ * ⁶C₂ * ⁵C₃   = (4 * 3)/(2 * 1) * (6 * 5)/(2 * 1) * (5 * 4 * 3)/(3 * 2 * 1)   = 6 * 15 * 10= 
6 * 15 * 10 = 900
900 ways.   Answer: 900 ways
Answer: C
What is 15 percent of 64? Choices.
A) 7.2  B) 8.4  C) 9.6  D) 10.4  E) 11.8

Solution: (15/100) * 64= 
(15/100) * 64 = 48/5 = around 9.6
9.6   The answer is 9.6.
Answer: C
Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.6 km? Choose the correct choice from the following options:
A) 600 m
B) 200 m
C) 300 m
D) 400 m
E) 100 m

Solution: 600 m   600 m   Distance covered by 600 mmar = 18/4.8 (1.6km) = 3/8(1600) = 600 m
Answer: A
Choose any 4 desserts from a menu of 10?  Pick.
A) 120 B) 140 C) 180 D) 210 E) 240

Solution: 10c4 = 210   Answer is 210
Answer: D
A rectangular field is 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 option:
A) 34
B) 40
C) 68
D) 88
E) 92

Solution: Given that length and area, so we can find the breadth.   Length x Breadth = Area   20 x Breadth = 680   Breadth = 34 feet   Area to be fenced = 2B + L = 2 (34) + 20 = 88 feet answer : 88
Answer: D
Anne bought doughnuts for a class breakfast party. She bought 6 chocolate doughnuts, 8 coconut doughnuts, and 8 jam-filled doughnuts. How many doughnuts did Anne buy in all? Pick one:	A) 22	B) 36	C) 39	D) 21	E) 11

Solution: Add the numbers of doughnuts.   6 + 8 + 8= 
6 + 8 + 8 = 22
22.   22nswer is 22.
Answer: A
Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?  Choose the correct choice:
A) 10 B) 12 C) 15 D) 16 E) 18

Solution: Let the numbers be x, x+2 and x+4 then   x + x+2 + x+4 = x+26   3x + 6 = x + 26   2x = 20   \inline \therefore x = 10   \inline \therefore Middle number = x + 2 = 10+2= 
10+2 = 12
12   12
Answer: B
Rs.1560 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
Answers:
A) s.528
B) s.542
C) s.528
D) s.720
E) s.549

Solution: A+B+C = 1560   4A = 3B = 2C = x   A:B:C = 1/4:1/3:1/2 = 3:4:6   6/13 * 1560 = Rs.720   Answer: s.720
Answer: D
John makes $65 a week from his job. He earns a raise andnow makes $72 a week. What is the % increase?
Choose the correct option:
A) 16%
B) 10.76%
C) 10.69%
D) 10.98%
E) 10%

Solution: Increase = (7/65)*100 = (7/65)*100 = 10.76%.   10.76%
Answer: B
Jimmy has a pot of soup, and he ate 1/5 of the soup for lunch. If Jimmy ate 1/6 of the remaining soup for dinner, what fraction of the soup was left after dinner?  Choose the correct choice from the following answers:  A) 1/2  B) 2/3  C) 3/4  D) 4/5  E) 5/6

Solution: Let x be the amount of soup at the beginning.   After lunch, the remaining soup was (4/5)x.   After dinner, the remaining soup was (5/6)(4/5)x = (2/3)x.   The answer is 2/3.
Answer: B
By investing Rs. 1800 in 9% stock, Syam earns Rs. 120. find out the stock is then quoted at which rate?	Choose the correct choice from the following answers.
A) 130  B) 135  C) 140  D) 150  E) 145

Solution: Assume that face value = Rs.100.   Dividend per share = Rs.9 (as it is a 9% stock)   By investing Rs. 1800, he earns Rs.120   Investment needed to earn Rs.9 = 1800×9/120 = Rs.135   ie, stock is then quoted (then market value) = Rs.135   Answer is 135.
Answer: B
Ashok secured average of 80 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?	Choose the correct option:
A) 38
B) 27
C) 99
D) 110
E) 80

Solution: Explanation:   Number of subjects = 6   Average of marks in 6 subjects = 80   Therefore total marks in 6 subjects = 80 * 6= 
80 * 6 = 480
480   Now, No. of subjects= 5   Total marks in 5 subjects = 74 * 5= 
74 * 5 = 370
370   Therefore marks in 6th subject= 480 – 370 = 110   ANSWER: 110
Answer: D
A large box contains 18 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box? Choose the correct choice from the following choices: A) 350 B) 250 C) 450 D) 550 E) 650

Solution: The number of chocolate bars is equal to   18 ? 25 = 450   correct answer 450
Answer: C
The average age of 50 students in a class is 14 years. If the age of teacher is also included, the average becomes 15 years, find the age of the teacher.  Pick one:
A) 30	B) 65	C) 60	D) 55	E) 56

Solution: Explanation:   If teacher's age is 14 years, there is no change in the average. But teacher has contributed 1 year to all the students along with maintaining his age at 15.   Age of teacher = Average age of all + Total increase in age   = 15 + (1 x 50 ) = 65 years   Answer:65
Answer: B
It costs a publishing company 50,000 dollars to make books. The 50,000 is a fixed cost or a cost that cannot change. To help the publishing company sell the books, a marketing company charges 4 dollars for each book sold. If the company charges 9 dollars per book, how many books should they sell to break even?
Pick:	A) 100	B) 1000	C) 10000	D) 100000	E) None

Solution: Let C be the cost of producing and selling x books   Let R be the revenue made for selling x books   R = selling price of 1 book × number of books sold   R = 9x   C = fixed cost + variable cost   variable cost = fee charged for 1 book × number of books sold   variable cost = 4x   C = 50000 + 4x   R = C   9x = 50000 + 4x   9x - 4x = 50000 + 4x - 4x   5x = 50000   x = 10000 since 5 × 10000 = 50000   The break even point is to sell 10000 books.   Answer 10000
Answer: C
How many positive integers less than 14 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?	Options.
A) 14
B) 13
C) 12
D) 11
E) 8

Solution: The number = 2a + 3b < 20   When a = 1, b = 1, 2, 3, 4, 5 -> 2a = 2; 3b = 3, 6, 9-> the number = 5, 8, 11 --> 3 numbers   when a =2, b = 1,2,3-> ....--> 3 numbers   when a =3, b = 1,2,3,4 --> ....--> 2 numbers   Total number is already 8. Look at the answer there is no number greater than 8 --> we dont need to try any more   Answer must be 8
Answer: E
01-Jan-2007 was Monday. What day of the week lies on 01-Jan-2008?
Choose the most appropriate option: A) Wednesday B) Sunday C) Friday D) Tuesday E) None of these

Solution: Explanation :   Given that January 1, 2007 was Monday.   Odd days in 2007 = 1 (we have taken the complete year 2007 because we need to find out the odd days from 01-Jan-2007 to 31-Dec-2007, that is the whole year 2007)   Hence January 1, 2008 = (Monday + 1 Odd day) = Tuesday. Answer : Option Tuesday
Answer: D
If x is 20 percent more than y and y is 50 percent less than z, then x is what percent of z? Pick one
A) 500%	B) 250%	C) 500/3%	D) 125%	E) 60%

Solution: Let's take values of x,y,z which can satisfy given equations.   Let Z= 200, so Y becomes 100 ( since Y is 50% less than Z),   X becomes 120 ( since 20% more than Y)   now req is (X/Z) * 100 = (120/200) *100= 
(120/200) *100 = 60
60 %   ANSW60%R:60%
Answer: E
Find the odd man out
864, 420, 200, 96, 40, 16, 6
Pick one:
A) 420 B) 200 C) 96 D) 40 E) 6

Solution: 6x2+4=16   16x2+8=40   40x2+12=92   92x2+16=200.. and so on.   ANSWER:96
Answer: C
In how many ways can the letters of the word "SUN" be arranged?
Choose the correct choice from the following answers: A) 4 B) 6 C) 8 D) 10 E) 12

Solution: The total ways of arranging the letters = 3! = 6   The answer is 6.
Answer: B
The below sequence is a bit tricky. Can you solve it to find the next number?
5, 25, 325, 4325, ?	Choose the correct choice from the following answers:
A) 56189  B) 54367  C) 54325  D) 53182  E) 62819

Solution: C   54325   Explanation:   Consider 1 = 5   2 = 25   3 = 325   4 = 4325   Then 5 = 54325   See the pattern. With every digit, the previous numbers are added after that digit   So the next number in the series is 54325
Answer: C
The bankerâ€™s discount of a certain sum of money is Rs. 78 and the true discount on the same sum for the same time is Rs. 66. The sum due is	Choose the correct choice from the following choices:
A) 429
B) 280
C) 360
D) 450
E) None

Solution: Sol.   Sum = B.D. * T.D. / B.D. - T.D. = Rs.[78 * 66 / 78 - 66] = Rs. [78 * 66 / 12] = Rs. 429   429nswer 429
Answer: A
Jim and John are workers in a department that has a total of 7 employees. Their boss decides that two workers from the department will be picked at random to participate in a company interview. What is the probability that both Jim and John are chosen? Answers:
A) 2/21 B) 4/21 C) 5/21 D) 6/21 E) 1/21

Solution: Probability = 2c2/7c2   = 1/21   Answer 1/21
Answer: E
In how many different ways can a group of 4 men and 4 women be formed out of 7 men and 8 women?
Pick one:
A) 2450
B) 105
C) 1170
D) Cannot be determined
E) None of these

Solution: Reqd no. of ways = 7C4 × 8C4   = 7×6×5×4/1×2×3×4 × 8×7×6×5/1×2×3×4   = 35 × 70 = 2450   2450nswer 2450
Answer: A
Anand and Deepak started a business investing Rs. 34,000 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?
Choose the correct choice: A) 2777 B) 2888 C) 8400 D) 7000 E) 2781

Solution: Ratio of their shares = 34000 : 35000 = 34:35   Deepak's share = 13800 * 35/69 = Rs. 7000.   Answer: 7000
Answer: D
number of ways by which 4digit no made where aless than b,bless than c,c less than d where all lies between 1 to 9
Choose the correct choice from the following.
A) 1290
B) 1296
C) 1380
D) 1480
E) 1580

Solution: we have to make 4 digit number   in which the format is d> c > b > a   __ __ __ __   1st position can be filled by 6 digits(9, 8, 7, 6, 5, 4)   2nd position can be filled by 6 digits(8, 7, 6, 5, 4, 3)   3rd position can be filled by 6 digits(7, 6, 5, 4, 3, 2)   4th position can be filled by 6 digits(6, 5, 4, 3, 2, 1)   hence every place can be filled by 6 digits,   6* 6* 6* 6= 
6* 6* 6* 6 = 1_296
1296   ANSWER:1296
Answer: B
The length of the longest tape in cm which can be used to measure exactly, the length 100cm; 2m25cm; and 7m80cm is: Select the correct option:
A) 30	B) 5	C) 10	D) 36	E) 25

Solution: The three lengths in cm are 100, 225 &780.   HCF of 100, 225 &780 is 5.   Hence, the answer is 5 cm.   ANSWER:5
Answer: B
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1000 resolutions?  Answers: A) 794 m B) 704 m C) 1408 m D) 1860 m E) 1760 m

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 1000 resolutions.   = 1000 * 2 * 22/7 * 22.4= 
1000 * 2 * 22/7 * 22.4 = 140_800
140800 cm= 1408 m   Answer: 1408 m
Answer: C
Grace has 16 jellybeans in her pocket. She has 8 red ones, 6 green ones, and 2 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?	Choose the correct choice from the following answers: A) 4 B) 8 C) 12 D) 13 E) 15

Solution: The worst scenario is when she takes 8 red and 6 green, total of 14 jellybeans, and still doesn't have 3 distinct colors. But the next draw (15th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket.   Answer: 15.
Answer: E
A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. The height of the cone is :  Pick one
A) 12 cm	B) 14 cm	C) 16 cm	D) 17 cm	E) None

Solution: Sol.   Volume of meterial in the sphere = [4/3 ∏ * {(4)³ - (2)²}] cm³   = [4/3 ∏ * 56] cm³   Let the height of the cone be h cm.   Then, 1/3 ∏ * 4 * 4 * h = [4/3 ∏ * 56]   ⇔ h = [4 * 56 / 4 * 4] = 14 cm.   Answer 14 cm
Answer: B
find value for x from below equation? x + 1 = -4 Choose the correct option.
A) -5	B) -4	C) 4	D) 3	E) 2

Solution: 1. Subtract 1 from both sides:   x + 1 - 1 = -4 - 1   2. Simplify both sides:   x = -5   -5
Answer: A
Prints a page 50 pg per min .If the printed for 2 hours except 15 min.Where there
was an paper jam,how many page did it print  Choose the correct option
A) 10,880
B) 12,880
C) 5,250
D) 8,880
E) 18,880

Solution: 50 pages ------->1 min   2 hrs except 15 mints means=2*60= 
2*60 = 120
120-15= 
120-15 = 105
105 mints   i.e.,105*50=5,250 pages printed.   ANSWER:5,250
Answer: C
A certain auto manufacturer sold 7% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.1 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?  Choose the correct option
A) 63,000  B) 1,960,000  C) 2,030,000  D) 2,040,000  E) 2,300,000

Solution: Let's assume in 2006 the manufacturer sold X.   In 2007 he sold X-7/100(X)   If sales in 2006,X= 2.1 million find X-7/100(X)   (2.1 x 10^6)-7/100(2.1 x 10^6)   2100000-147000=1,953,000-----> 1,960,000(approx)   ANSWER:1,960,000
Answer: B
Solve the given two equations and find the inequality of X and Y. (a) x^4- 227= 398 and (b) y^2 + 321=346 Select the correct option
A) If x>y  B) If x>y  C) If x<y  D) If x<=y  E) x=y or relationship cannot be established

Solution: Solution:-   X=+5,-5 and Y= +5,-5   Comparing, we get X=Y, XY.   Therefore, no relationship can be established between X and Y.   x=y or relationship cannot be established
Answer: E
If f(x)=7x+6 and g(y)=3y^2+ 5y-8 then g(f(x))  Choose the correct choice: A) 96x^2+78x+74 B) 857x^2+99x+89 C) 852x^2+96x+87 D) 147x^2+119x+58 E) 852x^2+69x+98

Solution: g(f(x))=3(7x+6)^2+5(7x+6)-8   =3(49x^2+36+84x)+35x+30-8   =147x^2+119x+58   the answer is 147x^2+119x+58
Answer: D
When positive integer x is divided by positive integer y, the remainder is 6. If x/y = 6.12, what is the value of y?  Choose the correct choice.
A) 96	B) 75	C) 50	D) 25	E) 12

Solution: Guys, one more simple funda.   5/2= 
5/2 = 5/2 = around 2.5
2.5   now .5 x2=1 is the remainder     25/4= 
  25/4 = 25/4 = around 6.25
6.25   now .25x4=1 is the remainder     32/5= 
  32/5 = 32/5 = around 6.4
6.4   now.4x5= 2 is the remainder   given x/y = 6.12 and remainder is 6   So .12 X y = 6   hence y= 50   Ans 50
Answer: C
An artist wishes to paint a circular region on a square poster that is 2.4 feet on a side. If the area of the circular region is to be 1/2 the area of the poster, what must be the radius of the circular region in feet?	Choose the correct answer:	A) 1/pi	B) sqrt(2.88/pi)	C) 1	D) 2/sqrt(pi)	E) pi/2

Solution: Area of the poster is 2.4x2.4 = 5.76   1/2 the area = 2.88   pi*r^2 = 2.88   r^2 = 2.88/pi   r = sqrt(2.88/pi) answer (sqrt(2.88/pi))
Answer: B
From a point P, on the surface of radius 3 cm, two cockroaches A and B started moving along two different circular paths, each having the maximum possible radius, on the surface of the sphere, that lie in the two different planes which are inclined at an angle of 45 degree to each other. If A and B takes 18 sec and 6 sec respectively, to complete one revolution along their respective circular paths, then after how much time will they meet again, after they start from P?	Choose the correct answer
A) 9 sec  B) 18 sec  C) 24 sec  D) 20 sec  E) 23 sec

Solution: Explanation :   Both the circular paths have the maximum possible radius hence, both have a radius of 3 cm each. Irrespective of the angle between the planes of their circular paths, the two cockroaches will meet again, at the point Q only, which is diametrically opposite end of P.   A will takes 9 seconds to reach point Q, completing half a revolution.   On the other hand, B would have completed 32 of his revolution and it will also reach pointQ simultaneously.   9 secnswer : 9 sec
Answer: A
If $5,000 is invested in an account at a simple annual rate of r percent, the interest is $250. When $16,000 is invested at the same interest rate, what is the interest from the investment? Choose the correct choice from the following choices.
A) $700  B) $750  C) $850  D) $800  E) $900

Solution: -> 250/5,000=5% and 16,000*5%=800.   Thus, $800 is the answer.
Answer: D
Plaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement. Given these choices, how many candle + flower groupings can she select?
Choose the correct choice from the following choices:
A) 54 B) 72 C) 96 D) 144 E) 432

Solution: Plaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement. 2 candles from 4 candles: 4C2: 6   8 flowers from 9 flowers: 9C8 : 9   So total grouping     9*6= 
  9*6 = 54
54.   54nswer is 54.
Answer: A
What is the place value of 2 in the numeral 2734?  Select:
A) 4500  B) 5000  C) 2000  D) 8000  E) 8400

Solution: Option '2000'    2 * 1000= 
 2 * 1000 = 2_000
2000
Answer: C
Mary can do a piece of work in 12 days. Rosy is 50% more efficient than Mary. The number of days taken by Rosy to do the same piece of work is?	Choose the most appropriate option.
A) 7	B) 8	C) 9	D) 11	E) 10

Solution: Ratio of times taken by Mary and Rosy = 150:100 = 3:2   Suppose Rosy takes x days to do the work.   3:2 :: 12:x => x= 8 days.   Hence, Rosy takes 8 days to complete the work.   Answer: 8
Answer: B