MU-NLPC/Calc-aqua_rat huggingface dataset:
During a certain two-week period, 75 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 2/3 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period?
Choose the correct option:
A) 5 A
B) 10 A
C) 15 A
D) 18 A
E) 25 A

Solution: Movies: 75 % comedies. 25 % remaining genre.   Now in this 25 %, there are only 2 categories. Action movies and Drama Movies.   If Action = x; Drama movies = 2x/3. Total 5x/3.   5x/3 = 25; x = 15   Action movies: 15 %   Drama movies: 10 %   we can say that out of 100 z,:   comedies: 75 z   action: 15 z   drama: 10 z   Now action movies were A   This means:   A = 15 z.   z = 5 A/ 15   Comedies: 75 z = 75 * (5 A/15)   5 5 A   5 A is the answer.
Answer: A
The average of Pratyush's marks in 7 subjects is 75. His average in six subjects excluding Science is 72. How many marks did he get in Science?	Choose the correct choice.
A) 72 B) 93 C) 99 D) 100 E) 56

Solution: Explanation :   Marks in Science (7*75 - 6*72)= 
(7*75 - 6*72) = 93
93.   Answer : 93
Answer: B
a, b, c are three distinct integers from 2 to 10 (both inclusive). Exactly one of ab, bc and ca is odd. abc is a multiple of 4. The arithmetic mean of a and b is an integer and so is the arithmetic mean of a, b and c. How many such triplets are possible (unordered triplets) ?  Choose the correct choice from the following answers:
A) 3 B) 4 C) 5 D) 2 E) 1

Solution: Explanation :   Exactly one of ab, bc and ca is odd⇒ Two are odd and one is evenabc is a multiple of 4⇒ the even number is a multiple of 4The arithmetic mean of a and b is an integer⇒ a and b are oddand so is the arithmetic mean of a, b and c.⇒ a+ b + c is a multiple of 3c can be 4 or 8.c = 4; a, b can be 3, 5 or 5, 9c = 8; a, b can be 3, 7 or 7, 9Four triplets are possible   Answer : 4
Answer: B
1397 x 1397 = ?	Choose one:
A) 1948609	B) 1949609	C) 1950609	D) 1950709	E) 1951609

Solution: 1397 x 1397	= (1397)2   = (1400 - 3)2   = (1400)2 + (3)2 - (2 x 1400 x 3)   = 1960000 + 9 - 8400   = 1960009 - 8400= 
1960009 - 8400 = 1_951_609
1951609.   1951609)
Answer: E
Jamshid and Irwin decided to make up their own version of basketball. In addition to being able to score 2-point baskets, they created ways to score 5-, 11-, and 13-point baskets. If at halftime the product of the point values of Irwin’s baskets was 2,420, how many 11-point baskets W did Irwin score? Choose the correct choice from the following.
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: First thing I noticed was that all these numbers are prime...   Prime factorization gives the following   Step 1:2*1210   Step 2:2*11*110   Step 4:2*11*11*10   Step 5:2*11*11*2*5   So he scored W=2 11-point baskets in my opinion.   Answer 2
Answer: C
An unbiased die is tossed .find the probability of getting a multiple of 3  Choose the correct choice from the following choices:
A) 3/9 B) 2/4 C) 1/3 D) 4/6 E) 4/7

Solution: Here S={1,2,3,4,5,6}   Let E be the event of getting the multiple of 3   then ,E={3,6}   P(E)=n(E)/n(S)=2/6=1/3   Ans: 1/3
Answer: C
Two variants of the CAT paper are to be given to 12 students. In how many ways can the students be placed in two rows of six each so that there should be no identical variants side by side and that the students sitting one behind the other should have the same variant. Find the number of ways this can be done Choose the correct choice from the following choices:  A) 2 x 12C6 x (6!)2  B) 2 x 6! x 6!  C) 2 x 12C6 x 6!  D) 2 x 6! x 8!  E) none of these

Solution: First select 6 people out of 12 for the first row.   The other six automatically get selected for the second row.   Arrange the two rows of people amongst themselves. Besides, the papers can be given a pattern of 121212 or 212121.   Hence the answer is 2 x 12C6 x (6!)2   2 x 12C6 x (6!)2NSWER:2 x 12C6 x (6!)2
Answer: A
A train crosses a platform of 90 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?  Choose the correct choice from the following answers
A) A)150m B) B)170m C) C)180m D) D)158m E) E)390m

Solution: Length of the train be ‘X’   X + 90/15 = X + 250/20   4X + 360 = 3X + 750   X = 390m   Answer: 390m
Answer: E
The total age of A and B is 16 years more than the total age of B and C. C is how many year younger than  Choose the correct option.
A) 14 years B) 12 years C) 56 years D) 16 years E) 55 years

Solution: Given that A+B = 16 + B + C   => A â€“ C = 16 + B â€“ B = 16   => C is younger than A by 16 years   Answer:16 years
Answer: D
Calculate the share of X , if Rs. 1628 is divided among X, Y and Z in the ratio 2 : 3 : 5?
Choose the most appropriate option: A) 321.6 B) 325.6 C) 305.6 D) 125.6 E) 225.6

Solution: 2 + 3 + 5= 
2 + 3 + 5 = 10
10   1628/10= 
1628/10 = 814/5 = around 162.8
162.8   so X's share=2*162.8= 
2*162.8 = 325.6
325.6   ANSWER:325.6
Answer: B
Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 38 miles per hour. How many miles from the station was train A overtaken by train B?	Select the correct option: A) 205 B) 245 C) 285 D) 325 E) 365

Solution: After two hours, Train A is ahead by 60 miles.   Train B can catch up at a rate of 8 miles per hour.   The time to catch up is 60/8= 
60/8 = 15/2 = around 7.5
7.5 hours.   In 7.5 hours, train A travels another  30*7.5= 
 30*7.5 = 225
225 miles for a total of 285 miles.   The answer is 285.
Answer: C
If 1 + 9 + 11 = 1, Then what is the value of
12 + 11 + 9 = ?	Choose the most appropriate option: A) 9 B) 11 C) 12 D) 13 E) 10

Solution: 10   10quation 1 + 9 + 11 = 1 can be derived from   One (o) + nine (n) + eleven (e) = one => 1   Similarly for equation,   12 + 11 + 9   Twelve (t) + eleven (e) + nine (n) => ten (10)
Answer: E
The entire contents of a full sack of flour can be used to make 15 cupcakes and 8 pizzas. The same full sack of flour can be used to make 3 cupcakes and 14 pizzas. If a full sack of flour is used to make only pizzas, how many pizzas can be made?
Pick:
A) 18 1/4	B) 15 1/2	C) 18 3/4	D) 19	E) 19 1/4

Solution: 15x+8y=3x+14y   x=1/2y. Answer 15 1/2
Answer: B
How many integerskgreater than 100 and less than 800 are there such that if the hundreds and the units digits ofkare reversed, the resulting integer is k+99?	Select
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 six pairs of such numbers   for every pair there will 10 numbers like for 12 => 102, 112,132,142,152, 162,172,182,192.   Total = 6 *10= 
6 *10 = 60
60 hence 60.
Answer: B
A table is bought for Rs.600/- and sold at Rs.700/- find gain or loss percentage	Select:
A) 25% loss
B) 30% gian
C) 25% gian
D) 30% loss
E) 45% gain

Solution: Explanation:   Formula = (Selling price ~ 25% gianost price)/25% gianost price * 100   = (700 - 600)/400 = 25% gain   Answer: Option 25% gian
Answer: C
A train covers a distance of 12 km in 10 minutes. If it takes 6 seconds to pass a telegraph post, then the length of the train is
Choose the correct choice from the following answers:
A) 100m
B) 120m
C) 140m
D) 160m
E) 170cm

Solution: Explanation:   Speed =12/10x 60 km/hr = 72 x5/18m/sec = 20 m/sec.   Length of the train = (Speed x Time) = (20 x 6) m = 120 m   Answer: Option 120m
Answer: B
Calculate the number of bricks, each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar?
Choose the correct choice from the following choices.
A) 4000	B) 5000	C) 6000	D) 7000	E) 8000

Solution: 10 * 4/100 * 5 * 90/100 = 25/100 * 15/100 * 8/100 * x   10 * 20 * 90 = 15 * 2 * x => x = 6000   ANSWER:6000
Answer: C
The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?  Choose the correct option
A) 25 cm2  B) 42 cm2  C) 49 cm2  D) 70 cm2  E) None of these

Solution: Area of a triangle = r * s   Where r is the inradius and s is the semi perimeter of the triangle.   Area of triangle = 2.5 * 28/2= 
2.5 * 28/2 = 35
35 cm2   ANSWNone of theseR:None of these
Answer: E
The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?	Choose the correct choice from the following answers
A) 34	B) 28	C) 12	D) 17	E) 15

Solution: Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.   P + Q = 10 ----- (1)   (10Q + P) - (10P + Q) = 54   9(Q - P) = 54   (Q - P) = 6 ----- (2)   Solve (1) and (2) P = 2 and Q = 8   The required number is = 28   ANSWER:28
Answer: B
A train covers a distance of 280 km in 4 hrs. What is its speed?  Answers:
A) 70 km/hr
B) 60 km/hr
C) 50 km/hr
D) 40 km/hr
E) 80 km/hr

Solution: Distance covered =280 km. Time taken =4 hrs. Speed =Distance/time =280/4= 
280/4 = 70
70 km/hr. 70 km/hrnswer : 70 km/hr
Answer: A
The perimeter of a square circumscribed about a circle of radius r is: Select
A) 2r  B) 4r  C) 6r  D) 9r  E) 8r

Solution: 8rach side of the square = 2r   Perimeter of the square = (4×2r) = 8r   Answer is 8r.
Answer: E
A certain quantity of 65% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%.
What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced? Choose the correct choice:  A) 1:3  B) 1:2  C) 2:3  D) 2:1  E) 3:1

Solution: 25% - - - - - - - - - 35% - - - - - - 65%   From 25 to 35 =10   From 35 to 65 = 30   So the ratio is 10/30 = 1 to 3   3:1 it is
Answer: E
The bus that travels from St. Louis to Chicago and back comes to St. Louis every 6 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 2 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 answer:	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 = 6 hours   Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 2 hours   Time taken by both buses to meet again in St. Louis will be LCM of 6 and 2 = 6   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
In covering a distance of 30 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:
Choose the correct choice from the following answers:	A) 5 km/h	B) 8 km/h	C) 10 km/h	D) 15 km/h	E) 20 km/h

Solution: Let A's speed be X km/hr.   Then, 30/x - 30/2x = 3   6x = 30   x = 5 km/hr.   5 km/hnswer : 5 km/h
Answer: A
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 answer:
A) 6.5	B) 6.25	C) 6.75	D) 6.0	E) 7.25

Solution: Runs scored in the first 10 overs = 10 × 3.2 = 32   Total runs = 282   Remaining runs to be scored = 282 - 32= 
282 - 32 = 250
250   Remaining overs= 40   Run rate needed = 25040=6.25   Answer is 6.25.
Answer: B
If three sides of the triangle are 8 , 15 and D respectively then the how many values can D ?
Choose the correct option
A) [A] 6 B) [B] 7 C) [C] 8 D) [D]9 E) [E] infinite number of values

Solution: Needed: How many Values can D take   Concept: Sum of any two sides of a triangle is greater then the third side.   Case 1: 8+5 > D => D<13   Case 2: 5+D > 8 => D >3   Case 3: 8+D > 5 => D > -3 (Always true since D is one side of a Triangle)   Finally, 3 < D < 13. So, we can have infinite number of sides between 3 and 13.   Answer = E   PS: If question said D can take only integer value, the D = 9. Answer choice [D]9.
Answer: D
Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 6%. What is the approximate interest he pays annually?  Answers:
A) $1200
B) $2000
C) $2150
D) $2500
E) $12000

Solution: An easy way too attempt this is by approximation:   For the first quarter, he pays 6% of 10,000 which is $600.   So for the four quarters in the year, he will approximately play  600*4= 
 600*4 = 2_400
2400 over the entire year.   The compound interest will be more than 2400. All other options are not right except D.   Answer : $2500
Answer: D
A farmer with 1,350 acres of land had planted his fields with corn, sugar cane, and tobacco in the ratio of 3:2:4, respectively, but he wanted to make more money, so he shifted the ratio to 2:2:5, respectively. How many more acres of land were planted with tobacco under the new system?  Choose the correct choice from the following answers.
A) 90  B) 150  C) 270  D) 300  E) 450

Solution: Originally (4/9)*1350= 
(4/9)*1350 = 600
600 acres were planted with tobacco.   In the new system (5/9)*1350= 
(5/9)*1350 = 750
750 acres were planted with tobacco.   Thus   750-600= 
  750-600 = 150
150 more acres were planted with tobacco.   The answer is 150.
Answer: B
What is the sum of all possible solutions to |x - 2|^2 + |x - 2| = 20 ?	Answers: A) -1 B) 6 C) 7 D) 8 E) 14

Solution: Denote |x - 2| as y: y^2 + y = 20 --> y = -5 or y = 4. Discard the first solution since y = |x - 2|, so it's an absolute value and thus cannot be negative.   y = |x - 2| = 4 --> x = 6 or x = -2. The sum = 8   Answer: 8.
Answer: D
Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:  Pick one
A) 15 B) 16 C) 22 D) 18 E) 25

Solution: Work done by Sakshi in 1 day = 1/20   Since Tanya is 25% efficient than Sakshi, she completes 25% more work in a day than Sakshi.   => Tanya's 1 day work = 1/20 + 1/20 * 25/100 = 1/16   So time taken by Tanya to finish the work = 16 days answer : 16
Answer: B
A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?	Options:
A) 228  B) 150  C) 88  D) 17  E) 113

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y = x/15   (x + 100)/25 = x/15 => x = 150 m.   Answer: 150
Answer: B
Find the odd man out. 1050, 510, 242, 105, 46, 16, 3	Pick.
A) 46  B) 106  C) 105  D) 1050  E) None of these

Solution: Explanation :   1050   (1050 - 30)/2= 
(1050 - 30)/2 = 510
510   (510 - 26)/2= 
(510 - 26)/2 = 242
242   (242 - 22)/2= 
(242 - 22)/2 = 110
110   (110 - 18)/2= 
(110 - 18)/2 = 46
46   (46- 14)/2= 
(46- 14)/2 = 16
16   (16- 10)/2= 
(16- 10)/2 = 3
3   Hence, 110 should have come in place of 105. Answer : Option 105
Answer: C
A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 270 metres long in 20 seconds. The length of the train (in metres) is: Choose one.
A) 180 B) 176 C) 175 D) 96 E) None of these

Solution: Explanation:   Let the length of train be L m.   Acc. to question   (270+L)/20 = L/8   2160+8L=20L   L= 2160/12= 
2160/12 = 180
180 m   180nswer 180
Answer: A
A company that ships goods in boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (assume that the order of the colors in a pair does not matter)	Select the correct option:  A) 9  B) 8  C) 7  D) 6  E) 5

Solution: Back-solving is the best way to solve this problem.   You basically need 12 combinations (including single colors)   If we start from option 1->   1=> 4C2 + 4 = 10 (Not enough)   2=> 5C2 + 5 = 15 (Enough)   Since the minimum number is asked. It should be 5.   Answer - 5
Answer: E
If there are 30 numbers and the average of the first 10 numbers is equal to the average of last 20 number what is the sum of last 20 numbers Choose the correct choice from the following:
A) same as the sum of first 10 numbers  B) 2 times the sum of first 10 numbers  C) average of first 10 numbers  D) 3 times the sum of first 10 numbers  E) none of the above

Solution: avg of first 10 no.s= sum of 10 no./10   avg of last 20 no.s= sum of 20 no./20   as gven in question,   sum of first 10 no./10= sum of last 20 no./20   so asnwr comes b)   2 times sum of first 10 no.s   ANSWER:2 times the sum of first 10 numbers
Answer: B
A man walk at 5 kmph uphill and 10 kmph downhill. He takes 6 hours to walk uphill from lower point A to upper point B and back to A. What is the total distance traveled by him in 6 hours?	Select.
A) 20
B) 22
C) 24
D) 30
E) 40

Solution: Uphill distance traveled per hour - 5 km,   distance traveled after 4 hours = 20 km.   He remained with 2 hours travel downhill, i.e. distance traveled in remaining 2 hours downhill = 20 km   so total distance traveled from A to B and Back to point A = 20 km uphill + 20 km downhill = 40 km   (Answer : 40)
Answer: E
If x#y is defined to equal x/y for all x and y, then (-1#2)#3 =  Select the correct option:  A) 4/3  B) -1/6  C) 1/12  D) -1/12  E) -4/3

Solution: (-1)/ 2 = -1/2   (-1/2) / 3 = -1/6   so -1/6 is my answer
Answer: B
In a St.Johns college students, 50 percent are third year students and 80 percent are not second-year students. What fraction of those students who are not third-year students are second-year students?  Answers.
A) 3/4 B) 2/5 C) 4/7 D) 1/2 E) 3/7

Solution: = 20/50. = 2/5   my answer is 2/5 too
Answer: B
The mass of the sun is approximately 2 × 10^30 kg and the mass of the moon is approximately 4 × 10^12 kg. The mass of the sun is approximately how many times the mass of the moon?  Choose the correct choice from the following:	A) 4.0 × 10^(−18)	B) 2.5 × 10^17	C) 4.0 × 10^18	D) 5 × 10^17	E) 4.0 × 10^42

Solution: Mass of sun = x * Mass of moon   x = Mass of sun / Mass of moon = (2 × 10^30) / (4 × 10^12) = 2*2^-2*10^18 = 10^18/2 = 5*10^17   Ans. 5 × 10^17) 5 × 10^17
Answer: D
A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
Choose one: A) 159 m B) 167 m C) 156 m D) 100 m E) 197 m

Solution: A can give B (5 min - 4 1/2 min) = 30 sec start.   The distance covered by B in 5 min = 1000 m.   Distance covered in 30 sec = (1000 * 30)/300= 
(1000 * 30)/300 = 100
100 m.   A can give B 100m start.   Answer: 100 m
Answer: D
In a certain group of 10 developers, 2 developers code only in C++ and the rest program in either Q-basic or Java - but not both. If a developer organization is to choose a 4-member team, which must have at least 1 developer who codes in C++, how many different programming teams can be chosen?	Choose the correct answer.
A) 100
B) 40
C) 70
D) 150
E) 140

Solution: The problem asks for a combination, since order doesn't matter. Now, selecting r items from a set of n gives the Combination Formula: nCr= n!/r!(n-r)!   n = 10   r = 4   So, total teams is 10C4 = 10!/(4!(10 - 4)!) = 210, and   n = 10 - 2= 
10 - 2 = 8
8   r= 4   for teams without C++ is 8C4 = 8!/(4!(8 - 4)!) = 70,   so, teams with at least 1 C++ = 210 - 70= 
210 - 70 = 140
140   Answer: 140
Answer: E
While playing a certain dice game, Chris wins if the sum of the two dice is 8, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win?
Choose the correct choice from the following answers.
A) 1/2  B) 17/36  C) 137/379  D) 11/36  E) 25/216

Solution: Probability of winning game = 1- Probability of losing game   Probability of losing game = (Probability of not getting sum 7 in any of the three attempts)   Ways of getting sum 8 = (2,6)(3,5)(4,4)(5,3)(6,2)= 5 ways   Total ways of getting outcome on two dice =6*6= 
6*6 = 36
36   Probability of getting sum as 8 in any attempt=5/36   Probability of NOT getting sum as 8 in any attempt = 1-(5/6)= 31/36   Probability of losing game =(31/36)*(31/36)*(31/36)=242/379   I.e. Probability of wining game = 1-(242/379) = 137/379   Answer : Option 137/379
Answer: C
The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 1 year?	Choose the correct choice:
A) 12300 B) 12350 C) 12000 D) 12500 E) 12600

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   10000 Ã— 120/100 = 12000   12000
Answer: C
The value of x + x(x^x) when x = 10 is  Choose the correct choice from the following choices
A) 100000000010
B) 10000000010
C) 10000000000
D) 1200000000
E) 12000000010

Solution: Solution:   x + x(x^x)   Put the value of x = 10 in the above expression we get,   10 + 10(10^10)   = 10 + 10(10 Ã— 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10)   = 10 + 10(10000000000)   = 10 + 100000000000= 
10 + 100000000000 = 100_000_000_010
100000000010   100000000010nswer: (a)
Answer: A
Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6
Pick one.
A) 4/3  B) 21/8  C) 18/7  D) 8/21  E) 7/18

Solution: Clearly n(S)=6*6= 
6*6 = 36
36   Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.Then   E={(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),   (6,6)}   n(E)=14.   Hence p(e)=n(e)/n(s)=14/36=7/18   Ans: 7/18
Answer: E
If x is 30 percent more than y and y is 40 percent less than z, then x is what percent of z?	Choose the correct choice:
A) 78% B) 250% C) 500/3% D) 125% E) 60%

Solution: Z = 100 ; Y = 60 so X = 78   X as % of Z = 78/100 * 100= 
78/100 * 100 = 78
> 78%   78%nswer will be (78%)
Answer: A
Alcohol cost 3.50 per litre and kerosene oil cost 2.50 per litre. In what proportion these should be mixed so that the resulting mixture may be 2.75 per litre? Choose the correct option.
A) 2 : 5	B) 1 : 3	C) 4 : 7	D) 2 : 3	E) None of these

Solution: ∴ Required ratio = 0.25⁄0.75 = 1⁄3 i.e, 1 : 3   Answer 1 : 3
Answer: B
A jogger is running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 meters long train . The train is running at 45 kmph in the same direction. how much time does it take for the train to pass the jogger? Choose the correct choice from the following answers:	A) 34	B) 36	C) 32	D) 30	E) 38

Solution: Distance to be covered = 240+ 120= 
240+ 120 = 360
360 m   Relative speed= 36 km/hr = 36×10/36 = 10 m/s   Time = distance/speed = 360/10= 
360/10 = 36
36 seconds   Answer is 36.
Answer: B
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?  Choices:
A) 200
B) 250
C) 400
D) 500
E) 600

Solution: C's 1 day's work =	1	- 1	+	1 =	1	-	7	1 - 1 + 1= 
1 - 1 + 1 = 1
1	-	7=	1	.   3	6	8	3	24	24   A's wages : B's wages : C's wages =	1	:	1	:	1	= 4 : 3 : 1.   6	8	24   C's share (for 3 days) = Rs. 3 x	1	x 3200 = Rs. 400.   24   Answer is 400
Answer: C
A car covers a distance of 930 km in 6 hours. Find its speed? Choose the correct option: A) 104 kmph B) 289 kmph C) 288 kmph D) 155 kmph E) 177 kmph

Solution: 930/6= 
930/6 = 155
155 kmph   Answer: 155 kmph
Answer: D
For how many different positive integers n is a divisor of n^3 + 8?
.
Choose the correct choice.
A) None
B) One
C) Two
D) Three
E) Four

Solution: n^3 + 8 = (n+2)(n^2-2n+4)   --> 2 divisors possible, plus 1 and n   we have 4 divisors. ANSWFourR:Four
Answer: E
A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long? Choose the correct choice.
A) 22	B) 89	C) 77	D) 66	E) 21

Solution: Speed = 240/24= 
240/24 = 10
10 m/sec.   Required time= (240 + 650)/10= 
(240 + 650)/10 = 89
89 sec.   Answer:89
Answer: B