MU-NLPC/Calc-aqua_rat huggingface dataset:
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is? Choose the most appropriate option
A) 4:6	B) 4:3	C) 4:1	D) 4:9	E) 4:2

Solution: Let us name the trains A and B.   Then, (A's speed) : (4:3's speed)   = √b : √a = √16 : √9 = 4:3   Answer: 4:3
Answer: B
Two pipes A and B can fill a tank in 4 and 5 hours respectively. If they are turned up alternately for one hour each, the time taken to fill the tank is?	Answers
A) 4 hrs 46 min  B) 4 hrs 24 min  C) 4 hrs 34 min  D) 3 hrs 34 min  E) 4 hrs 14 min

Solution: 1/4 + 1/5 = 9/20   20/9 = 2 2/9   9/20 * 2 = 9/10 ---- 4 hours   WR = 1 - 9/10 = 1/10   1 h ---- 1/4   ? ----- 1/10   2/5 * 60= 
2/5 * 60 = 24
24= 4 hrs 24 min   Answer: 4 hrs 24 min
Answer: B
Tina’s cat weighs 2.6 kilograms. Her dog weighs 8 times as much as her cat. How much does her dog weigh in kilograms? Choose the correct choice from the following
A) A)10.4kg	B) B)20.8kg	C) C)22kg	D) D)48kg	E) E)20kg

Solution: 2.6*8= 
2.6*8 = 20.8
20.8kg.Answer is 20.8kg.
Answer: B
The true discount on a bill due 9 months hence at 16% per annum is Rs. 150. The amount of the bill is	Choose the correct choice from the following answers.
A) 1200  B) 1764  C) 1400  D) 1354  E) None of these

Solution: Explanation:   Let P.W. be Rs.x.   Then, S.I. on Rs. x at 16% for 9 months = Rs. 150.   x Ã— 16 Ã— (9/12) Ã— (1/100) = 150 or x = 1250.   P.W. = Rs. 1250   Sum due = P.W. + T.D. = Rs.(1250   150) = Rs. 1400   Answer: 1400
Answer: C
Find the number of triangles which can be formed by joining the angular points of a polygon of 8 sides as vertices.	Options:
A) 56	B) 24	C) 16	D) 8	E) 7

Solution: Solution: A triangle needs 3 points.   And polygon of 8 sides has 8 angular points.   Hence, number of triangle formed,   = 8C3 = (8*7*6)/(1*2*3)= 
(8*7*6)/(1*2*3) = 56
56.   56nswer: Option 56
Answer: A
A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 18, what is the total amount?
Choose the correct choice.
A) 70  B) 105  C) 178  D) 177  E) 169

Solution: x:y:z = 100:45:30   20:9:6   9 --- 18   35 --- ? => 70   70nswer: 70
Answer: A
Each Machine of type A has 4 steel parts and 2 chrome parts. Each machine of type B has 2 steel parts and 1 chrome parts. If a certain group of type A and type B machines has a total of 30 steel parts and 33 chrome parts, how many machines are in the group
Answers
A) 12  B) 13  C) 14  D) 16  E) 19

Solution: Look at the below representation of the problem:   Steel Chrome total   A 4 2 30 >>no. of type A machines=30/6= 
30/6 = 5
5   B 2 1 33 >>no. of type B machines=33/3= 
33/3 = 11
11   So the answer is 16 i.e D.   Hope its clear .
Answer: D
Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 5 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 5 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 5 jars?	Choose the correct choice.
A) m+n B) 5n/25-mn C) m-n D) m E) n

Solution: working rate p = 5/m ; working rate pq =( 1/p +1/q)* n =5 or mn/5 +n/q =5 0r n/q = 5-mn/5 = 25-mn/5   q = 5n/25-mn   5n/25-mn
Answer: B
A can do a certain job in 18 days. B is 60% more efficient than A. How many days does B alone take to do the same job?  Choose the correct choice from the following choices
A) 11 1/4 days  B) 8 days  C) 5 days  D) 9 days  E) None of them

Solution: Ratio of times taken by A and B = 160 : 100 = 8 : 5.   Suppose B alone takes x days to do the job.   Then, 8 : 5 :: 18 : x = 8x = 5 x 18 =x = 11 1/4 days.   11 1/4 daysnswer is 11 1/4 days.
Answer: A
If the digits 31 in the decimal 0.00031 repeat indefinitely, what is the value of (10^5-10^3)(0.00031)?
Pick one
A) 31
B) 0.31
C) 0.0031
D) 0.00031
E) 3.1e-05

Solution: 99*0.31= 
99*0.31 = 30.69
30.69 approx. 31   31nswer : 31
Answer: A
1.5, 2.5, 4.5, 7.5, 11.5, (....) Pick
A) 16.5  B) 15.5  C) 14.5  D) 17.5  E) 17

Solution: Explanation:   1, 2, 3, 4, 5, etc.   Hence 5=16.5   16.5nswer : 16.5
Answer: A
Source: Knewton
A cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 14.0 miles per hour, inclusive. What is the maximum distance, in miles, that the cyclist could travel in 5 hours?	Choose the correct choice from the following answers
A) 42 B) 56 C) 70 D) 98 E) 140

Solution: We are told that:generallya cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 14.0 miles per hour, inclusive. Is it possible the cyclist to travel with maximum speed for some time? Why not, if there is right terrain for that. So, if there is long enough terrain for the maximum speed of 14 mph then the maximum distance, in miles, that the cyclist could travel in 5 hours would be  5*14= 
 5*14 = 70
70 miles.   Answer: 70.
Answer: C
What is the probability of flipping a fair coin six times and the coin landing on heads on at least two flips? Choose the correct choice from the following options
A) 11/16	B) 23/32	C) 29/32	D) 51/64	E) 57/64

Solution: The number of possible outcomes is 2^6=64.   0 heads: There is 1 way to have all tails.   1 head: There are 6 ways to have one head.   P(0 or 1 head)=7/64   P(at least 2 heads)=1 - 7/64 = 57/64   The answer is 57/64.
Answer: E
What number should replace the question mark?
100, 93, 79, 58, ?
Options.
A) 30 B) 26 C) 37 D) 33 E) 17

Solution: 30   30   The sequence progresses –7, –14, –21, –28.
Answer: A
A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets
Choose the correct choice from the following.
A) 30%
B) 50%
C) 40%
D) 55%
E) 60%

Solution: Number of runs made by running = 110 - (3 x 4 + 8 x 6)   = 120 - (60)= 
120 - (60) = 60
60   Now, we need to calculate 60 is what percent of 120.=> 60/120 * 100= 
60/120 * 100 = 50
50%   50%
Answer: B
With what number must 0.987 be multiplied in order to obtain the number 987?
Choose one:
A) 100	B) 1,000	C) 10,000	D) 100,000	E) None of these

Solution: Explanation: The decimal must be moved three places to the right. To do this, we must multiply by a number with three zeroes. The correct answer is 1000.The decimal must be moved three places to the right. To do this, we must multiply by a number with four zeroes. The correct answer is 1000.   Answer : (1,000)
Answer: B
I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?  Choose the correct answer:
A) 327  B) 280  C) 277  D) 216  E) 287

Solution: x*(85/100) = (480 - x)119/100   x = 280   Answer: 280
Answer: B
Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 245. What was Simran share in the profit?  Choose the correct choice from the following choices:  A) s 950.10  B) s 10,000  C) s 125.00  D) s 105.00  E) s 140.00

Solution: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.   Simran's share = Rs.245 x	3/7	= Rs. 105.   ANSWER :s 105.00
Answer: D
Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 4 percent tax on the clothing, no tax on the food, and an 10 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?	Choose the correct choice from the following options.
A) 2.8% B) 3.6% C) 4.4% D) 5% E) 6.0%

Solution: Let amount spent by Jill = 100   Clothing=50, Food=20, others=30   Tax on clothing= 2   Tax on others=3   Percentage= 5/100 =5%   Answer: 5%
Answer: D
A number Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |X|<3?	Choose one:  A) 2/5  B) 3/5  C) 3/7  D) 4/9  E) 4/11

Solution: |X||X| can take 7 values.   To get |X|<2|X|<2 ( i.e., −2<x<+2−2<x   ⇒ P(|X|<2)= Favourable 3/7asesTotal 3/7asesP(|X|<2)= Favourable 3/7asesTotal 3/7ases   = 3/7   3/7
Answer: C
The average (arithmetic man) of three integers a, b, and c is exactly poland the median. If a < b < c and a = 0, what is the value of c/b? Pick.
A) 2	B) 3	C) 8	D) 5	E) Cannot be determined from the information given.

Solution: The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=3b --> since a=0, then (0+b+c)/3=3b --> c=8b --> c/b=8.   Answer: 8.
Answer: C
A car traveled 80% of the way from Town X to Town Y at an average speed of 80 mph. The car traveled at an average speed of v mph for the remaining part of the trip. The average speed for the entire trip was 50 mph. What is v in mph? Choose the correct choice from the following answers:
A) 25 B) 35 C) 45 D) 55 E) 20

Solution: Assume total distance = 100miles   Time taken for 80 miles = 80/80= 
80/80 = 1
1 hour   Time taken for the rest of the 20 miles= 20/v hours.   Average speed = 50   Therefore the total time needed = 2 hours.   2 = 1 + 20/v   Hence v = 20 mph   Answer : 20
Answer: E
A wears black shoes 25% of the time while B wears black shoes 68% of the time. 20% of the time A and B wear black shoes on the same day. Over a period of 100 days, how many days will they both not have black shoes?
Choose the correct option
A) 27%
B) 12%
C) 45%
D) 17%
E) 80%

Solution: 27% and B both wear black shoes 20% of the time: 0.20x100=20 days   .68x100=68-20= 
68-20 = 48
48 days 27% is wearing black shoes when B is not   .25x100=25-20= 
25-20 = 5
5 days B is wearing black shoes when 27% is not     48+5+20= 
  48+5+20 = 73
73/100 either 27% or B is wearing black shoes   1-73/100= 27% either 27% or B is NOT wearing black shoes   27%nswer is 27%
Answer: A
A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?  Choose the correct choice from the following:  A) Rs.42  B) Rs.46  C) Rs.40  D) Rs.41  E) Rs.34

Solution: 800*(25/100)= 
800*(25/100) = 200
200 ---- 5   ? ---- 1=> Rs.40   Answer: Rs.40
Answer: C
If X gets 25% more than Y and Y gets 20% more than Z, the share of Z out of Rs. 370 will be:
Pick one:	A) Rs. 300	B) Rs. 200	C) Rs. 100	D) Rs. 350	E) None of these

Solution: Z share = Z,   Y = 1.2Z   X = 1.25Ã—1.2Z,   X+Y+Z =740   (1.25Ã— 1.2+1.2+1)Z=37   3.7Z=370, Z=100   Answer: . Rs. 100
Answer: C
An agent, gets a commission of 2.5% on the sales of cloth. If on a certain day, he gets Rs. 18 as commission, the cloth sold through him on that day is worth  Select:	A) 333	B) 500	C) 887	D) 720	E) 132

Solution: Explanation:   Let the total sale be Rs. x.   Then, 2.5%. of x = 18 <=> (25/10 * 1/100 * x) = 18 <=> x = 720.   Answer: 720
Answer: D
A circular plate with a diameter of 10 inches is kept on another plate of 12 inches diameter. What fraction of the big plate's surface is not covered by the small plate? Choose the correct choice from the following answers:  A) 11/36  B) 23/10  C) 5/14  D) 22/11  E) 3/4

Solution: The questions asks us to find the surface which is not covered by the plate i.e., area of the surface not covered.   Where as circumference is the length along the edge of the circle,   2*pi*r implies the length of the curve   pi*r^2 implies area enclosed by that curve..hence 11/36rea of the circle is considered for this problem   11/36rea of the big plate=pi* r^2, where r=6   =>pi*36   11/36rea of the small plate=pi*25   Surface not covered by the plate=pi*36-pi*25=Pi*11   fraction of big plate's surface is not covered by small plate= Pi*11/total area of the big plate   =>Pi*11/Pi*36   11/36nswer 11/36
Answer: A
A , B and C are standing on a circular track of 4300m such that A and C are diametrically opposite and B is in between A and C .There clockwise order are ABC , B and C runs clockwise while A runs anti-clockwise .If the speed of A B and C are 5m/s , 8m/s and 10m/s respectively . They all start running at 10:00 AM. calculate the distance covered by B when A and C meet for the first time after 10:05AM .  Select the correct option.
A) 3240 metres	B) 3440 metres	C) 3640 metres	D) 4440 metres	E) 2440 metres

Solution: Relative speed of A & C will be.. 15 m/s.. hence for first they will meet at   2150/15= 143.33 sec (around 2min 23sec).. so time will be 10:02:23..this case will not be considered as it is before 10:05.. Again they will meet at   4300/15=286.66 sec(around 4min 46sec).. time will be 10:07:10.. this case will be considered   Hence in 7min10 sec i.e 430   In 430sec 3440 metres will cover  430*8= 
 430*8 = 3_440
3440 metres   ANSWER:3440 metres
Answer: B
Janey covered a distance of 340 miles between city A and city B taking a total of 5 hours. If part of the distance was covered at 60 miles per hour speed and the balance at 80 miles per hour speed, how many hours did she travel at 60 miles per hour?	Choose one.
A) 1 hour 45 minutes
B) 2 hours
C) 2 hours 30 minutes
D) 3 hours
E) None of these

Solution: Janey covered a distance of 340 miles between city A and city B taking a total of 5 hours.time taken at 60:time taken at 80::(greater speed-average speed):(average speed-lower speed)   average speed is   340/5= 
  340/5 = 68
68   That gives the answer 3:2=3 hours
Answer: D
A circular rim 50 inches in diameter rotates the same number of inches per second as a circular rim 15 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?	Choose the correct answer
A) 48pi/x B) 75x C) 48x D) 24x E) 200x

Solution: Revolutions - circumference of the rim.   => 50pi*X*60 = 15pi*Revolutions   => 10/3 *X *60 = Revolutions => 200X - Option 200x
Answer: E
I chose a number and divide it by 4. Then I subtracted 175 from the result and got 10. What was the number I chose?
Select:
A) 200
B) 740
C) 780
D) 500
E) 100

Solution: Let x be the number I chose, then   x/4−175=10   x/4=185   x=740   Answer is 740.
Answer: B
There are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly thenwhat is the probability that neither blue nor green?  Choose the most appropriate option:
A) 2/21
B) 3/25
C) 4/41
D) 4/23
E) 8/21

Solution: Total number of balls = (8 + 7 + 6)= 
(8 + 7 + 6) = 21
21   Let E= event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.   Therefore, n(E) = 8.   P(8/21) = 8/21.
Answer: E
The total age of A and B is 17 years more than the total age of B and C. C is how many years younger than A ?
Choose the most appropriate option.
A) 12
B) 27
C) 21
D) 17
E) 11

Solution: (A+B) - (B+C) = 17   A - C = 17.   C is younger than A by 17 years.   Answer: 17
Answer: D
The operation # is defined for all nonzero x and y by x#y = x + x/y. If S>0, then 1#(1#S) =  Pick:
A) S B) S+1 C) S/(S+1) D) (S+2)/(S+1) E) (2S+1)/(S+1)

Solution: x#y = x + x/y. If S>0, then 1#(1#S) =   You can see that a stands for y and 1 stands for x. I like to work with numbers so I did x=1 S=2 and S=y so y=2   1#S= 1+(1/2)= 
1+(1/2) = 3/2 = around 1.5
1.5 so now a is 1.5 --> 1+(1/1.5)=1 2/3 = 5/3   So now you can check by filling in S, which is 2:   A. S --> 2   B. S+1 --> 2+1=3   C. S/(S+1)-->2/(2+1)=2/3   D. (S+2)/(S+1)-->(2+2)/(2+1)=4/3   E. (2S+1)/(S+1)-->(2*2+1)/(2+1)=5/3   So (2S+1)/(S+1) is the answer.
Answer: E
A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?
Choose the correct choice from the following choices
A) 6%
B) 8%
C) 4%
D) 3%
E) 5%

Solution: C   4%   SP of first article = 1000   Profit = 20%   CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3   SP of second article = 1000   Loss = 20%   CP = (SP)*[100/(100-L)] = 5000/4= 
5000/4 = 1_250
1250   Total SP= 2000   Total CP = 2500/3 + 1250 = 6250/3   CP is more than SP, he makes a loss.   Loss = 4%P-SP = (6250/3)- 2000 = 250/3   Loss Percent = [(250/3)/(6250/3)]*100 =   0.04 * 100= 
0.04 * 100 = 4
4%
Answer: C
The larger of two negative consecutive even integers 2t and 2(t-1) is multiplied by 4 and then added to the smaller of the two original integers. Which of the following represents this operation? Choose the correct choice from the following:
A) 6t-2
B) 10t-2
C) -2
D) 3
E) -2-4t^2

Solution: larger of 2t-2, 2t (when they are negative) is 2t. the smallest of 2t and 2t-2 when they are positive is 2t-2.   therefore 4* 2t + 2t-2 = 10t-2.   option 10t-2.
Answer: B
Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes 20 seconds and his sister’s time is currently 9 minutes 36 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?	Select the correct option.
A) 3%  B) 5%  C) 7%  D) 10%  E) 12%

Solution: Bob's time = 620 secs.   His sis' time = 576 secs.   Percent increase needed = (620-576/620) * 100 = 44/640 * 100 = 7%. Ans (7%).
Answer: C
If n = 2ef, where e and f are distinct prime numbers greater than 2, how many different positive even divisors does n have, including n ? Choose one.
A) Two B) Three C) Four D) Six E) Eight

Solution: Answer - 'C' - Four.   For a number 2ef with primes ef,there will be four even divisors - 2,2*e,2*f,2*e*f
Answer: C
According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 4 cans of water to make orange juice. How many 12 ounce cans of concentrate are required to prepare 140 six-ounce servings of orange juice? Choose the correct choice from the following options:
A) 12  B) 14  C) 16  D) 18  E) 20

Solution: 1 X 12 ounce can of concentrate + 4 X 12 ounce cans of water = 60 ounces of the mixture.   60 ounces of mixture gives  (60 / 6 )= 
 (60 / 6 ) = 10
10 servings.   Thus 1 x 12 ounce can of concentrate is used to produce 10 servings of the mixture.   To make 140 servings of the mixture, we need 140 / 10= 
140 / 10 = 14
14 cans of the concentrate.   The answer is 14.
Answer: B
A hexagon of side a cm is folded along its edges to obtain another hexagon
What is the % decrease in the area aof orignal hexagon	Choose the correct option:
A) 30% B) 50% C) 75% D) 80% E) 90%

Solution: As we know, area of hexagon is = (3√3)(a^2)/2   now lets take a=2   then area = 6√3   after fold it will side become half ; a=1   new area = 1.5√3   percentage= 6√3/ 1.5√3* 100=25 %   so decrease in area =100 - 25= 
100 - 25 = 75
75%   ANSWER:75%
Answer: C
What is the average (arithmetic mean) of all multiples of 10 from 10 to 400 inclusive?
Choose the most appropriate option:	A) 190	B) 195	C) 200	D) 205	E) 210

Solution: We're asked for the average of all of the multiples of 10 from 10 to 400, inclusive.   To start, we can figure out the total number of terms rather easily:   1(10) = 10   2(10) = 20   ...   40(10) = 400   So we know that there are 40 total numbers.   We can now figure out the SUM of those numbers with 'bunching':   10 + 400= 
10 + 400 = 410
410   20 + 390= 
20 + 390 = 410
410   30 + 380= 
30 + 380 = 410
410   Etc.   Since there are 40 total terms, this pattern will create 20 'pairs' of 410.   Thus, since the average= (Sum of terms)/(Number of terms), we have...   (20)(410)/(40) =   410/2= 
410/2 = 205
205   Final Answer:205
Answer: D
A firm is comprised of partners and associates in a ratio of 2:63. If 45 more associates were hired, the ratio of partners to associates would be 1:34. How many partners are currently in the firm?  Choose the correct choice from the following choices:  A) 12  B) 14  C) 16  D) 18  E) 20

Solution: The ratio 1:34 = 2:68 so the ratio changed from 2:63 to 2:68.   68-63= 
68-63 = 5
5 which is 1/9 of the increase in 45 associates.   The ratio changed from 18:567 to 18:612.   Thus the number of partners is 18.   The answer is 18.
Answer: D
If 35% of a number is 24 less than 50% of that number, then the number is ? Choose the correct choice:
A) 180 B) 450 C) 160 D) 170 E) 185

Solution: Explanation:   Let the number be n. Then,   50% of n - 35% of n = 24   50/100 n - 35/100 n = 24   n = (24 x 100)/15 = 160.   Answer 160
Answer: C
A single discount equivalent to the discount series of 16%, 10% and 5% is?
Choose the correct choice from the following choices
A) 28.18  B) 38.9  C) 41.6  D) 31.4  E) 31.1

Solution: 100*(84/100)*(90/100)*(95/100)= 
100*(84/100)*(90/100)*(95/100) = 3_591/50 = around 71.82
71.82   100 - 71.82= 
100 - 71.82 = 28.18
28.18   28.18nswer: 28.18
Answer: A
In how many ways Chief Minister and Minister be elected from a team of 12 members?  Choose the correct option:
A) 128  B) 134  C) 132  D) 145  E) 150

Solution: To do this, if captain is elected first, then we have 12 ways of doing this.   For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)   So, the ans is 12*11= 
12*11 = 132
132 ways.   132
Answer: C
A grocer has a sale of Rs. 435, Rs. 927, Rs. 855, Rs. 230 and Rs. 562 for 5 consecutive days. How much sale must he have in the sixth day so that he gets an average sale of Rs. 625?
Choose the correct choice from the following choices:
A) Rs 741  B) Rs 5991  C) Rs 6001  D) Rs 6991  E) None of these

Solution: Explanation :   Total sale for 5 days = Rs. (435 + 927 + 855 + 230 + 562)   = Rs. 3009.   Required sale = Rs. [ (625 x 6) - 3009 ]   = Rs. (3750 - 3009)   = Rs. 741.   Rs 741nswer : Rs 741
Answer: A
When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 4/9 of its capacity. In terms of n, what is the capacity of the tank, in liters?  Pick one:
A) 10/9 n B) 4/3 n C) 3/2 n D) 9/4 n E) 7/3n

Solution: E is the answer.   To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra.   Given   - tank was already 1/3 full.   - When n ltr added, it became 4/9   So 1/3 + n = 4/9   n = 4/9 - 3/9   n = 1/9   capacity of the tank is full fraction . i.e. 1 i.e. 9/9   so the question is 9/9 is how much times n   = 9/9= 
9/9 = 1
1= xn   so x = 9/1= 
9/1 = 9
9/1= 
9/1 = 9
9n
Answer: E
Four people each roll a die once. Find the probability that at least two people will roll the same number?	Choose one.
A) 13/18
B) 14/18
C) 15/18
D) 16/18
E) 17/18

Solution: atleast 2 means   1-p(no one has same number)   p(no person has same number)=6*5*4*3/6^4=10/36   reqd probability=1-10/36   =26/36=13/18   13/18NSWER:13/18
Answer: A
Gary’s Gas Station serves an average of 16 cars per hour on Saturdays, 10 cars per hour on Sundays, and 9 cars per hour on all other days of the week. If the station is open from 6 a.m. to 10 p.m. every day, how many cars does Gary’s station serve over the course of a typical week?	Choose the correct choice from the following answers: A) 1,136 B) 1,200 C) 1,240 D) 1,280 E) 1,320

Solution: 6 a.m. to 10 p.m. = 16 hours   Number of cars serviced on weekdays = (16 * 9 * 5)   Number of cars serviced on Saturday = (16 * 16)   Number of cars serviced on Sunday = (16 * 10)   Number of cars served in a week = 16(45 + 16 + 10) = 16 * 71= 
16 * 71 = 1_136
1136   1,136nswer: 1,136
Answer: A
Two pipes A and B can fill a cistern in 12 and 15 minutes respectively. Both are opened together but after 5 minutes A is turned off. After how much more time will the cistern be filled?	Choose the correct answer.
A) 8 1/7  B) 8 1/1  C) 3 3/4  D) 8 1/2  E) 8 3/7

Solution: 5/12 + (5 + x)/15 = 1   x = 3 3/4   Answer: 3 3/4
Answer: C
Along a yard 434 metres long, 32 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees
Choose the correct choice
A) 14 B) 16 C) 10 D) 11 E) 12

Solution: Explanation:   32 trees have 31 gaps between them,   Required distance (434/31)= 
(434/31) = 14
14   Option 14
Answer: A
A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?	Choose the most appropriate option:
A) 22 B) 20 C) 92 D) 82 E) 28

Solution: 1: 2/5 = 5: 2   2/7 * 70= 
2/7 * 70 = 20
20.Answer:20
Answer: B