mathewhe/aqua_rat huggingface dataset:
Question: The speeds of three asteroids were compared. Asteroids X-13 and Y-14 were observed for identical durations, while asteroid Z-15 was observed for 2 seconds longer. During its period of observation, asteroid Y-14 traveled three times the distance X-13 traveled, and therefore Y-14 was found to be faster than X-13 by 8000 kilometers per second. Asteroid Z-15 had an identical speed as that of X-13, but because Z-15 was observed for a longer period, it traveled five times the distance X-13 traveled during X-13's inspection. Asteroid X-13 traveled how many kilometers during its observation?
(A) 500
(B) 1,600/3
(C) 1,000
(D) 1,500
(E) 2,000
Rationale: X13: (t, d, s)
Y14: (t, 3d, s+8000mi/hour)
Z15: (t+2 seconds, s, 5d)
d=?
Distance = Speed*Time
x13: d = s*t
x14: 3d = (s+8000)*t ===> 3d = ts+8000t
z15: 5d = s*(t+2t) ===> 5d = st+2st ===> 5d - 2st = st
3d = 5d - 2st + 8000t
-2d = -2st + 8000t
2d = 2st - 8000t
d = st -4000t
x13: d = s*t
st - 4000t = s*t
s - 4000 = s
-2000 = s
I got to this point and couldn't go any further. This seems like a problem where I can set up individual d=r*t formulas and solve but it appears that's not the case. For future reference how would I know not to waste my time setting up this problem in the aforementioned way? Thanks!!!
The distance of Z15 is equal to five times the distance of X13 (we established that x13 is the baseline and thus, it's measurements are d, s, t)
S(T+2) = 5(S*T)What clues would I have to know to set up the equation in this fashion? Is it because I am better off setting two identical distances together?
ST+2S = 5ST
T+2 = 5T
2=4T
t= 1/2
We are looking for distance (d=s*t) so we need to solve for speed now that we have time.
Speed y14 - speed x13
Speed = d/t
3d/t - d/t = 8000 (remember, t is the same because both asteroids were observed for the same amount of time)
2d = 8000
2 = 4000
d=s*t
d=4000*(1/2)
d=2000
ANSWER: E
Answer: (E) 2,000
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 7 seconds. Find the length of the faster train?
(A) 70
(B) 20
(C) 30
(D) 75
(E) 15
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 7 * 10 = 70 m.
The length of the faster train = 70 m.
Answer: A
Answer: (A) 70
Question: A lady grows Cauliflower in her garden that is in the shape of a square. Each Cauliflower takes 1 square foot of area in her garden. This year, she has increased her output by 401 Cauliflower when compared to last year. The shape of the area used for growing the Cauliflower has remained a square in both these years. How many Cauliflowers did she produce this year?
(A) 44001
(B) 44000
(C) 40400
(D) 40401
(E) Cannot be determined
Rationale: Explanatory Answer
The shape of the area used for growing Cauliflower has remained a square in both the years.
Let the side of the square area used for growing Cauliflower this year be X ft.
Therefore, the area of the ground used for cultivation this year = X2 sq.ft.
Let the side of the square area used for growing Cauliflower last year be Y ft.
Therefore, the area of the ground used for cultivation last year = Y2 sq.ft.
As the number of Cauliflower grown has increased by 401, the area would have increased by 401 sq ft because each Cauliflower takes 1 sq ft space.
Hence, X2 - Y2 = 401
(X + Y)(X - Y) = 401.
401 is a prime number and hence it will have only two factors. i.e., 401 and 1.
Therefore, 401 can be expressed as product of 2 numbers in only way = 401* 1
i.e., (X + Y)(X - Y) = 401 * 1
So, (X + Y) should be 401 and (X - Y) should be 1.
Solving the two equations we get X = 201 and Y = 200.
Therefore, number of Cauliflower produced this year = X2 = 2012 = 40401
Alternative Approach : Use answer choices
The area in both the years are squares of two numbers.
That rules out choice A,B and C . as 44001,44000 and 40400 are not the square of any number.
Check Choice D: If this year's produce is 40401, last year's produce would have been 40401- 401= 40000
40000 is the square of 200.
So, 40401 is the answer.
Choice D.
Answer: (D) 40401
Question: An workshop has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee?
(A) 10
(B) 12
(C) 15
(D) 24
(E) 30
Rationale: An workshop has 6 employees;for male 1C1 = 1 ........ A
foe female = 5C2 = 10.........B
total = 10*1
= 10 - answer=A
Answer: (A) 10
Question: haresh went to buy fruits.she bought 1 apple , 3 bananas , 5 oranges and paid 21 rupees.another person bought 7 apple ,5 bananas , 3 oranges and paid 51 rupees.if i want to buy 1 apple, 1 banana , 1 orange then how much i have to pay?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 7
Rationale: There can be multiple possible rates of apple, banana and orange to satisfy given conditions, But cost of 1 apple, 1 banana , 1 orange will be Rs 9.
1x+3y+5z = 21........(1)
7x+5y+3z = 51........(2)
Adding (1) and (2), we get
8x+8y+8z = 72
8*(x+y+z)=72
x+y+z=9
ANSWER:B
Answer: (B) 9
Question: The speed of a boat in still water is 8km/hour. If it can travel 1 km upstream in 1 hourr, what time it would take to travel the same distance downstream?
(A) 2 minutes
(B) 4 minutes
(C) 6 minutes
(D) 7 minutes
(E) 8 minutes
Rationale: Speed of the boat in still water = 8 km/hr
Speed upstream =11 = 1 km/hr
Speed of the stream = 8-1 = 7 km/hr
Speed downstream = (8+7) = 15 km/hr
Time taken to travel 1 km downstream =115 hr = 1×6015= 4 minutes
B
Answer: (B) 4 minutes
Question: A dog is tied to a tree by a long nylon cord. If the dog runs from the due North side of the tree to the due South side of the tree with the cord extended to its full length at all items, and the dog ran approximately 30 feet, what was the approximate length of the nylon cord, in feet?
(A) 30
(B) 25
(C) 15
(D) 10
(E) 5
Rationale: Because the cord was extended to its full length at all items, the dog ran along a semi-circular path, from north to south.
The circumference of a full circle is 2*pi*r, but since we only care about the length of half the circle, the semi-circle path is pi*r.
pi*r = 30. Round pi = 3, then r = 10.
Chord is about 10 feet long
ANSWER:D
Answer: (D) 10
Question: X can finish a work in 21 days. Y can finish the same work in 15 days. Y worked for 5 days and left the job. how many days does X alone need to finish the remaining work?
(A) 12
(B) 13
(C) 16
(D) 14
(E) 18
Rationale: Work done by X in 1 day = 1/21
Work done by Y in 1 day = 1/15
Work done by Y in 5 days = 5/15 = 1/3
Remaining work = 1 – 1/3 = 2/3
Number of days in which X can finish the remaining work = (2/3) / (1/21) = 14
D
Answer: (D) 14
Question: During the first two weeks of January, the total rainfall in Springdale was 30 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall during the second week of January?
(A) 5 inches
(B) 6 inches
(C) 9 inches
(D) 10 inches
(E) 18 inches
Rationale: Total rainfall in 2 weeks = 18 inches.
Assume the rainfall in second week = 1.x
Rainfall in first week = x
Total rainfall = 2.5x = 18 inches
x = 12 and 1.5x = 18
Rainfall during second week = 18 inches
Option E
Answer: (E) 18 inches
Question: The least number which when divided by 4, 6, 7 and 8 leaves a remainder 6, but when divided by 9 leaves no remainder, is
(A) 340
(B) 342
(C) 523
(D) 363
(E) None of these
Rationale: Explanation:
L.C.M of 4, 6, 7, 8 = 168
therefore Required Number is of the form 168k+6.
Least value of k for which (168k+6) is divisible by 9 is k = 2
therefore Required Number = (168 x 2+6)=342. Answer: B
Answer: (B) 342
Question: Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
(A)  $ 165
(B)  $ 145
(C)  $ 175
(D)  $ 180
(E)  $ 170
Rationale: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by (B)$ 145.
Answer: (B)  $ 145
Question: A fair price shopkeeper takes 10% profit on his goods. He lost 20% goods during theft. His loss percent is:
(A) 8
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: Explanation:
Suppose he has 100 items. Let C.P. of each item be Re. 1.
Total cost = Rs. 100. Number of items left after theft = 80.
S.P. of each item = Rs. 1.10
Total sale = 1.10 * 80 = Rs. 88
Hence, loss % = 12/100 * 100 = 12%
Answer is D
Answer: (D) 12
Question: An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2400, what will be the difference between Q and R's share?
(A) 3009
(B) 3000
(C) 3002
(D) 3001
(E) 3005
Rationale: 4 --- 2000
5 --- ? => 3000
Answer: B
Answer: (B) 3000
Question: If the sides of a triangle are 91 cm, 84 cm and 35 cm, what is its area?
(A) 120 cm2
(B) 1470 cm2
(C) 216 cm2
(D) 197 cm2
(E) 275 cm2
Rationale: The triangle with sides 91 cm, 84 cm and 35 cm is right angled, where the hypotenuse is 91 cm.
Area of the triangle
= 1/2 * 84 * 35
= 1470 cm2
Answer: B
Answer: (B) 1470 cm2
Question: Little John had $10.50. He spent $2.25 on sweets and gave to his two friends $2.20 each. How much money was left?
(A) $1.85
(B) $ 3.85
(C) $4.85
(D) $6.85
(E) $5.85
Rationale: John spent and gave to his two friends a total of
2.25 + 2.20 + 2.20 = $6.65
Money left
10.50 - 6.65 = $3.85
correct answer is B) $ 3.85
Answer: (B) $ 3.85
Question: (√112+√567)/√175=?
(A) 2√2
(B) 13/5
(C) 3√2
(D) 3√3
(E) √2
Rationale: (√112+√567)/√175=(4√7+9√7)/5√7
=13/5
Hence, the correct answer is B.
Answer: (B) 13/5
Question: When a metallic ball bearing is placed inside a cylindrical container, of radius 2 cm, the height of the water, inside the container, increases by 0.6 cm. The radius, to the nearest tenth of a centimeter, of the ball bearing is
(A) 1 cm
(B) 1.2 cm
(C) 2 cm
(D) 0.6 cm
(E) None
Rationale: Solution
When the ball was put in water, the volume of water increased by.
pi*22*0.6 = 2.4 pi cubic cm
The above volume is equal to the volume of the ball with radius r to find. Hence
(4/3)*pi*r3 = 2.4 pi
Solve the above for r
r = 1.2 cm
Answer B
Answer: (B) 1.2 cm
Question: What is the least number that should be added to 1054, so the sum of the number is divisible by 23?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: (1054 / 23) gives a remainder 19 so we need to add 4.
The answer is D.
Answer: (D) 4
Question: The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (9,0) and (9,4). If a line through (1,1) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
(A) 1/5
(B) 2/7
(C) 3/8
(D) 2/9
(E) 1/4
Rationale: We should know that a rectangle can be divided into two equal areas by a straight line only when the straight line passes through the center of the rectangle.
The center of the rectangle is the point (4.5,2).
The slope of line passing through points (1,1) and (4.5,2) = (2-1)/(4.5-1) = 1/3.5 = 2/7
The answer is B.
Answer: (B) 2/7
Question: A batsman makes a scores of 98 runs in his 19th inning and thus increases his average by 4. What is his average after 19th inning ?
(A) 22
(B) 24
(C) 28
(D) 26
(E) None of the above
Rationale: Let the average score of 19 innings be x.
Then, 18x+98/19=x+4
The average score after 20th innings
= x + 4 = 22 + 4 = 26
Answer D
Answer: (D) 26
Question: 0.1+0.1^2+0.1^3 =
(A)  0.1
(B)  0.111
(C)  0.1221
(D)  0.2341
(E)  0.3
Rationale: You have a mistake in your question. Choice B should be (.111) and not (.11).
The equation in the solution can be simplified to (.1 + .01 + .001).
Adding those together you get:
.100
.010
.001
------
.111 - Which is answer choice (B)
Answer: (B)  0.111
Question: Solve the equation for x : 14(-x + z) + 18 = -14(x - z) - 10
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: D
1
-14x + 14z + 18 = -14x + 14z - 10
-28x + 28 = 0
-28x = -28
=> x = 1
Answer: (D) 1
Question: The average age of a husband and a wife is 25 years when they were married five years ago but now the average age of the husband, wife and child is 21 years(the child was born during the interval). What is the present age of the child?
(A) 3 years
(B) 5 years
(C) 9 years
(D) 4 years
(E) 1 years
Rationale: 30 * 2 = 60
21 * 3 = 63
-----------
3 years
Answer:A
Answer: (A) 3 years
Question: A cube is painted such that one pair of surfaces is painted brown and the other pair of surfaces is painted orange. The cube is cut in to 64 small cubes of equal size. Find how many cubes have both the color brown and orange?
(A) 22
(B) 16
(C) 11
(D) 12
(E) 10
Rationale: There are 6 surfaces to the cube. In which opposite surfaces are painted brown and other 2 opposite surfaces are painted orange. Then 4 edges of the cube have both the colors. Since the big cube cut in to 64 smaller cubes, the 4 edges of the cube have both the colors. Since the big cube cut into 64 smaller cubes, the 4 edges of the big cube has 4×4=16 smaller cubes have both brown and orange colors. Answer = 16
Answer:B
Answer: (B) 16
Question: At a speed of 50 miles per hour, a certain car uses 1 gallon of gasoline every 30 miles. If the car starts with a full 20 gallon tank of gasoline and travels for 5 hours at 50 miles per hour, the amount of gasoline used would be what fraction of a full tank?
(A) 3/25
(B) 11/36
(C) 5/12
(D) 2/3
(E) 25/36
Rationale: Gas used = (5 hours)*(50 miles/hour)*(1 gallon/30 miles) = 8+1/3 gallons
Portion used = (8+1/3) / 20 = 5/12
Ans C
Answer: (C) 5/12
Question: If x > 0, x/50 + x/25 is what percent of x?
(A) 6%
(B) 25%
(C) 37 1/2%
(D) 60%
(E) 75 %
Rationale: Just plug and chug. Since the question asks for percents, pick 100. (but any number will do.)
100/50 + 100/25= 2+4 =6
6 is 6% of 100. ANSWER:A
Answer: (A) 6%
Question: There is a ratio of 5 : 4 between two numbers. If forty percent of the first number is 12 then what would be the 50 percent of the second number?
(A) 12
(B) 24
(C) 18
(D) Data inadequate
(E) None of the above
Rationale: a⁄b = 5⁄4, b = 4⁄5a Given (40% of a) = 2⁄5a = 12
a = 5 × 6 and b = 4⁄5 × 5 × 6 = 24
∴ 50% of b = 24⁄2 = 12
Answer A
Answer: (A) 12
Question: How many liters of water must be added to 18 liters of milk and water containing 10% water to make it 70% water?
(A) 28
(B) 32
(C) 36
(D) 40
(E) 44
Rationale: By rule of alligation:
70% - 10% = 60%
100% - 70% = 30%
Quantity of pure water : Quantity of the mixture = 6 : 3
There are 18 liters of mixture, so we need to add 36 liters of pure water.
The answer is C.
Answer: (C) 36
Question: Four people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
(A) 7/8
(B) 1/8
(C) 1/3
(D) 1/7
(E) 1/9
Rationale: Original share of 1 person =1/4
New share of 1 person =1/3
Increase =1/3 -	1/4	=1/12
Required fraction =	(1/12)/(1/4)	=1/3
Answer is C.
Answer: (C) 1/3
Question: A music band that must consists of 4 members is to be formed from a pool of 9 candidates. How many different bands are possible
(A) 100
(B) 144
(C) 126
(D) 56
(E) 336
Rationale: Note that the band must consist of 4 members, not at least 4 members. Hence, all you have to do is 9C4 = 56
Answer (D)
Answer: (D) 56
Question: A sum of money invested at compound interest amounts to Rs.800 in 3 years and to Rs.840 in 4 years. The rate of interest per annum is
(A) 2x1/2%
(B) 4%
(C) 5%
(D) 6x2/3%
(E) None
Rationale: Solution
S.I. on Rs.800 for 1 year	=Rs[840 - 800]
= Rs.40
Rate	=(100x40/800x1)%
= 5%
Answer C
Answer: (C) 5%
Question: A sum of Rs. 2691 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
(A) 1656
(B) 1640
(C) 1632
(D) 2789
(E) 6386
Rationale: (x*8*3)/100 = ((2691 - x)*3*5)/100
24x/100 = 40365/100 - 15x/100
39x = 39975 => x = 1035
Second sum = 2691 – 1035
=1656
Answer:A
Answer: (A) 1656
Question: What is the 100th term of the series 2,4,8,14,22?
(A) 9902
(B) 9903
(C) 9904
(D) 9905
(E) 9906
Rationale: this is in the form
the every N th number is (N-1)*N+2
for 1st numner aplly above formula
1st number=0*1+2=2
2nd number=1*2+2=4
3rd number=2*3+2=8
4th number=3*4+2=14
5th number=4*5+2=22
so 100 th number will be
99*100+2=9902.
ANSWER:A
Answer: (A) 9902
Question: A water tank is one-fifth full. Pipe A can fill a tank in 15 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how many minutes will it take to empty or fill the tank completely?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: The combined rate of filling/emptying the tank = 1/15 - 1/6 = -1/10
Since the rate is negative, the tank will be emptied.
A full tank would take 10 minutes to empty.
Since the tank is only one-fifth full, the time is (1/5) * 10 = 2 minutes
The answer is A.
Answer: (A) 2
Question: A sporting goods store sold 60 Frisbees in one week, some for $3 and the rest for $4 each. If receipts from Frisbee sales for the week totaled $200, what is the fewest number of $4 Frisbees that could have been sold?
(A) 24
(B) 12
(C) 20
(D) 4
(E) 2
Rationale: The wording of the question is slightly misleading. When a question asks what is thefewestthatcouldhave been sold, it is suggesting that there could be many different quantities sold.
In this question however, because we are told that exactly 64 Frisbees have been sold and revenue was exactly $204, there is only one possible solution for the number of $3 and $4 Frisbees sold.
To solve, we have 2 equations and 2 unknowns
Let x = number of $3 Frisbees sold
Let y = number of $4 Frisbees sold
x + y = 60
3x + 4y = 200
x = 60 - y
3(60-y) + 4y = 200
180 - 3y + 4y = 200
y = 20
Answer: C
Answer: (C) 20
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the integers between 1 and 50?
(A) 1275
(B) 1542
(C) 985
(D) 1024
(E) 1125
Rationale: sum = 50*51/2 = 25*51 = 1275
Answer is A
Answer: (A) 1275
Question: A rectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. If regular tiles cover 70 square feet of the wall, and no tiles overlap, what is the area of the entire wall?
(A) 160
(B) 240
(C) 385
(D) 440
(E) 560
Rationale: The number of jumbo tiles = x.
The number of regular tiles = 2x.
Assume the ratio of the dimensions of a regular tile is a:a --> area = a^2.
The dimensions of a jumbo tile is 3a:3a --> area = 9a^2.
The area of regular tiles = 2x*a^2 = 70.
The area of jumbo tiles = x*9a^2 = 4.5(2x*a^2 ) = 4.5*70 = 315.
Total area = 70 + 315 = 385
Answer: C.
Answer: (C) 385
Question: If P represents the product of the first 16 positive integers, then P is not a
multiple of:
(A) a) 99
(B) b) 84
(C) c) 72
(D) d) 65
(E) e) 57
Rationale: a) 99 = 9*11
b) 84 = 4*7*3
c) 72 =9*8
d) 65 = 5*13
e) 45 =9*5
since 11 is not there in first 15 positive numbers it is the only possibility
A
Answer: (A) a) 99
Question: A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers Q are possible?
(A) 2
(B) 4
(C) 6
(D) 3
(E) Not possible
Rationale: Firstly , we should note that 1 is NEITHER a prime nor a composite number.The first composite number is 4.Thus, when the problem states that there are 4 factors that are not composite, these nos are 1,2,3,5. Thus, the given number = 2^a*3^b*5^c. Also, (a+1)*(b+1)*(c+1) = 32. We can break down 32 into 3 integers as : 2*2*8 or 4*4*2
Also, the only possible combinations for a,b,c are : 3,3,1 OR 1,1,7. Thus, each combination has 3 possible orders and we have a total of Q= 6 possibilities.
C.
Answer: (C) 6
Question: If a man buys 20 lollipops for $90 and sold them for $2 dollars determine his loss
(A) $25
(B) $30
(C) $50
(D) $40
(E) $42
Rationale: 20 lollipops = $90, sold each for $2, so he sold 20 lollipops for 20 * $2= $40, Loss = $(90-40), loss = $50. correct answer : (C)
Answer: (C) $50
Question: How many 4-digit even numbers are possible such that if one of the digits is 5, the next/succeeding digit to it should be 7?
(A) 5
(B) 305
(C) 365
(D) 50
(E) 495
Rationale: 5700, 5710,......5798, so total 50. Hence Option D.
Answer: (D) 50
Question: Jack bought 200 packets of swiss chocolate. He was able to sell 1/2 of them at a 5% profit, another 1/4 of them at zero profit and the remainder was sold at a 10% loss. Find the total profit or loss made by Jack after selling those 200 packets. A packet sold at a loss had a price of $9.
It's a bit confusing to say 5% of profit. Please provide an intuitive answer if possible. Thanks!!
(A) 0
(B) Profit of $10
(C) Loss of $25
(D) Profit of $30
(E) Loss of $35
Rationale: A packet sold at a 10% loss had a price of $9, thus the cost of a packet is $10.
100 packets was sold at a 5% profit --> gives profit of 10*0.05*100 = $50.
50 packets was sold at a 10% loss --> gives loss of 10*0.1*50 = $50.
The overall loss is $50 - $50 = $0.
Answer: A.
Answer: (A) 0
Question: The cross-section of a stream is a trapezium in shape. If the stream is 10 m wide at the top and the area of cross-section is 640 sq m, the depth of stream is 80m and width at the bottom is?
(A) 2 m
(B) 6 m
(C) 4 m
(D) 8 m
(E) 9 m
Rationale: 1/2 * 80 (10 + b) = 640
b = 6m
ANSWER:B
Answer: (B) 6 m
Question: A can do a work in 6 days , B can do a work in 8 days and C can do it in 12 days. B left work after 4 days. For how many number of days should A and C should work together to complete the remaining work ?
(A) 0.1
(B) 0.2
(C) 0.3
(D) 0.4
(E) 0.5
Rationale: b work 1/8 * 4=1/2
remaining work =1-1/2=1/2
a and c work together =1/6+1/12=3/12=1/4
take reciprocal 4 * remaining work =2 *1/4=0.5
ANSWER:E
Answer: (E) 0.5
Question: 1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?
(A) 12.6
(B) 12.9
(C) 12.5
(D) 12.0
(E) 12.1
Rationale: 1000*15 = 1200*x
x = 12.5
Answer: C
Answer: (C) 12.5
Question: John and Cindy were each given X dollars in advance for each day they were expected to perform at a community festival. John eventually performed on all 25 days of the festival, while Cindy performed on 5 fewer days than John performed. If Cindy gives John y dollars of her advance payment so that they would have each received the same daily rate, what was John paid in advance, in terms of Y?
(A) 12Y
(B) 11Y
(C) 9Y
(D) 10Y
(E) 8Y
Rationale: Both of them were given X $ each
Cindy to adjust Y $ in advance to John
So Cindy now has (X-Y)$ and John has (X+Y) $ such that their daily rate becomes same
So Rate of CIndy= Rate of John
Also , Cindy works for 20 days and John works for full 25 days
(X-Y) / 20 = (X+Y) / 25
Solving 25x-25y=20x+20y =>5x=45y => x=45/5y
X= 9Y
Answer : C
Answer: (C) 9Y
Question: in a railway station, there are tow trains going. One in the harbour line and one in the main line, each having a frequency of 10 minutes. the main line service starts at 5 o'clock. the harbour line starts at 5.02a.m. a man goes to the station every day to catch the first train. what is the probability of man catchinhg the first train
(A) 1/5
(B) 2/5
(C) 3/5
(D) 4/5
(E) 6/5
Rationale: Probability of catching first train(train1) is 8/10=4/5
ANSWER:D
Answer: (D) 4/5
Question: A dishonest dealer uses a scale of 95 cm instead of a metre scale and claims to sell at cost price. His profit is
(A) 9%
(B) 5.26%
(C) 12%
(D) None of these
(E) Cannot be determined
Rationale: Solution
Gain%	= (5 / 95 x 100)%
= 5.26%
Answer B
Answer: (B) 5.26%
Question: A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $948 in total compensation, how many total hours did he work that week?
(A) 36
(B) 40
(C) 44
(D) 48
(E) 51
Rationale: For 40 hrs = 40*16=640
Excess = 948-640=308
For extra hours =.75(16)=12+16=28
Number of extra hrs =308/28=77/7=11
Total hrs =40+11=51
Answer E 51
Answer: (E) 51