mathewhe/aqua_rat huggingface dataset:
Question: In a certain math department, students are required to enroll in either Calculus or Trigonometry, each of which is offered in beginner and advanced courses. The number of students enrolled in Trigonometry is 50% greater than the number of students enrolled in Calculus, and 90% of Calculus students are enrolled in the beginner course. If 4/5 of students are in the beginner courses, and one student is selected at random, what is the probability that an advanced Trigonometry student is selected?
(A) 12%
(B) 16%
(C) 20%
(D) 24%
(E) 40%
Rationale: Let x be the number of students in calculus.
Then the number of students in trigonometry is 1.5x
The number of students on beginner calculus is 0.9x
The number of students in beginner trigonometry is 4/5*(2.5x) - 0.9x = 1.1x
The number of students in advanced trigonometry is 0.4x
The percentage in advanced trigonometry is 0.4x / 2.5x = 16%
The answer is B.
Answer: (B) 16%
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age seven years back was?
(A) 12yr
(B) 15yr
(C) 20yr
(D) 25yr
(E) 30yr
Rationale: Let the son's present age be x years
Then, 38-x = x
x = 19
Son's age 7 years back = 19-7 = 12 years
Answer is A
Answer: (A) 12yr
Question: A store owner estimates that the average price of type A products will increase by 35% next year and that the price of type B products will increase by 20% next year. This year, the total amount aid for type A products was $3500 and the total price paid for type B products was $6300. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?
(A) $14,755
(B) $15,325
(C) $16,000
(D) $12,285
(E) $17,155
Rationale: cost of type A products next year = 1.35 * 3500 = 4725
cost of type B products next year = 1.2 * 6300 = 7560
total 4725 + 7560 = 12285
ANSWER:D
Answer: (D) $12,285
Question: Of 70 players on a football team, 52 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
(A) 54
(B) 59
(C) 63
(D) 64
(E) 92
Rationale: Total = 70
Thrower = 52
Rest = 70 - 52 = 18
Left Handed = 18/3 = 6
Right handed = 12
If all Thrower are right handed then total right handed is 52 + 12 = 64
so D. 64 is the right answer
Answer: (D) 64
Question: If a(a + 2) = 35 and b(b + 2) = 35, where a ≠ b, then a + b =
(A) -5
(B) -6
(C) -7
(D) -2
(E) -10
Rationale: i.e. if a = 5 then b = -7
or if a = -7 then b = 5
But in each case a+b = 5-7 = -2
Answer: D
Answer: (D) -2
Question: Two trains run in opposite directions on a circular track. Train A travels at a rate of 4π miles per hour and Train B runs at a rate of 6π miles per hour. If the track has a radius of 6 miles and the trains both start from Point W at the same time, how long, in hours, after the trains depart will they again meet at Point W?
(A) 3
(B) 6
(C) 9
(D) 18
(E) 22
Rationale: I don't agree with your solutions, first. And second the answer choices don't seem to contain the right answer.
My solution is as follows, and I ask anyone to correct me if I am wrong.
Solution 1
Let the distance covered by train A be X, thus that covered by the train B will be 12*3.14-X
dA = X dB = 12*3.14 - X
Times taken by A and B are
tA= X/4*3.14 , tB = (12*3.14 - X)/6*3.14 (ii)
Since they have been traveling for the same period of time, then
X/4*3.14 = (12*3.14 - X)/6*3.14
X/2 =(12*3.14 -X)/3
3X = 2(12*3.14 -X)
5X = 24*3.14
X = 24*3.14/5
Plugging that in either equation of (ii) yields t = 6/5
Solution 2
We add the speed of A and B: totalSpeed W= 4*3.14 + 6*3.14 = 10*3.14
Total distance covered = 12*3.14
t ime = distance / speed = 12*3.14/10*3.14 = 6/5.
tA =( X/4*3.14) =(24*3.14/5)/4*3.14 = 6/5=B
Answer: (B) 6
Question: In what time will a train 100 m long cross an electric pole, it its speed be 90 km/hr?
(A) 2.5
(B) 2.9
(C) 4 sec
(D) 2.8
(E) 2.1
Rationale: Speed = 90 * 5/18 = 25 m/sec
Time taken = 100/25
= 4 sec.
Answer:C
Answer: (C) 4 sec
Question: The total circumference of two circles is 80. If the first circle has a circumference that is exactly twice the circumference of the second circle, then what is the approximate sum of their two radii?
(A) 5.7
(B) 6.0
(C) 10.6
(D) 9.7
(E) 18.0
Rationale: Let r= Radius of smaller circle. Let R = Radius of larger circle
Therefore:
2πr + 2πR = 80
where 2r = R
Thus:
2πr + 4πr = 80
6πr = 80
r = approx 4.2
πR + 2Rπ = 80
3πR = 80
R = approx 8.4
r + R = approx 10.6
Answer is C
Answer: (C) 10.6
Question: Which of the following equations has a root in common with x^2−3x+2=0 ?
(A) x^2-2x+1=0
(B) x^2-2x-1=0
(C) x^2-x+1=0
(D) x^2-3x+3=0
(E) x^2-7x=0
Rationale: If we carefully look at the given equation we can arrange it in the following manner:
(x-1)(x-2)= 0
so the two roots are 1 and 2.
Now put 1 and 2 in given equations. The equation in which one of them gives value 0, that will be our answer.
(A) putting 1: we get 0. This is the equation.
We are lucky. No need to check other options.
A is the answer.
Answer: (A) x^2-2x+1=0
Question: Three different containers contain 496 litres, 403 litres and 713 litres of mixtures of milk and water respectively. What biggest measure can measure all the different quantities exactly ?
(A) 30 litres
(B) 31 litres
(C) 32 litres
(D) 33 litres
(E) 34 litres
Rationale: 403)713(1
403
---------
310)403(1
310
----------
93)310(3
279
--------
31)93(3
93
-------
X
so answer is 31 litres......
ANSWER:B
Answer: (B) 31 litres
Question: Find the missing number. 1, 4, 9, 16, 25, 36, 49, (....)
(A) 64
(B) 54
(C) 56
(D) 81
(E) 85
Rationale: Explanation :
The series is 1^2, 2^2, 3^2, 4^2, 5^2, 6^2, 7^2,
Hence, next term = 8^2 = 64
Answer : Option A
Answer: (A) 64
Question: A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 36 grams of protein daily, how many grams of food X are in the mixture.
(A) 120
(B) 140
(C) 150
(D) 160
(E) 180
Rationale: Let x be the amount of food X.
0.1x + 0.15(300-x) = 36
0.05x = 9
x = 180
The answer is E.
Answer: (E) 180
Question: When positive integer m is divided by positive integer x, the reminder is 7 and when positive integer n is divided by positive integer y, the reminder is 11. Which of the following E is a possible value for x + y?
I. 18
II. 19
III. 20
(A) I only
(B) II only
(C) E=III only
(D) II and III only
(E) None
Rationale: TIP FOR SUCH QUESTIONS:Make Algebraic Equation in the beginning to understand how to proceed further. Then Start thinking the possible values of variables asked about
i.e.When positive integer m is divided by positive integer x, the reminder is 7can be understood as
m = ax +7which means thevalue of x must be greater than 7as the remainder 7 is possible only when the Divisor is bigger than the Remainder 7
i.e. Min Value of x = 8
AND
i.e.When positive integer n is divided by positive integer y, the reminder is 11can be understood as
n = by +11which means thevalue of y must be greater than 11as the remainder 11 is possible only when the Divisor is bigger than the Remainder 11
i.e. Min Value of y = 12
i.e. Minimum Value of x+y = 8+12 = 20
Hence III only can be True
Answer: Option
C
Answer: (C) E=III only
Question: 96% of the population of a village is 23040. The total population of the village is?
(A) 29992
(B) 24000
(C) 26892
(D) 29991
(E) 29878
Rationale: X * (96/100) = 23040
X = 240 * 100
X = 24000
Answer: B
Answer: (B) 24000
Question: The average age of 15 students of a class is 16 years. Out of these, the average age of 5 students is 14 years and that of the other 10 students is 16 years. Tee age of the 15th student is?
(A) 18years
(B) 16years
(C) 14years
(D) 12years
(E) 10years
Rationale: Age of the 15th student
=[15 * 16 - (14 * 5 + 16 * 10)]
= (240 - 230) = 10 years.
Answer:E
Answer: (E) 10years
Question: The length of a train and that of a platform are equal. If with a speed of 108 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 752
(B) 799
(C) 719
(D) 750
(E) 900
Rationale: Speed = [108 * 5/18] m/sec = 30 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 30 Ã¨ x = 30 * 60 / 2 = 900
Answer: E
Answer: (E) 900
Question: We made a down payment of $100 and borrowed the balance on a new piano which cost $1000. The balance with interest was paid in 23 monthly payments of $40 each and a final payment of $70. The amount of interest paid was what percent of the amount borrowed?
(A) 6%
(B) 7%
(C) 8%
(D) 9%
(E) 10%
Rationale: We borrowed $900.
To pay back this loan, we paid 23*$40 + $70=$990.
The interest was $990-$900=$90.
The percentage was $90/$900=0.1=10%.
The answer is E.
Answer: (E) 10%
Question: A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
(A) 100 m
(B) 200 m
(C) 600 m
(D) 800 m
(E) 400 m
Rationale: Explanation:
Relative speed of the thief and policeman = (11 â€“ 10) km/hr = 1 km/hr
Distance covered in 6 minutes = {\color{Blue} \left ( \frac{1}{60}\times 6 \right )} km = {\color{Blue} \frac{1}{10}} km = 100 m
{\color{Blue} \therefore } Distance between the thief and policeman = (200 â€“ 100) m = 100 m.
Answer: A
Answer: (A) 100 m
Question: P is a prime number. If 6p is between 15 and 95, which of the following W can be a value of 7p + 2?
(A) W=15
(B) W=79
(C) 121
(D) 65
(E) 21
Rationale: [3,5,7,11,13] are prime numbers that fits this equation 15< 6X <95. Afterwards subtract 2 from all the answer n see if it's divisible by 7. Therefore A and E are out. Leaves out with B C D.
B =11
C =17
D = 9
Only 11 is the set of prime numbers that fit between 15 and 95. Therefore 79 is the answer.B
Answer: (B) W=79
Question: David has s pairs of shoes, which is 1/4 as many as Mary and twice as many as Jones. In terms of s, how many pairs of shoes do the three of them have combined?
(A) 9/2*s
(B) 7/2*s
(C) 3s
(D) 11/2*s
(E) 5/2*s
Rationale: == s +4s + s/2 ==> 5s + 1/2 s = 11/2*s
Ans .D
Answer: (D) 11/2*s
Question: 2224 × 9997 = ?
(A) 22244428
(B) 22255538
(C) 22233328
(D) 22266628
(E) 22233327
Rationale: C
22233328
2224 × 9997 = 2224 × (10000-3)
= 2224 × 10000 - 2224 × 3
= 22240000 - 6672
= 22233328
Answer: (C) 22233328
Question: If Finn was 15 months old one year ago, how old was he, in months, x months ago?
(A) x − 30
(B) x − 12
(C) 18 − x
(D) 27 − x
(E) 30 − x
Rationale: Age Today = 15 months + 12 months (1year) = 27 months
X months ago- Today's Age - X = 27 - X
Ans- D
Answer: (D) 27 − x
Question: A, B and C can do a work in 6 days, 8 days and 12 days respectively. In how many days can all three of them working together, complete the work?
(A) 6 2/3 days.
(B) 2 2/3 days.
(C) 7 2/3 days.
(D) 1 2/3 days.
(E) 5 2/3 days.
Rationale: B
2 2/3 days.
Work done by all three of them in one day = 1/6 + 1/8 + 1/12 = 3/8.
The number of days required = 8/3 = 2 2/3 days.
Answer: (B) 2 2/3 days.
Question: (A% of 4B + B% of A) is equal to ?
(A) A% of B
(B) B% of A
(C) 5% of AB
(D) AB% of 3
(E) None
Rationale: Answer
A% of 4B + B% of A =4AB/100 + AB/100
= 5AB/100 = 5% of AB
Correct Option: C
Answer: (C) 5% of AB
Question: Pipes A and B can fill a tank in 4 and 7 hours. Pipe C can empty it in 12 hours. If all pipes are opened together, then the tank will be filled in?
(A) 60/17 hr
(B) 13/12 hr
(C) 42/13 hr
(D) 13/42hr
(E) 14/11 hr
Rationale: Net part filled in 1 hour = 1/4 + 1/7 - 1/12 = 13/42
The tank will be full in 42/13 hr
Answer is C
Answer: (C) 42/13 hr
Question: After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?
(A) 1400
(B) 1300
(C) 1200
(D) 1100
(E) None of these
Rationale: Explanation:
CP* (76/100) = 912
CP= 12 * 100 => CP = 1200
Answer is C
Answer: (C) 1200
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
(A) 187
(B) 190
(C) 177
(D) 188
(E) 112
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer: B
Answer: (B) 190
Question: 5358 x 51 = ?
(A) 273232
(B) 273243
(C) 273247
(D) 273250
(E) 273258
Rationale: 5358 x 51	= 5358 x (50 + 1)
= 5358 x 50 + 5358 x 1
= 267900 + 5358
= 273258.
E)
Answer: (E) 273258
Question: Elena’s bread recipe calls for 5 ounces of butter for each 7 cups of flour used. She needs to make 4 times the original recipe. If 12 ounces of butter is used, then how many cups of flour are needed?
(A) 1
(B) 4
(C) 9
(D) 13
(E) 28
Rationale: Solving through algebra route:
5B + 7F = x amount
If we multiply this equation with 4 we get:
20B + 28F =4X
Therefore, we got 20 ounces of butter and 4X amount of quantity when we use 28 ounces of floor.
Ans:E
Answer: (E) 28
Question: The price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980. If its price of $1.20 in 1970 was 150 percent of its price in 1960, what was its price in 1980?
(A) $ 1.80
(B) $ 2.00
(C) $ 2.40
(D) $ 2.70
(E) $ 3.00
Rationale: The price in 1970 was 150 percent of its price in 1960, means that the percent increase was 50% from 1960 to 1970 (and from 1970 to 1980).
Therefore the price in 1980 = $1.2*1.5 = $1.8.
Answer: A.
Answer: (A) $ 1.80
Question: Solve for x and check: x + 5 = 3
(A) 2
(B) 3
(C) 1
(D) -2
(E) 4
Rationale: Solution :
x+5-5=3-5
x=-2
Check :
x+5=3
-2+5=3
3=3
ANSWER : D
Answer: (D) -2
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
(A) 32 km
(B) 25 km
(C) 28 km
(D) 24 km
(E) 20 km
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.
ANSWER:E
Answer: (E) 20 km
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 G 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 G of 6 possibilities.
C.
Answer: (C) 6
Question: 19 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
(A) 286
(B) 342
(C) 422
(D) 540
(E) 618
Rationale: 2*19C2 = 2*171 = 342
The answer is B.
Answer: (B) 342
Question: The sector of a circle has radius of 21 cm and central angle 130o. Find its perimeter?
(A) 89.7
(B) 91.4
(C) 91.7
(D) 91.3
(E) 91.1
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (130/360 * 2 * 22/7 * 21) + 2(21)
= 47.7 + 42 = 89.7 cm
Answer:A
Answer: (A) 89.7
Question: Twenty one identical machines, running continuously at the same constant rate, take 9 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by two days?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 9
Rationale: From the question you know that 21R = 1/9. The question asks you (partially) to make the rate from 1/9 to 1/7 (drop from 9 day to 7). So the only thing that you need to do is to find the magic number than can convert 1/9 to 1/7.
So 1/9 * x = 1/7 (1 equation with one unknown). So by solving this you get x = 9/7 . Thats it then! Take the magic number 9/7 and multiply BOTH sides of the original equation and you have:
21*(9/7)*R = (9/7) * 1/9
27* R = 1/7, Hence 27R = 1/7, therefore 6 more machines!
D
Answer: (D) 6
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: 1 woman's 1 day's work =	1
70
1 child's 1 day's work =	1
140
(5 women + 10 children)'s day's work = 5	+	10 = 1	+	1 =	1
70	140	14	14	7
5 women and 10 children will complete the work in 7 days.
Option A
Answer: (A) 7
Question: A man borrows Rs. 1200.00 from a bank for a period of 3 months. He finds that he has to repay Rs.1236.00. The bank rate of interest is:
(A) 3%
(B) 12%
(C) 6%
(D) 22%
(E) 14%
Rationale: amount returnd s 1236 , so interst Rs.36, borrowd 1200, n=3/12, so 36=(1200*3*r)/12*100, thus r=12%
ANSWER:B
Answer: (B) 12%
Question: In a camp, there is a meal for 90 men or 160 children. If 110 children have taken the meal, how many men will be catered to with remaining meal?
(A) 20
(B) 30
(C) 50
(D) 28
(E) 40
Rationale: There is a meal for 160 children. 110 children have taken the meal.
Remaining meal is to be catered to 50 children.
Now, 160 children 90 men.
50 children (90/160)	* 50 = 28 men
Answer is D.
Answer: (D) 28
Question: Three printing presses, E, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take E, working alone at its constant rate, to do the same job?
(A) 8
(B) 10
(C) 12
(D) 15
(E) 20
Rationale: =1/4-1/5=1/20
E can do 1/20 job in 1 hour
E can do the whole job in 20 hours=E
Answer: (E) 20
Question: If y > 0, (2y)/10 + (3y)/10 is what percent of y?
(A) 40%
(B) 50%
(C) 60%
(D) 70%
(E) 80%
Rationale: can be reduced to y/5+3y/10 =2y/5=50%
B
Answer: (B) 50%
Question: If x = y+4.5x and y = x+18, what is the value of x/y ?
(A) -6/5.
(B) -7/20.
(C) 1/4.
(D) -2/7.
(E) 1.5.
Rationale: (1) x = y + 4.5x
Substitute y for y = x + 18 (Eq. we are given)
x = x + 18 + 4.5x
Combine like terms
x = 5.5x + 18 --> -4.5x =18 --> x = -4
(2) y = x + 18
Substitute x for x = -4
y = (-4) + 18 = 14
(3) x/y = ?
Substitute x and y we found above
x/y = (-4) / (14) =-2/7
My answer: D
Answer: (D) -2/7.
Question: Jill works as a waitress at the local diner where she earns an hourly wage of $7.00 per hour and a standard tip rate of 5% of the cost of the orders she serves. If she worked four 12-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?
(A) 280
(B) 300
(C) 320
(D) 432
(E) 400
Rationale: Jill earns 7 dollars/hour and the hourly tip is (1/20)*40.
Jill thus earns 7*12+12*2 per day(or 7(12)+2(12)=9(12)=108).
Jill has worked for 4 days -> 108*4=432.
This matches answer choice D.
Answer: (D) 432
Question: Ramesh, Kiran and Ram started a business with capitals of Rs. 2000, Rs. 8000 and Rs. 6000 respectively. At the end of the year, the profit share of Kiran is Rs. 400. The difference between the profit shares of Ramesh and Ram is?
(A) 694
(B) 369
(C) 200
(D) 2356
(E) 1547
Rationale: Ratio of investments of Ramesh, Kiran and Ram is 2000 : 8000 : 6000 = 1 : 4 : 3
And also given that, profit share of Kiran is Rs. 400
=> 4 parts out of 8 parts is Rs. 400
Now, required difference is 3 - 1 = 2 parts
Required difference = 2/4 (400) = Rs. 200.Answer: C
Answer: (C) 200
Question: Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/12 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 20%, then Al would have exactly $20 more than Eliot in his account. How much money does Eliot have in his account right now?
(A) $110
(B) $120
(C) $180
(D) $200
(E) $260
Rationale: Lets assume Al have amount A in his bank account and Eliot's bank account got E amount. We can form an equation from the first condition.
A-E = 1/12*(A+E) ==> 11A = 13E ------------ (1)
Second condition gives two different amounts, Al's amount = 1.1A and Eliot's amount = 1.2E
1.1A = 20 + 1.2E ==> 11A =200 +12E -------(2)
Substituting (1) in (2):
13E = 200+12E ==>E = 200
D
Answer: (D) $200
Question: Carol is Five times Alice’s age but only twice as old as Betty. Alice is twelve years younger than Carol. How old is Betty?
(A) 6
(B) 9
(C) 12
(D) 18
(E) 24
Rationale: given that C=5A=2B..AND A=C-12=5A-12-->4A=12-->A=3
substituting the values A=3,C=15 AND B=6..
ans A=6..
Answer: (A) 6
Question: In a certain random experiment, exactly one of the outcomes A, B, and J will occur. In each random experiment, the probability that outcome A will occur is 1/3 , and the probability that outcome B will occur is 1/3. What is the probability that when the random experiment is conducted 6 independent times, each of outcomes A, B, and J will occur twice?
(A) 5/243
(B) 1/12
(C) 10/81
(D) 1/6
(E) 16/81
Rationale: Number of ways in which a group of 2A,2B,2J can be formed in any order = 6!/(2!*2!*2!) [ formula for total of 6 items with 2 each of similar kind)
Total number of ways in which the die can be thrown independently = _ _ _ _ _ _ ; there are 6 places .First can be filled in 3 different ways A/B/J; Second in 3 diff ways again and so on.
So total number of ways = 3X3X3X3X3X3 = 3^6
There fore probability = 6!/(2!x2!x2!) by 3^6 = 90/3^6 = 10/81 Answer C
Answer: (C) 10/81
Question: 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. 4000. With the help of C, they completed the work in 3 days. How much is to be paid to C?
(A) s. 375
(B) s. 400
(C) s. 500
(D) s. 800
(E) s. 850
Rationale: C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24
A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24 = 4: 3 : 1
C's share (for 3 days) = Rs.	(3 * 1/24 * 4000) =Rs.500
Answer = C
Answer: (C) s. 500
Question: The smallest value of n, for which n+1 is not a prime number, is
(A) 5
(B) 6
(C) 8
(D) 3
(E) 10
Rationale: (1 + 1) = 2.
(2 + 1) = 3.
(3 + 1) = 4.
(4 + 1) = 5.
which is not prime , n=3.
ANSWER:D
Answer: (D) 3
Question: Two trains leave a station traveling in the same direction. Train A leaves at 2:00 PM traveling at a constant speed of 40 mph, while train B leaves at 3:00 PM traveling at a constant speed of 60 mph. At what time will train B overtake train A if neither train deviates from its constant speed?
(A) 80
(B) 90
(C) 100
(D) 110
(E) 120
Rationale: We can use D=RT [distance=rate*time]
when train B overtakes train A, train A will have traveled for 1 hour longer than train B so
time of train B: T
time of train A: T+1 hour
rate of train B: 60 mph
rate of train A: 40 mph
when B overtakes A, they will have traveled the same distance D=RT, so set the RT for each trains equal to each other
40*(T+1) = 60*T
40T+40 = 60T
40 = 20T
2 = T
2 hours = 120 minutes
E
Answer: (E) 120
Question: The value of a machine depreiates at the rate of 10% per annum. If its present is Rs.1,62,000 what will be its worth after 2 years ? What was the value of the machine 2 years ago ?
(A) Rs.200000
(B) Rs.100000
(C) Rs.500000
(D) Rs.300000
(E) Rs.800000
Rationale: Value of the machine after 2 years
=Rs.[162000*(1-(10/100))^2] = Rs.[162000*(9/10)*(9/10)]
=Rs. 131220
Value of the machine 2 years ago
= Rs.[162000/(1-(10/100)^2)]=Rs.[162000*(10/9)*(10/9)]=Rs.200000
Answer is A.
Answer: (A) Rs.200000
Question: a man prpare the technical document it takes 2 hours for half an hour presentation and technical preparation. its screening takes 30 more minuts to prepare with the other guy.for to present a 7 half an hours how much time it will take
(A) 37 hours
(B) 35 hours
(C) 37 1/2 hours
(D) 33 hours
(E) 34 hours
Rationale: here first 2 hours to prepare a technical document and half-an-hour to screen it ..so total 2 1/2 hour work is need to 1/2 hour presentation....
For 7 1/2 hours presentation...
1/2 hour presentation-------------->>2 1/2 hour work done
7 1/2 hr presentation --------------> x hours work done
just do cross multiplication u will get x value i.e. required amount of time
since 7 1/2 hours contains 15 half-an-hours ...15* 2 1/2===== 30+7.5===total 37 1/2 hours
ANSWER:C
Answer: (C) 37 1/2 hours