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Sunday, March 22, 2015

GMAT Sample Questions Problem Solving Part 4

GMAT math questions are very much important for recruitment exams. Part 4 questions are given below. These questions are also important for bank recruitment exams. You can practice these questions for GMAT exams or for university admission test.

1. If 3x = 243 then find out the value of 'x' to get this result.
a. 2
b. 3
c. 4
d. 5
e. None of the above
Correct answer: d
Explanation:
According to the data given in the question, we know that the result is a multiple of 3
We have to find out the power such that when we raise 3 to that power the result is equal to 243
Therefore, we will try out each of the option given in the question to find out the correct answer
Now, 3 raise to the power 2 = 3*3 = 9
Now, 3 raise to the power 3 = 3*3*3 = 27
Now, 3 raise to the power 4 = 3*3*3*3 = 81
And, 3 raise to the power 5 = 3*3*3*3*3 = 243
Hence, the correct answer is option d

2. In some arithmetic sequence, the sum of the digits of the first and the second term is the third term. The series starts from the whole number 0. Find the seventh term in this series.
a. 5
b. 7
c. 6
d. 8
e. None of the above
Correct answer: d
Explanation:
According to the data given in the question, the numbers are in arithmetic sequence start from the number 0
Also, the sum of the first and the second term make up the third term in the sequence
We have to find out the seventh term in this sequence. Hence, as per the description we will go on adding the numbers in the series until we get the seventh term of the series.
Starting from 0, we get, the second term as 1, the third term as 1, the fourth term as 2, the fifth term as 3, the sixth term as 5 and lastly the seventh term as 8, in the following manner.
0+1 = 1
1+1 = 2
2+1 = 3
3+2 = 5
5+3 = 8
Hence, the correct answer is option d.

3. Adam got 5 academic text books and 15 note books. If the average cost of Adam's academic text books was $ 105 and the average cost of his writing note books was $ 150, then find out the average cost of the total number of books purchased by Adam.
a. 30.125
b. 31.875
c. 28.125
d. 55.550
e. None of the above
Correct answer: b
Explanation:
According to the data given in the question, Adam got 5 academic text books and 15 writing note books respectively.
∴ Number of text books = 5 ……….i
And, number of note books = 15 …………….ii
Average cost of 5 academic text books = $ 105 ……..iii
∴ Cost of 1 academic text book = $ 105 / 5 = $ 25 …………iv
Also given that, average cost of 15 writing note books = $ 150 ………..v
∴ Cost of 1 writing note book = $ 150 / 15 = $ 10 …………..vi
Now, Total number of books purchased by Adam = 5 + 15 = 20 …………vii
∴ Average Cost of all the text books and note books = ($ 105 + $ 150) / 8
∴ Average Cost of all the text books and note books = $ 255 / 8 = $ 31.875 ….viii
Hence, the correct answer is option b.

4. If (a / b) = 0.12 then find the negative value of the reciprocal of the same fraction.
a. (b / a)
b. – (b / a)
c. 0.833
d. -8.33
e. None of the above
Correct answer: d
Explanation:
According to the data given in the question the value of the fraction (a / b) = 0.12
We have to find the negative value of the reciprocal of this fraction which means we have to find the value of –(b / a)
First we will find the value of (b / a)
∴ If (a / b) = 0.12, then (b / a) = (1 / 0.12)
∴ (b / a) = 8.33
Now, we will negate the sign of the result of (b/a) to get the value of –(b/a) as -8.33
Hence, the correct answer is option d.

5. If 4 - a = 8(1 – a), then find the value of 'a' according to this equation.
a. 1 / 5
b. 2 / 5
c. 4 / 7
d. 4 / 5
e. None of the above
Correct answer: c
Explanation:
According to the data given in the question,
4 – a = 8(1 – a) …………..i
∴ 4 – a = 8 – 8a
∴ 8a – a = 8 – 4
∴ 7a = 4
∴ a = 4 / 7
Hence, the correct answer is option c.
Must Read: Why Banking Career?

6. A line named as AB consists of two other points namely X and Y between the two end points. The distance between the points A and X is 6.5 units and the distance between the points and Y and B is 2.5 units. The line segment AB measures 16.5 units in length. Find out the distance between the points X and Y respectively.
a. 7.5 units
b. 8.5 units
c. 5.7 units
d. 5.8 units
e. None of the above
Correct answer: a
Explanation:
According to the data given in the question,
Length of line AB = 16.5 units …….i
Length of line segment AX = 6.5 units …………….ii
Length of line segment YB = 2.5 units ……………..iii
Points A and B are the two endpoints of the line segment AB
We have to find out the distance between the points X and Y respectively
∴ With the help of the data given in i, ii as well as iii, we can say that,
AB = AX + XY + YB
∴ 16.5 = 6.5 + XY + 2.5
∴ XY = 16.5 – 6.5 – 2.5
∴ XY = 16.5 – 9 units
∴ XY = 7.5 units
Hence, the correct answer is option a

7. If the square root of the cube root of some positive integer is 3, then find the integer which results in this answer.
a. 3
b. 6
c. 9
d. 27
e. None of the above
Correct answer: e
Explanation:
According to the data given in the question, the square root of the cube root of some positive integer is 3.
Let this integer be 'a'.
Then, according to the above mentioned condition,
((a)1/3)1/2 = 3 …………….i
∴ Taking squares on both the sides of the equation (i), we get, (a)1/3 = (3)2 = 9 …..ii
Now, taking cubes on both the sides of the equation (ii), we get, (a) = (9)3 = 729
∴ a = 729
But, none of the options represents this value
Hence, the correct answer is option e

8. If a + b = 30 and a – b = 6, then find the value of the (a + b)2 and also find the product of ab.
a. 30, 6
b. 5, 30
c. 6, 30
d. 30, 4
e. None of the above
Correct answer: e
Explanation:
According to the data given in the question,
a + b = 30 ……………..i
a – b = 6 ……………….ii
Now according to the standard mathematical formula,
(a + b)2 = a2 + 2ab + b2 ……………iii
With the help of equation (i), we get,
(a + b)2 = (30)2 = 30 * 30 = 900 ………..iv
We also have to find out the product of ab.
Hence, adding equations i and ii, we get,
2a = 36
∴ a = 18 ………………v
Now, substituting this value of 'a' in equation ii, we get,
18 – b = 6
∴ 18 – 6 = b
∴ 12 = b
∴ b = 12 ………………vi
Hence, the derived values of 'a' and 'b' are 18 and 12 respectively
Now, the product of 'a' and 'b' = a * b = 18 * 12 = 216
But, neither of the options contains this answer
Hence, the correct answer is option e.

9. The integer 'a' is inversely proportional to the integer 'b' and a * b = 7. Find out the value of integer variable 'b', for the value of the integer variable a = 1.5.
a. 1.5
b. 4.66
c. 7.0
d. 10.5
e. 0.21
Correct answer: b
Explanation:
If two quantities are inversely proportional to each other, then in that case, increase in one quantity results in decrease in the other quantity
Now, according to this property and according to the data given in the question 'a' is inversely proportional to the integer 'b'
Hence, the product of 'a' and 'b' will result in some constant
Now, given that, a * b = 7 ……………….i
Hence, substituting the value of 'a' in (i), we get,
1.5 * b = 7
∴ b = 7 / 1.5
∴b = 4.66
Hence, the correct answer is option b.

10. When a 36 inch long pole is leaned against a vertical wall, it forms an angle of 30 degree with that wall. Find out the height of the point at which the pole touches the wall.
a. 20.125 units
b. 30.234 units
c. 31.176 units
d. 35.425 units
e. None of the above
Correct answer: d
Explanation:
Let us have a look at the diagrammatic representation of the description given in the question.

Now, according to the description,
AC is the pole. Thus, the length of AC = 36 units ……i
Also, it is given that the pole makes an angle of 30° with the wall AB
∴ The angle BAC = 30° …………..ii
Also, it is given that the wall is vertical so, the measure of angle CBA = 90° …….iii
∴ The measure of angle ACB = 60°, because the sum of the measures of all angles of a triangle = 180°
This tells us that the triangle ABC is a 30° - 60° - 90° type of triangle ………….iv
Now, we have to find out the height of the point at which the pole touches the wall i.e. the length of side AB
According to the standard property of 30° - 60° - 90° type of triangle,
Length of hypotenuse i.e. side AC is twice the length of side BC
∴ Length of side BC = 1 / 2 * length of side AC
∴ Length of side BC = 1 /2 * 36 = 18 units ………………v
Now, according to the property of 30° - 60° - 90° type of triangle, the length of side opposite to the 60° angle = √3 * length of side BC
∴ Length of side AB = √3 * 18 = 1.732 * 18 = 31.176 units.
Thus, the pole touches the wall at a height of about 31.176 units on the vertical wall
Hence, the correct answer is option d.
11. When a women weighing 65 kg is replaced by another women, then the average weight of a group of 10 women is found to be increased by 1 kg. Find out the weight of the new woman that is added to the group.
a. 65 kg
b. 75 kg
c. 85 kg
d. 60 kg
e. None of the above
Correct answer: b
Explanation:
According to the data given in the question,
Total number of women in the group = 10 ……………i
The average weight of a group of 10 women increases by 1 kg when a women weighing 65 kg is replaced with a new woman.
∴ Total increase in the weight of a group of 10 women = 10 * 1 = 10 kg ………ii
Now, weight of the new woman added to the group = weight of the woman that is replaced + total increase in the weight of the entire group of 10 women
∴ Weight of the new woman added to the group = 65 + 10 = 75 kg ………….iii
Hence, the correct answer is option d.

12. In what proportion should we mix the wheat of Rs. 2.50 per kg with the wheat of Rs. 3.50 per kg such that the resultant mixture of wheat costs Rs. 3.00 per kg?
a. 1 : 1
b. 1 : 2
c. 2 : 1
d. 1 : 1.5
e. None of the above
Correct answer: a
Explanation:
We will solve this solve using the concept of allegation.
According to the data given in the question,
Rate of the first type of wheat = R1 = Rs. 2.50 = 250 paise ………….i
Rate of the second type of wheat = R2 = Rs. 3.50 = 350 paise …………..ii
The mean rate of the mixture of the two types of wheat = Rm = 250 +350 / 2 = 600 / 2 = 300 paise …………iii
The quantity of the first type of wheat = N1 = Rm – R1 = 300 – 250 = 50 paise …………….iv
The quantity of the second type of wheat = N2 = R2 – Rm = 350 – 300 = 50 paise …………….v
Now, N1 / N2 = 50 / 50 = 1 : 1
So the required ratio = 1 : 1
Hence, the correct answer is option a.

13. The working capacity of John is twice as that of Jim and hence, John can finish a piece of work in 15 days less than the number of days required by Jim to do the same piece of work. In how much time can they complete the same piece of work when both John and Jim work together?
a. 10 days
b. 20 days
c. 30 days
d. 40 days
e. None of the above
Correct answer: a
Explanation:
According to the data given in the question,
Let, Jim finishes the piece of work in 'x' days ………….i
∴ John can complete the work in (x – 30) days …………….ii
The working capacity of John is twice as that of Jim.
∴ Time taken by John is 1 / 2 of the time taken by Jim ………..iii
∴ From equations (i), (ii) and (iii), we can say that,
(x – 30) = x / 2 ………..iv
∴2 (x – 30) = x
∴ 2x – 60 = x
∴ x = 30 ………….v
∴ Time taken by Jim to complete the work = 30 days
Since, it is given that John can complete the piece of work in 15 days less than the days required by Jim.
Thus, we can say that the time taken by John = 30 – 15 = 15 days ……………..vi
Now, work done by John in 1 day = 1 / 15 ………………vii
Work done by Jim in 1 day = 1 / 30 ………………….viii
Work done by both John and Jim in 1 day = (1 / 15) + (1 / 30) = (3 / 30) = 1 / 10
∴ John and Jim together can finish the whole work in 1 / (1 / 10) = 10 days.
Hence, the correct answer is option a.

14. Certain numbers of boys are able to finish a work in 25 days. If the number of boys is increased by 10, then they can finish the same work in 10 days less. How many boys were employed originally to do the work?
a. 10
b. 20
c. 15
d. 40
e. None of the above
Correct answer: c
Explanation:
Let the original number of boys employed = 'x' …………..i
Then, according to the data given in the question,
Number of boys is increased by 10
∴ New number of boys = x + 10 …………ii
Time required by x boys to do the work = 25 days …………..iii
Time required by the new number of boys = 25 – 10 = 15 days ………….iv
Now, equating equations (i), (ii), (iii) as well as (iv), we get,
x : (x + 10) :: 15 : 25
∴ (x / x + 10) = 15 / 25
∴ 25x = 15 (x + 10)
∴ 25x = 15x + 150
∴ 25x – 15x = 150
∴ 10x = 150
∴ x = 15 ……………..v
Thus, there were 15 boys employed originally to do the work.
Hence, the correct answer is option c.

15. Two pipes A and B can fill a tank in 10 hours and 12 hours respectively when they are opened at the same time to fill the tank. But, because of one leakage at the bottom of the tank, it takes 30 more minutes to fill up the tank. In what time will the leakage empty the tank, if the tank is filled completely?
a. 10 hours
b. 12 hours
c. 30 hours
d. 60 hours
e. None of the above
Correct answer: d
Explanation:
According to the data given in the question,
Time taken by pipe A to fill the tank = 10 hours ………….i
Time taken by pipe B to fill the tank = 12 hours ………….ii
∴ Work done by both the pipes A and B in 1 hour = (1 / 10) + (1 / 12)
∴ Work done by both the pipes A and B in 1 hour = 22 / 120 ……………iii
∴ Time taken by both the pipes A and B to fill the tank completely in the absence of the leakage = 120 / 22 hours = 5 hours and 30 minutes ……………iv
Time taken to fill the tank with leakage = (5 hours 30 minutes) + (30 minutes) = 6 hours …………….v
∴ The amount of work done by the pipes A as well as B and the leak in 1 hour = 1 / 6 ……….vi
∴ Work done by the leak in 1 hour = (22 / 120) – ( 1 / 6) = 1 / 60
∴ Time required by the leakage to empty the tank = 1 / (1 / 60) = 60 hours.
Hence, the correct answer is option d.
16. A piece of work is done by Tina in 10 days. The same piece of work is done by Amy in 15 days. In how many days will Tina and Amy finish the same amount of work if they work together?
a. 10 days
b. 6 days
c. 12.5 days
d. 13 days
e. None of the above
Correct answer: b
Explanation:
According to the data given in the question,
Time taken by Tina to do the work = 10 days ………………i
Time taken by Amy to do the work = 15 days ………………ii
∴ Work done by Tina in 1 day = 1 / 10 ………..iii
Similarly, work done by Amy in 1 day = 1 / 15 …………iv
∴ Work done by both Tina and Amy in 1 day = (1 / 10) + (1 / 15)
∴ Work done by both of Tina and Amy in 1 day = 1 / 6 ……………v
∴ When Tina and Amy work together they can complete the work in (1 / (1 / 6)) = 6 days.
Hence, the correct answer is option b.

17. Which of the following algebraic formulas are true?
i. Speed = Distance / Time
ii. Distance = speed * time
iii. Time = Distance / Speed
iv. Time = speed * distance
e. Only statement (i) is true
f. Only statements (i) and (ii) are true
g. Only statements (i), (ii) and (iii) are true
h. All statements are true
i. all statements are false
Correct answer: c
Explanation:
The formulae given in the statements (i), (ii) as well as (iii) are true.
But, the formula given in the fourth statement is false.
Hence, the correct answer is option c.

18. Two trains X and Y are moving in opposite direction, one from station A to station B and the other from station B to station A. the train X reaches its destination i.e. station A in 14 hours and the train Y reaches its destination i.e. station B in 20 hours after the trains meet. If the speed of train X is 20 km per hour, then what is the speed of the train Y?
 a. 30 km per hour
b. 35 km per hour
c. 27 km per hour
d. 38.57 km per hour
e. None of the above
Correct answer: d
Explanation:
According to the data given in the question,
Train X travels at a speed of = 20 km / hr …………..i
Train x reaches its destination station B in time = 14 hours ……………ii
Train Y reaches its destination station A in time = 20 hours after they meet ………..iii
Now, let the speed of train Y be x km per hour ………………..iv
∴ From equation (i), (ii), (iii) and (iv), we can say that,
20 : x :: 14 : 20
∴ 20 / x = 14 / 20
∴ 20 * 20 = 14 * x
∴ x = 400 / 14
∴ x = 28.57 km / hr
Thus, train B travels at a speed of 28.57 km per hour.
Hence, the correct answer is option d.

19. David observes that it takes 6 sec for a train to pass him when he is standing at the railway platform. But, to pass the platform the train takes 10 sec. If the length of the train is 150 meters, then what is the speed of the train?
a . 20 km / hr
b. 25 km / hr
c. 30 km / hr
d. 35 km / hr
e. None of the above
Correct answer: b
Explanation:
According to the data given in the question,
Time taken by the train to cross David = 6 sec …………….i
Time taken by the train to cross the platform = 10 sec ……………..ii
Length of the train = 150 meters ……………iii
The standard formula to calculate the speed of the train when it passes a stationary object without considerable length = length of the train / time taken by the train to pass the object
∴ Speed of the train = 150 / 6 = 25 km / hr
Hence, the correct answer is option b.
20. When the man rows a boat in still water his speed is 7 km / hr. But, if the river water runs at speed of 3 km / hr, then the man takes 1.5 hours to reach a certain place and come back. What is the distance covered by the man?
 a. 4.285 km
b. 3.285 km
c. 1.285 km
d. 2.285 km
e. None of the above
Correct answer: a
Explanation:
According to the data given in the question,
Speed of the man in still water = 7 km / hr ……………i
Speed of the moving river water = 3 km / hr …………ii
Time taken by the man to reach a certain place and come back = 1.5 hours = 1 hr and 30 min ………………….iii
We have to find the distance covered by the man.
Let this distance be 'x' km.
The speed of man while going downstream = 7 + 3 = 10 km / hr ………iv
The speed of man while upstream = 7 – 3 = 4 km / hr …………….v
Total time taken by the man to row x km and come back = (x / 10) + (x / 4)
But, the man takes 90 minutes or 1 hour and 30 min to cover this distance.
∴ (x / 10) + (x / 4) = 1.5
∴ 4x + 10x = 40 * 1.5
∴ 14x = 60
∴ x = 4.285 km = 4 km and 285 meters
∴ The total distance covered by man is 4.285 km
Hence, the correct answer is option a.

21. Tina can do a piece or work in 15 days, whereas Mina can do the same piece of work in 20 days. If they work together for 7 days and then Tina goes away for a leave. Then, in how many days will Mina alone complete the remaining piece of work?
a. 3.66 days
b. 2 days
c. 1 day
d. 10 days
e. None of the above
Correct answer: a
Explanation:
According to the data given in the question,
Number of days required by Tina to complete the work = 15 days …………i
Number of days required by Mina to complete the work = 20 days …………ii
Now, work done by Tina in 1 day = 1 / 15 ……….iii
And, work done by Mina in 1 day = 1 / 20 ………………iv
∴ Work done by both Tina and Mina in 1 day = (1 / 15) + (1 / 20) = 7 / 60 ……v
∴ Work done by both Tina and Mina in 7 days = 7 (7 / 60) = 49 / 60 ……vi
Now, remaining amount of work = 1 – 49 / 60
∴ Remaining amount of work = 60 – 49 / 60 = 11 / 60 ……………vii
Since, according to the data in statement (iv), 1 / 20 of the work is done by Mina in 1 day.
∴ 11 / 60 of the work will be done Mina in (20) * (11 / 60) = 11 / 3 = 3.66 days
Hence, Mina will complete the remaining work in 3.66 days.
Hence, the correct answer is option a.

22. A can complete a piece of work in 12 days, whereas B and C can complete the same piece of work in 15 days and 18 days respectively. A, B and C start working together. But, A leaves the work after 3 days and B leaves the job incomplete just before 2 days before the completion of the work. For how many days did the work last?
a. 7 days
b. 7.7727 days
c. 8 days
d. 8.7727 days
e. None of the above
Correct answer: b
Explanation:
According to the data given in the question,
Days required by A to do the work = 12 days ……….i
Days required by B to do the work = 15 days ……….ii
Days required by C to do the work = 18 days ……….iii
Hence, from data i, ii and iii, we can say that,
A, B and C work together for 3 days ……………iv
C works alone for 3 days …………….v
Work done by A, B and c in 3 days = 3 * (1 / 12 + 1 / 15 + 1 / 18) = 37 / 60
∴ A, B as well as C complete 37 / 60 of the total work in 3 days ……………vi
Now, work done by C alone in 3 days = 3 * (1 / 18) = 1 / 6 …………..vii
Remaining work to be done = 1 – (37 / 60 + 1 / 6) = 13 / 60 ……………viii
∴ Work done by both B and C in 1 day = (1 / 15 + 1 / 18) = 11 / 90
Thus, 11 / 90 of the total work is completed by both B and C in 1 day ………………ix
∴ Time required by both B and C to complete 13 / 60 of the total work = (90 / 11) * (13 / 60) = 39 / 22 days = 1.7727 days ……………..x
∴ Total time taken by all three of A, B and C to complete the work = 3 + 3 + 1.7727 = 7.7727 days
Hence, the correct answer is option b.
23. Pipe A can fill the bucket in 10 minutes while pipe B can fill the same bucket in 15 minutes respectively. First both pipes are opened together to fill the bucket. But, after 2.5 minutes the pipe A is turned off. In how much time will the bucket can be filled?
a. 5 minutes
b. 6 minutes
c. 8.125 minutes
d. 7.125 minutes
e. None of the above
Correct answer: c
Explanation:
According to the data given in the question,
Time taken by pipe A to fill the bucket = 10 minutes …………….i
Time taken by pipe B to fill the bucket = 15 minutes …………….ii
∴ Part of the bucket filled by A in 1 minute = 1 / 10 …………iii
And, part of the bucket filled by B in 1 minute = 1 / 15 ………..iv
∴ Part of the bucket filled by both A and B in 2.5 minutes = 2.5 * (1 / 10 + 1 / 15)
∴ Part of the bucket filled by both A and B in 2.5 minutes = 2.5 / 4 …………..v
Now, part of the bucket left to be filled = 1 – (2.5 / 4) = (4 – 2.5 / 4) = 1.5 / 4 ……vi
As, 1 / 15 part of the bucket is filled by pipe B in 1 minute
∴ 1.5 / 4 part of the bucket will be filled by pipe B in 15 * (1.5 / 4) = 5.625 minutes.
∴ Total time required to fill the bucket completely = 2.5 + 5.625 = 8.125 minutes
Hence, the correct answer is option c.

24. Tom and Jerry can complete a piece of work in 12 days when they work together. When only Tom works, he can finish the work in 20 days. How long will Jerry take to complete the work?
a. 10 days
b. 20 days
c. 25 days
d. 30 days
e. None of the above
Correct answer: d
Explanation:
According to the data given in the question,
Time taken by both Tom and Jerry to do a piece of work = 12 days ………i
Time taken by tom alone to do the work = 20 days …………..ii
∴ Work done by both Tom and Jerry in 1 day = 1 / 12 ……….iii
And, similarly, work done by Tom alone in 1 day = 1 / 20 ………..iv
∴ Work done by Jerry alone in a day = (1 / 12) – (1 / 20) = 1 / 30 …………v
∴ Time taken by Jerry to finish the work alone = 30 days.
Hence, the correct answer is option d.
25. X and Y together can do a piece of work in 18 days. When Y and Z work together, they can do the work in 24 days. But, when X and Z work together, they can do the same piece of work in 30 days. In how much time will the three of X Y as well as z will complete the same work?
a. 3.8297 days
b. 3 days
c. 4 days
d. 5 days
e. None of the above
Correct answer: a
Explanation:
According to the data given in the question,
Time taken by both X and Y to do a piece of work = 18 days ………i
∴ Work done by both X and Y in 1 day = 1 / x + 1 / y = 1 / 18 …………..ii
Time taken by both Y and Z to do a piece of work = 24 days ………iii
∴ Work done by both, Y and Z in 1 day = 1 / y + 1 / z = 1 / 24 …………..iv
Time taken by both X and Z to do a piece of work = 30 days ………v
∴ Work done by both X and Z in 1 day = 1 / x + 1 / z = 1 / 30 …………..vi
Now, let, X, Y and z complete the work in x, y and z days respectively …………..vii
Thus, work done by X, Y and Z in 1 day = 1 / x, 1 / y, 1 / z respectively ……………viii
Now, adding equations ii, iv and vi we get,
2(1 / x + 1 / y + 1 / z) = 1 / 18 + 1 / 24 + 1 / 30
∴ (1 / x + 1 / y + 1 / z) = 2(1 / 18 + 1 / 24 + 1 / 30)
∴ (1 / x + 1 / y + 1 / z) = 423 / 1620
∴ X, Y and Z can complete the work together in 1620 / 423 days = 3.8297 days.
Hence, the correct answer is option a.

26. Raven walks at a certain speed daily from his home to school. If the speed of raven is reduce by 3 / 7th part of his normal speed then, it takes 20 more minutes for Raven to reach his school. Calculate the time taken by Raven to reach his school when he walks at his usual speed?
a. 15 minutes
b. 20 minutes
c. 25 minutes
d. 30 minutes
e. None of the above
Correct answer: a
Explanation:
According to the data given in the question,
Decrease in the usual speed of Raven = 3 / 7 …………i
Now, let 'x' be the time taken by Raven to reach the school when he is walking at his normal speed ………………..ii
But, as the speed is reduced by 3 / 7 of the regular speed,
∴ The time now taken by Raven to reach the school = 7 / 3 of the usual time.
But, it is given that, it takes 20 minutes more than the normal time 'x' for Raven to reach the school with reduced speed.
∴ (7 / 3) x = x + 20
∴ 7x = 3x + 60
∴ 4x = 60
∴ x = 60 / 4 = 15 minutes
Thus, it takes 15 minutes for Raven to reach his school when he is walking at his normal speed.
Hence, the correct answer is option a.

27. Rose leaves her home early in the morning so that she can reach her college on time. If she walks at the rate of 7 km / hr then she reaches her college 8 minutes late. But, if she walks at a speed of 8 km / hr, then she reaches her college 4 minutes early. What is the distance between Rose's house and her college?
a. 10 km
b. 11.2 km
c. 11.5 km
d. 12 km
e. None of the above
Correct answer: b
Explanation:
Time taken by Rose to cover a distance of say 1 km at a speed of 7 km / hr = 1 / 7 hr ……………..i
Similarly, time taken by rose to cover a distance of say 1 km at a speed of 8 km / hr = 1 / 8 hr ……………ii
Hence, the difference in both the time = 1 / 7 * 1 / 8 = 1 / 56 …………..iii
Now, according to the data given in the question,
When Rose walks at a speed of 7 km / hr she reaches late by 8 minutes
And, when Rose walks at a speed of 8 km / hr she reaches early by 4 minutes
∴ The total difference of time in covering the entire distance (d) = (8 + 4) = 12 minutes = 1 / 5 hours.
Now, if the time difference of 1 / 56, the distance covered by Rose is 1 km, then, the distance covered by Rose for a time difference of (1 / 5) hour = (1) * (1 / 5) / (1 / 56) = 56 / 5 = 11.2 km.
Thus, the distance between Rose's house and college = 11.2 km.
Hence, the correct answer is option b.

28. In a hurdle race, Tom is beaten by Patrick by a distance of 25 meters or 10 seconds. How much time did Patrick take to finish the hurdle race of total 1 km?
a. 5 minutes and 20 seconds
b. 4 minutes and 20 seconds
c. 6 minutes and 30 seconds
d. 7 minutes and 20 seconds
e. 8 minutes and 20 seconds
Correct answer: c
Explanation:
According to the data given in the question,
Tom covers a distance of 25 meters in 10 seconds.
Total distance to be covered in the hurdle race = 1 km = 1000 m
∴ Time taken by Tom to complete the race = (10 / 25) * 1000 = 400 seconds
∴ Time taken by Patrick to complete the entire hurdle race = 400 – 10 = 390 seconds.
Now, 390 seconds = 6 minutes and 30 seconds
Hence, the correct answer is option c.

29. Rose, Lilly and Jasmine participate in a km race. Rose gives a start of 20 meters to Lilly. Also, Jasmine is given a start of 350 meters by Rose. How many meters of start can be given by Lilly to Jasmine?
a. 10.15 meters
b. 15 meters
c. 16.31 meters
d. 15.31 meters
e. None of the above
Correct answer: d
Explanation:
Rose gives a start of 20 meters and 35 meters to Lilly and Jasmine means that, Lilly starts 20 meters ahead of Rose and Jasmine starts 35 meters ahead of Rose.
Now, according to the data given in the question,
Distance covered by Rose = 1000 meters ………..i
Distance covered by Lilly = (1000 – 20) meters = 980 meters ………..ii
Distance covered by Jasmine = (1000 – 35) meters = 965 meters ………..iii
Now, when Lilly covers a distance of 980 meters, Jasmine covers a distance of 965 meters.
∴ When Rose covers a distance of 1000 meters, distance covered by Lilly = (965 / 980) * 1000 = 984.69 meters.
∴ Lilly can give a start of (1000 – 984.69) meters to Jasmine
∴ Lilly can give a start of 15.31 meters to Jasmine.
Hence, the correct answer is option d.

30. A, B and C are playing a game of billiards. In a game of 60 points, A can give B 15 points, while in a game of 90; A can give 20 points to C. How many points can C give to B in a game of 70 points?
a. 5.5 points
b. 6.5 points
c. 8 points
d. 7.5 points
e. None of the above
Correct answer: d
Explanation:
According to the data given in the question,
In a game of billiards of 60 points, points given by A to B = 15 points ……….i
∴ If 60 points are scored by A, then points scored by B = 60 – 15 = 45 points ….ii
In a game of billiards of 90 points, points given by A to C = 20 points ……….iii
∴ If 90 points are scored by A, then points scored by C = 90 – 20 = 70 points ……iv
∴ If A scores 60 points, then points scored by C = (70 / 90) * 60 = 420 / 9 points ….v
Thus, we can say that, when C scores 420 / 9 points, then points scored by B = 45 points ………from equation i and v
∴ When C scores 70 points, then points scored by B = (45 * 70 * 9) / 420 = 67.5 points
Thus, the points that C can give to B in a game of 70 = 67.5 / 9 = 7.5 points
Hence, the correct answer is option d.

31. What will be the result of [12] – [10], if it is given that [x] = -x2.
a. -44
b. 44
c. 144
d. 100
e. None of the above
Correct answer: a
Explanation:
According to the data given in question, [x] = -x2.
Substituting the value of x as x=12 in this equation, we get, [12] = -144
Now, substituting the value of x as x=10 in this equation, we get, [10] = -100
Now, substituting these values in [12] – [10] = (-144) – (-100) = -144 + 100 = -44
Hence, the correct answer is option a.

32. The annual income of Ralph is 35 percent less than the annual income of Mike. Calculate the increase in the annual income of Mike in terms of percentage in comparison to the annual income of Ralph.
a. 25 %
b. 35 %
c. 20 %
d. 30 %
e. None of the above
Correct answer: b
Explanation:
Let $100 be the annual income of Mike.
Now, according to the data given in the question, annual income of Ralph is less than the annual income of Mike by 35 percent.
∴ 35% of 100 = $ 35
Hence, we can say that the annual income of Ralph is $ 65, when annual income of Mike is $ 100.
But, we have to find the percentage increase in the annual income of Mike as compared to annual income of Ralph.
∴ Percentage increase in annual income of Mike = 100 - 65 = 35 %.
Hence, the correct answer is option b.

33. There are in all 27 balls in a basket which are red and green in color. The number of red balls was 13 and the number of green balls is 1 more than the number of red balls. Ravi is said to pick a ball that is only green in color. Find out the probability that Ravi picks out only a green color ball from this bag.
a. 13 / 27
b. 27 / 13
c. 14 / 27
d. 27 / 14
e. None of the above
Correct answer: c
Explanation:
According to the data given in the question,
Total number of balls in the bag = 27 …………….i
Total number of red balls in the bag = 13 ……………ii
Total number of green balls in the bag = 14 ………………..iii
∴ The probability that Ravi picks out only a green colored ball = 14 / 27 ………..iv
Hence, the correct answer is option c.

34. Certain numbers of children were playing a game of football. There was a trial taking place on the field. In this trial the probability that a goal is scored is 2/5. The probability that a girl hits a goal is 7/10 whereas the probability that a boy hits a goal is 1/5. What will be the probability that not only a goal is hit but it is also hit by a boy?
a. 14 / 50
b. 7 / 50
c. 2 / 5
d. 2 / 25
e. None of the above
Correct answer: d
Explanation:
According to the data given in the question,
The probability that a girl scores a goal = 7 / 10 ………………….i
The probability that a boy hits a goal = 1 / 5 …………….ii
The probability that a goal is scored by any of the child = 2 / 5 ……………….iii
We know that, the probability that two events will take place simultaneously is denoted by the product of the individual occurrences of each of the different events.
∴ The probability that the two events namely a goal is scored and it is also scored by a boy, will take place at one and the same time = (2 / 5) * (1 / 5) = 2 / 25
Hence, the correct answer is option d.

35. The price at which Jim sold his 26 articles is the same as that of the price at which he bought 25 articles. What is the gain in percentage that Jim made in this business?
a. 4 %
b. 5 %
c. 6 %
d. 10 %
e. None of the above
Correct answer: a
Explanation:
According to the data given in the question,
Total number of articles purchased by Jim = 25
Total number of articles sold by Jim = 26
The cost price (C.P.) of 25 articles = The selling price (S.P.) of 26 articles …………..i
Now, let the cost price of 1 article be $ 1 …………ii
∴ The cost price of 25 articles = $ 25 ………….iii
Also, from data (i) as well as (ii),
The selling price of 26 articles = The cost price of 25 articles = $ 25 ………….iv
∴ Jim's gain in terms of percentage = (26 – 25) * 100 / 25 = 1 * 100 / 25
∴ Jim's gain in terms of percentage = 100 / 25 = 4 %
Hence, the correct answer is option a.

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