   ## Friday, March 13, 2015

### GMAT Sample Questions Problem Solving Part 1

GMAT math questions are very much important for Bank Recruitment Exams. GMAT practice questions are given below. You can follow various problem solving strategies to complete these questions. You can even perform GMAT practice test at your home.

1. One of the sides of a square measures 10 cm in length. If we increase the size of two opposite sides by a couple of centimeters and decrease the length of the remaining two opposite sides by the same measure, then what will be the area of the resulting figure in meter?
a. 192 m
b. 19.2 m
c. 192 cm
d. 1.92 m
e. 0.192 m
Explanation:
It is given that the sides of the square measure 10cm in length. Therefore the area of square is side * side = 10 * 10 = 100 square cm.
Now, the question says that the length of some two opposite sides is reduced by a couple of centimeters i.e. it is reduced by 2 cm and the length of the other two opposite side is increased by the same measure i.e. 2 cm only.
Hence, as per this, the length of the sides of the square has changed to 8 cm and 12 cm respectively. From this we can conclude that the resulting figure is a rectangle.
Now the area of a rectangle is 2 * length * breadth = 2 * 8 * 12 = 192 square cm.
But the question asks the area in meters. Hence, 192 cm = 192 * 10-3 meter = 0.192 square meter.
Hence the correct answer is option e.

2. If a man drives a car at a speed of 50 km per hour; then calculate the distance covered by the man in 10 minutes if he is driving at the same speed constantly.
a. 8.000 km
b. 8.900 km
c. 8.350 km
d. 8.335 km
e. 0.875 km
Explanation:
It is given that man is driving at a speed of 50 km/hr for 10 minutes.
We know that, distance = speed * time---------(i)
After substituting the value of speed and time in this formula we get,
Distance = 50 km/hr * 10 minutes-------(ii)
Now, 1 hour = 60 minutes Therefore, x hours = 10 minutes → x = 10 / 60 → x = 0.1667 hours.
Now, substituting the value of 'x' in equation (ii), we get,
Distance = 50km/hr * 0.1667 hr
∴ Distance = 8.335 km
Hence, the correct answer is option d.

3. If the scale used for drawing a map states that the actual distance of 50 km is represented by 1cm on the map; then according to this scale what will be the actual distance between Los Angeles and Washington D.C. if Washington D.C. is 12.22 cm away from America on the map?
a. 611 km
b. 61 km
c. 61.1 km
d. 611 cm
e. None of the above
Explanation:
It is given that, 1cm on map is equal to 50 km on the road.
We have to find out the actual distance for a distance of 12.22cm on the map.
We can write the above equalities as follows,
1 cm = 50 km \ 12.22 cm = say 'x' cm.
∴ x = 50 * 12.22 = 611 km.
Hence, the correct answer is option a.

4. It is given that the weight of an empty box is 1000 gm and the total weight of the box when filled with apples and mangoes is 10kg. If there are 3 dozens of apple in the box and the weight of each apple is 200 gm whereas the weight of every mango is 300 gm, then, find out the total number of mangoes in the box.
a. 6
b. 8
c. 9
d. 10
e. None of the above
Explanation:
According to the data given in the question:
Weight of an empty box is 1000 gm = 1kg
Total weight of the box when filled with apples and mangoes is 10kg = 10000 gm
There are 3 dozens of apple in the box = 12*3 = 36 apples in all
Weight of each apple is 200 gm and
∴ Weight of an empty box i.e. 36 apples = 200gm * 36 = 7200gm
Now weight of total mangoes in the box = (Total weight of the box when filled with apples and mangoes) – (Weight of an empty box + Weight of an empty box)
∴ Weight of total mangoes in the box = (10000) – (1000 + 7200) = (10000 – 8200)
∴ Weight of total mangoes in the box = 1800
But, it is given that weight of every mango is 300 gm.
Hence, weight of say 'x' mangoes = 1800 gm
∴ x = 1800 / 300 = 6
Therefore, there are in all 6 mangoes in the box.
Hence, the correct answer is option a.
5. If we increase the area of a circle by 32 % then, calculate the approximate increase in the radius of the same circle in terms of percentage.
a. 32 %
b. 42 %
c. 22 %
d. 20 %
e. None of the above
Explanation:
Say for example radius = 4 units and pi = 3.14
Then area of this circle = pi * 4 * 4 = 3.14 * 4 * 4 = 55.04
Now, we have to find out the percentage increase in the radius if we increase the area by 32 %.
(32 * 55.04) / 100 + (55.04) = 72.6258
This is 32 percent increased area of the circle.
Now, we have to find out the radius,
Say 'x' is the percentage increase in the radius of the circle.
Therefore, pi * (x + 4) * (x + 4) = 72.6258
∴ (x + 4) 2 = 72.6258/3.14 = 0.004
On solving the equation we can say that, for 20% increase in the radius the area of the circle increases by 32%.
Hence, the correct answer is option d.

6. Tim, Tom and Max decide to go out for dinner. Tom had \$ 50 whereas; Tim and Max had \$ 110 and \$ 400 respectively. The bill charged them \$ 113 for their dinner. They paid \$ 120 and the extra \$ 7 was given as a tip to the waiter who served them. They first decide to share the bill equally. But, since Tim had very less money with him he paid only 25 % of the bill whereas; Tom and Max paid 35 % and 40 % of the bill respectively. Calculate the amount of money paid by Tim.
a. \$ 30
b. \$ 42
c. \$ 48
d. \$ 50
e. None of the above
Explanation:
The total bill for the dinner = \$ 113.
They paid \$120 and gave the extra \$7 as tip.
Tim paid 25 % of the bill. ∴ (25 * 120) /100 = \$ 30
Tom paid 35 % of the bill. ∴ (35 * 120) /100 = \$ 42
Tim paid 25 % of the bill. ∴ (40 * 120) /100 = \$ 48
From this we come to know that Tim paid \$ 30 for dinner.
Hence, the correct answer is option a.

7. The measures of the sides of an irregular polygon are given in the figure as follows. Look at the figure and calculate the perimeter of the irregular polygon.

a. 20 m
b. 35 m
c. 30 m
d. 45 m
e. None of the above
Explanation:
Perimeter of an irregular polygon is equal to the sum of all its sides.
According to the data given in the question, the sides measure as 8, 10, 12 and 15
Hence, we can calculate the perimeter of this figure as (8 + 10 + 12 + 15 = 45 m)
Hence, the correct answer is option d.

8. Consider the following figure and find out the ratio between the areas of the largest and the smallest circles. Given that all the circles are drawn considering the same center i.e. all the circles are concentric.

a. 1 : 3
b. 3 : 1
c. 1 : 6
d. 6 : 1
e. 6 : 3
Explanation:
According to the figure, the radius of the circles are denoted by a, 3a and 6a where 'a' can be any variable that represents certain value or some unit of measurement.
From the figure we can say that the radius of the smallest circle is 'a'.
The radius of the middle circle is 3a and the radius of the outermost circle is 6a.
Now, we have to find out the ratio between the areas of the biggest and the smallest circles.
Therefore, area of the smallest circle = pi (a2)
And area of the largest circle = pi (6a2)
Hence, Ratio of the areas of these circles = pi (6a2): pi (a2) = 6: 1
∴ The areas of the biggest and the smallest circles are in the ratio 6: 1
Hence, the correct answer is option d.

9. If a + b = 10 and a – b = 20, then what will be the value of a/b?
a. 10/20
b. 1/3
c. -1/3
d. -3
e. None of the above
Explanation:
According to the data given in the question,
a + b =10 -----------i
a – b = 20-----------ii
On adding equations I and ii we get,
2a = 30
∴ a = 15
Substituting the value of 'a' in equation I we get,
15 + b = 10
∴ b = 10 – 15
∴ b = -5
Hence we have the values of 'a' and 'b' as a = 15 and b = -5
Now, we have to find out the value of a/b
∴ a/b = 15/-5
∴a/b = 3/-1 = -3
Hence, the correct answer is option d.

10. The ratio between the ages of Mary and her mother is 1: 2 and that of Mary and her father is 1: 3 at the time of Mary's birth. Mary is 10 years old now. Find out the ratio between the ages of Mary's mother and father at this age of Mary.
a. 1 : 2
b. 1 : 3
c. 2 : 3
d. 3 : 2
e. None of the above
Explanation:
According to the data given in the question, when Mary took birth,
The ratio between the ages of Mary and her mother is 1: 2
The ratio between the ages of Mary and her father is 1: 3
Now, if we say 'x' is the age of Mary when she is born
Hence, we can say that her mother's age is 2x and her father's age is 3x---------i
Now, Mary is 10 years old.
Therefore, from equation 1 we can say,
Her mother's age is 2x i.e. 2 * 10 = 20 and her father's age is 3x i.e. 3 * 10 = 30 at this age of Mary.
Thus, the ages of Mary's mother and Mary's father are in the ratio 20:30 = 2:3
Hence, the correct answer is option c.

11. If 45x = 1024, then find out the value of 'x' to get this result.
a. 2
b. 3
c. 4
d. 5
e. 1
Explanation:
According to the data given in the question, we know that the result is a multiple of 4. Also, since 4 is raise to power 5 first we will find out the result of 4 raise to the power 5.
Therefore, we get, 45 = 1024 i.e. 4 5*1 = 1024
Hence, the correct answer is option e.

12. In some arithmetic sequence, the sum of the digits of the third term is 27 and the fourth term is 81. What is the fifth term in this arithmetic sequence?
a. 243
b. 81
c. 9
d. 27
e. 3
Explanation:
According to the data given in the question, all the numbers are in arithmetic sequence.
The third term in the sequence is 27 and the fourth term in the sequence is 81.
From this we can say that the numbers are in the sequence of increasing powers of 3, because 3 raise to the power 3 = 27 and 3 raise to the power four is 81.
This means we have to find out the value of 35, which is ultimately the fifth term of the sequence.
∴ 35 = 243.
Hence, the correct answer is option a

13. Andrew purchased 3 science text books and 5 mathematics text books. If the average cost of Andrew's science text books was \$75 and the average cost of his mathematics text books was \$150, then find out the average cost of the total number of books purchased by Andrew.
a. 30.125
b. 25.125
c. 28.125
d. 55.550
e. 75.125
Explanation:
According to the data given in the question, Andrew purchased 3 text books of science and 5 text books of mathematics respectively.
Number of science text books = 3
Average cost of 3 science text books = \$75
∴ Cost of 1 science text book = \$75/3 = \$25
Number of mathematics text books = 5
Average cost of 5 mathematics text books = \$150
∴ Cost of 1 mathematics text book = \$150/5 = \$30
Total number of text books purchased by Andrew = 3 + 5 = 8
∴ Average Cost of all the text books = (\$75 + \$150)/8 = \$28.125
Hence, the correct answer is option c

14. If (a/b) = 0.6789, then find the value of the reciprocal of the same fraction.
a. (b/a)
b. 0.6789
c. -0.6789
d. 1.4729
e. -1.4729
Explanation:
According to the data given in the question the value of (a/b) = 0.6789
We have to find the value of the reciprocal of this fraction which means we have to find the value of (b/a).
∴If (a/b) = 0.6789, then (b/a) = (1/0.6789)
∴ (b/a) = 1.4729
Hence, the correct answer is option d.

15. If 3 - a = 6(1 - a), then find the value of 'a' according to this equation.
a. 1/5
b. 2/5
c. 3/5
d. 4/5
e. None of the above
Explanation:
According to the data given in the question,
3 - a = 6(1 - a)--------i
∴ 3 - a = 6 - 6a
∴ 6a - a = 6 - 3
∴ 5a = 3
∴ a = 3/5
Hence, the correct answer is option c.

16. A line named as XY consists of two other points namely A and B between the two end points. The distance between the points X and A is 10 units and the distance between the points B and Y is also 10 units. The line segment XB measures 20 units in length. Find out the distance between the points A and B respectively.
a. 10
b. 20
c. 30
d. 15
e. None of the above
Explanation:
According to the data given in the question, we can draw a line XABY of total length as 30 units.
The length of line segment XA is 10 units.
The length of line segment YB is 10 units.
The length of line XY is 30 units.
∴ We can make an equation using this data as follows:
XY = XA + AB + BY
∴ 30 = 10 + AB + 10
∴ AB = 30 – 20
∴ AB = 10 units
Hence, the correct answer is option a.

17. If the square root of the cube root of some positive integer is 2, then find the integer which results in this answer.
a. 4
b. 8
c. 16
d. 32
e. 64
Explanation:
According to the data given in the question, the square root of the cube root of some positive integer is 2.
Let this integer be 'a'.
Then, according to the above mentioned condition,
((a)1/3)1/2 = 2
∴ Taking squares on both the sides of the equation we get, (a)1/3 = (2)2 = 4
Now, taking cubes on both the sides of the equation we get, (a) = (4)3 = 64
∴ a = 64
Hence, the correct answer is option e.

18. If 5a + 6b = 30 and a – 6b = 6, then find the value of the variables 'a' as well as 'b'.
a. 30, 6
b. 5, 30
c. 6, 30
d. 30, 4
e. None of the above
Explanation:
According to the data given in the question,
5a + 6b = 30---------i
a – 6b = 6----------ii
Now adding equations I and ii, we get,
6a = 36
∴ a = 6
Now, substituting this value of 'a' in equation ii, we get,
6 – 6b = 6
∴ 6 – 6 = 6b
∴ 0 = 6b
∴ b = 0/6
∴ b = 0
Hence, the derived values of 'a' and 'b' are 6 and 0 respectively.
But, neither of the options contains this answer.
Hence, the correct answer is option e.

19. The integer 'a' is directly 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. 0.7
c. 7.0
d. 10.5
e. 0.21
Explanation:
If two quantities are directly proportional to each other, indicates that they always have the same quotient.
Now, according to this property and according to the data given in the question, as 'a' is directly proportional to the integer 'b' and a/b = 7 (-----i); then they both will always have the same quotient irrespective of the values of both 'a' and 'b'.
Hence, substituting the value of 'b' in (i), we get,
1.5/b = 7
∴ b = 1.5/7
∴ b = 0.21
Hence, the correct answer is option e.

20. Find out the area of the figure with all its sides equal in length if it is given that the perimeter of this regular polygon is 100.
a. 25
b. 100
c. 125
d. 625
e. 1025
Explanation:
According to the data given in the question, the figure is having all its sides equal in length. From this we can conclude that the given geometrical figure is a square.
Now, it is given that the perimeter of the square is 100 units.
And, perimeter of a square = sum of all its sides
Since, all its sides are equal in length, we can say that perimeter of the square = 4(side) = 100
∴ Side = 100/4 = 25
Now, we have to find out the area of the square.
Area of a square = side * side
∴ Area of the square with side 25 units = 25 * 25 = 625 square units
Hence, the correct answer is option d.
21. Solve the following and find out the answer for ((x6)3 * (x5)6)/ (x3).
a. X5
b. X6
c. X40
d. X45
e. None of the above
Explanation:
According to the basic rules of exponents, we multiply the exponents when powers are raised to powers……….i
When we multiply the exponents having the same base, then in that case we add the exponents and not multiply………….ii
When we divide the powers having the same base, then in that case we subtract the exponents and not multiply………….iii
In this problem, we have to make use of all these three properties in order to get the correct answer to the question.
First comes the multiplication of the exponents with the same base: ((x6)3 * (x5)6)
∴ ((x6)3 * (x5)6) = x6*3 * x5*6 = x18 * x30 = x18+30 = x48
Now we will solve the division part i.e. x48/x3 = x 48-3 = x45.
Hence, the correct answer is option d.

22. If the volume of a sphere is 75 cubic centimeters, then find out the area of this sphere in terms of centimeter square units.
a. 1079.3322
b. 1080
c. 1090.7933
d. 2233.1023
e. None of the above
Explanation:
Formula for the volume of a sphere is V = 4/3(pi*r*r*r); where 'r' is the radius of the circle.
According to the data given in the question, volume of the sphere V = 75 cubic centimeter.
∴ 4/3(pi*r*r*r) = 75
∴r*r*r = 17.8977
∴r = 2.6157 cm
Now, formula for the area of regular sphere A = 4*pi*r*r; where 'r' is the radius of the sphere.
∴ A = 4*3.14*(2.6157)*(2.6157)
∴ A = 1079.3322 square centimeter
Hence, the correct answer is option a.

23. A man 2 meters tall casts a shadow of 1.5 meters in length. At the same time, some building next to the man casts a shadow which is 6 meters in length. Calculate the height of this building in centimeters.
a. 1.5 m
b. 200 cm
c. 600 cm
d. 350 cm
e. 800 cm
Explanation:
Let (h) denote the height and (sh) denote the shadow.
Let (ht) be the height of the building that we have to calculate.
Now, height of man (h1) : shadow of man (sh1) :: height of building(ht) : shadow of building(sh2)
∴ 2 : 1.5 :: ht : 6
This ratio can also be represented as, 2/1.5 = ht/6
∴ ht = (2 * 6)/1.5
∴ ht = 12/1.5 = 8 meters
But, we have to find out the height of the building in terms of cm.
Now, 1m = 100 cm
∴ 8m = 8*100 = 800cm
Hence, the height if the building whose shadow is 6 meters in length is 800 cm.
Hence, the correct answer is option e.

24. 5 men and 3 women can do a piece of work in 10 consecutive working days. The same piece of work is done by 7 men and 2 women in a time period of 8 working days. Find the number of days required to complete the same amount of work if there are 9 men and women working on it.
a. 10.2 days
b. 8.9 days
c. 9.8 days
d. 11.0 days
e. 4.07 days
Explanation:
According to the data given in the question,
5 men + 3 Women can do the piece of work in 10 days.
Thus, we can say that, 50 men + 30 women can do the piece of work in 1 day……….i
Also, it is given that,
7 men + 2 Women can do the piece of work in 8 days.
Thus, we can say that, 70 men + 20 women can do the same piece of work in 1 day………..ii
As equation I and ii show the work done in 1 day we can equate the number pof men and women working to complete the task.
i.e. 5 men + 3 Women = 7 men + 2 Women
∴ 1 women = 2 men or 2 men = 1 women
∴ 3 women = 3 * 2 = 6 men
∴ We can say that, 11 men can do a piece of work in 10 days.
But, we have to find out the number of days required to complete the same amount of work if there are 9 men and women working on it.
Now, 9 women = 9 * 2 = 18 men.
∴ 9 men + 18 men = 27 men, can do the work in, (11*10)/ 27 = 110/27 = 4.07 days.
Hence, the correct answer is option e.

25. Find the greatest fraction from the following set of fractions (8/9, 9/8, 7/5)
a. 8/9
b. 9/8
c. 7/5
d. 1.5
e. None of the above
Explanation:
We will have to find the quotients of all the fractions first and then compare them to find the correct answer to the question.
Now, 8/9 = 0.8889
9/8 = 1.125
And, 7/5 = 1.4
∴ The greatest of all is the fraction 7/5
Hence, the correct answer is option c.

26. Out of the two candidates who were standing against each other for the post of an MLA, one of them got 40 % of the total number of vote and the other who won the election got the remaining 60% of all the votes. The defeated candidate got 460 votes less than the number of votes secured by the winner of the election. Find out the total number of votes and the total number of votes gained by the winner of the election.
a. 966, 2300
b. 2300, 966
c. 1380, 2300
d. 2300, 1380
e. None of the above
Explanation:
Suppose the total number of votes = 100
Then, 40% of total number of 100 votes = 40 = number of votes secured by the loser.
And, 60% of total number of 100 votes = 60 = number of votes secured by the winner.
∴ Difference in the votes secured by the two candidates = 60 – 40 = 20.
Hence, we can say that, for total number of votes equal to 100, the difference in the votes earned by the two is equal to 20.
∴ According to the data given in the question, the actual difference of votes between the candidates is = 460
∴ Total number of votes earned by the two candidates = 460*100/20 = 2300
But, we also to find out the number of votes secured by the winner.
It is given that the winner secured 60% of the total number of votes.
∴ 60% of 2300 = 60*2300/100 = 1380
Hence, the correct answer is option d.

27. If a - b = 3 and a2 - b2 = 25, then find the sum of both the variables 'a' and 'b'.
a. 8.6
b. 3.5
c. 2.4
d. 8.33
e. 3.88
Explanation:
We know the standard algebraic formula for (a)2 – (b)2
(a)2 – (b)2 = (a + b) (a – b)
Now, according to the data given in the question, a - b = 3 and a2 - b2 = 25.
Substituting these values in above equation, we get,
25 = (a + b) (3)
∴ (a + b) = 25/3
∴ a + b = 8.3333
Hence, the correct answer is option d.

28. If x + y = 6 and x2 + y2 = 30, then find the product of both the variables 'x' and 'y'.
a. 6
b. 36
c. 2
d. 5
e. 3
Explanation:
We know the standard algebraic formula for (x+y)2
(x+y)2 = x2 + 2xy + y2
Now, according to the data given in the question, x + y = 6 and x2 + y2 = 30
Substituting these values in above equation, we get,
(6)2 = 30 + 2xy
∴ 36 – 30 = 2xy
∴ 6 = 2xy
∴ xy = 3
Hence, the correct answer is option e.

29. If f(x) = 4(x + 2), then what will be the value of f(3)?
a. 20
b. 30
c. 40
d. 10
e. None of the above
Explanation:
According to the data given in the question, f(x) = 4(x + 2)
We have to find out the value of f(3).
∴ Substituting, x = 3 in the equation for f(x), we get,
f(3) = 4(3 + 2)
∴ f(3) = 4(5) = 20
Hence, f(3) = 20
Hence, the correct answer is option a.

30. Find the value of g(2,3) if g(x,y) = x2 + y2/ x+y
a. 12/5
b. 11/12
c. 13/12
d. 5/12
e. 13/5