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GMAT Sample Questions » GMAT Sample Problem Soving Ability

# Quantitative Section : GMAT Sample Problem Solving Ability

Solve the following questions and select the correct answer from the given five options.

1. 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.

1. 10
2. 20
3. 30
4. 15
5. 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.

2. If the square root of the cube root of some positive integer is 2, then find the integer which results in this answer.

1. 4
2. 8
3. 16
4. 32
5. 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.

3. If 5a + 6b = 30 and a – 6b = 6, then find the value of the variables 'a' as well as 'b'.

1. 30, 6
2. 5, 30
3. 6, 30
4. 30, 4
5. 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.

4. 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.

1. 1.5
2. 0.7
3. 7.0
4. 10.5
5. 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.

5. 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.

1. 25
2. 100
3. 125
4. 625
5. 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.

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GMAT Sample Problem Solving Ability Question Number : 1-5 | 6-10 | 11-15 | 16-20 | 21-25 | 26-30 | 31-35 | 36-40 | 41-45 | 46-50 | 51-55 | 56-60 | 61-65 | 66-70 | 71-75 | 76-80 | 81-85 | 86-90 | 91-95 | 96-100 | 101-105 | 106-110 | 111-115 | 116-120 | 121-125
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