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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 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.

1. 7.5 units
2. 8.5 units
3. 5.7 units
4. 5.8 units
5. None of the above

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

2. If the square root of the cube root of some positive integer is 3, then find the integer which results in this answer.

1. 3
2. 6
3. 9
4. 27
5. None of the above

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

3. If a + b = 30 and a – b = 6, then find the value of the (a + b)2 and also find the product of ab.

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,

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.

4. 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.

1. 1.5
2. 4.66
3. 7.0
4. 10.5
5. 0.21

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.

5. 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.

1. 20.125 units
2. 30.234 units
3. 31.176 units
4. 35.425 units
5. None of the above

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.

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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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