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GMAT Sample Questions » GMAT Sample Problem Soving Ability

# Quantitative Section : GMAT Sample Problem Solving Ability

Select the correct answer from the given five options by solving the following questions.

1. Solve the following and find out the answer for ((x6)3 * (x5)6)/ (x3).

1. X5
2. X6
3. X40
4. X45
5. 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.

2. If the volume of a sphere is 75 cubic centimeters, then find out the area of this sphere in terms of centimeter square units.

1. 1079.3322
2. 1080
3. 1090.7933
4. 2233.1023
5. 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.

3. 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.

1. 1.5 m
2. 200 cm
3. 600 cm
4. 350 cm
5. 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.

4. 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.

1. 10.2 days
2. 8.9 days
3. 9.8 days
4. 11.0 days
5. 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.

5. Find the greatest fraction from the following set of fractions (8/9, 9/8, 7/5)

1. 8/9
2. 9/8
3. 7/5
4. 1.5
5. 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.

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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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