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GMAT Sample Questions » GMAT Sample Problem Soving Ability

# Quantitative Section : GMAT Sample Problem Solving Ability

Solve the following set of questions by selecting the correct answer from the given five options.

1. The following table shows the details of marks secured by Tom, Jerry and Sam in 3 different subjects namely History, Geography and Science. The total marks that each subject is composed of are 150. Look at the table and answer the following questions.

 Tom Jerry Sam History 110 95 115 Geography 100 105 120 Science 105 115 130

1. By what percent did Tom score more than Jerry in History?
2. Also find out by what percent did Sam secure more marks in Science than Tom?

1. i = 15.78, ii = 23.80
2. i = 16.78, ii = 20.80
3. i = 15, ii = 22.80
4. i = 10.78, ii = 23
5. None of the above

Explanation:

Solution for part (i):

According to the data given in the question,

Marks secured by Tom in History = 110 ..i

Marks secured by Jerry in History = 95 ..ii

Maximum marks to be scored in History = 150 .iii

From equation i and equation ii, we can that,

Tom secured 15 marks more than Jerry in History.iv

But, we have to find out the answer in terms of percentage.

∴ Increase in terms of percentage = (15/95) * 100 = 15.78 % . Solution for part (i)

Now, solution for part (ii):

According to the data given in the question,

Marks secured by Tom in Science = 105 ..v

Marks secured by Sam in Science = 130 ..vi

Maximum marks to be scored in Science = 150 .vii

From equation i and equation ii, we can that,

Sam secured 25 marks more than Tom in Science.viii

But, we have to find out the answer in terms of percentage.

∴ Increase in terms of percentage = (25/105) * 100 = 23.80 % . Solution for part (ii)

Hence, the correct answer is option a.

2. The amount of \$ 1180 is divided among X, Y and Z in such a way that 5 times of the amount that X receives, 6 times of the amount that Y receives and 8 times of the amount that Z receives are one and the same. Find the amount received by each of the X, Y and Z.

1. X = \$ 480, Y = \$ 400, Z = \$ 300
2. X = \$ 450, Y = \$ 430, Z = \$ 300
3. X = \$ 300, Y = \$ 480, Z = \$ 400
4. X = \$ 480, Y = \$ 300, Z = \$ 400
5. None of the above

Explanation:

Let the amount received by X, Y and Z be equal to x, y and z respectively.

∴ According to the data given in the question, 5x = 6x = 8x .i

Because it is given that 5 times of the amount that X receives, 6 times of the amount that Y receives and 8 times of the amount that Z receives are one and the same.

The total amount = \$ 1180

∴ We can say that, x + y + z = 1180 ..ii

Using equation I and ii we can say that,

(x/24) + (y/20) + (z/15) = 1180/59

∴ x = \$ 480

Y = \$ 400

And z = \$ 300

Hence, the correct answer is option a.

3. If we divide 1690 into three parts such that the ratio of these parts is equal to 1/2 : 1/3 : 1/4, then find out the actual values that result in this ratio.

1. 100, 200, 300
2. 780, 520, 390
3. 700, 600, 690
4. 600, 780, 310
5. None of the above

Explanation:

According to the data given in the question,

The ratio of the parts in which 1690 is divided = 1/2 : 1/3 : 1/4i

Let the actual numbers represented by the parts = a/2, a/3 and a/4 respectively .ii

Then, the sum of these parts = a/2 + a/3 + a/4 = 13a/12 .iii

But, according to the data given in the question, the actual number = 1690 .iv

∴ From equation iii and equation iv, we can say that, 13a/12 = 1690 v

∴ a = (1690 * 12) / 13

∴ a = 1560

∴ The value of the first part = 1/2 * 1560 = 780

∴ The value of the second part = 1/3 * 1560 = 520

∴ The value of the third part = 1/4 * 1560 = 390

Hence, the correct answer is option b.

4. Divide the number 395 into three different parts such that the second part is 25 % more than the first part and 20 % more than the third part.

1. 125, 150, 120
2. 120, 125, 150
3. 120, 150, 125
4. 125, 120, 150
5. None of the above

Explanation:

According to the data given in the question,

Second part is 25 % more than the first part .i

Second part is 20 % more than the third part ..ii

Let the third part = x iii

∴ The second part = x = 20 % of x

∴ The second part = x + (x/5) = 6x/5 = 1.20x iv

Similarly, the first part = 1.20x  25 % of 1.20x

∴ The first part = 0.96x ..v

But, the sum of all the three parts = 395 .vi

∴ From equations iii, iv, v and vi, we can say that,

x + 1.20x + 0.96x = 395

∴ x = 125 = third part

∴ Second part = 1.20 * x = 150

And, the first part = 0.96 * x = 120

Hence, the correct answer is option c

5. Which of the following discount scheme is better?

 Discount 1 Discount 2 10 % 20 % 20 % 15 % 15 % 10 %

1. Discount 1 is better
2. Discount 2 is better
3. Both of them are equal
4. Both of  them are unequal
5. None of the above

Explanation:

Let the total amount be equal to 100.

Now, according to the first discount scheme,

After the first discount of 10 %, the amount = 90 i

∴ Discount = 10

After the second discount of 20 %, the amount = (20 * 90) / 100 = 72 ..ii

∴ Discount = 18

And, after the third discount of 15 %, the amount = (15 * 72) / 100 = 61.2 iii

∴ Discount = 10.8

Hence, the total discount = 10 + 18 + 10.8 = 38.8 ..iv

Now, according to the second discount scheme,

After the first discount of 20 %, the amount = 80 i

∴ Discount = 20

After the second discount of 15 %, the amount = (15 * 80) / 100 = 68 ..ii

∴ Discount = 12

And, after the third discount of 10 %, the amount = (10 * 68) / 100 = 61.2 iii

∴ Discount = 6.8

Hence, the total discount = 20 + 12 + 6.8 = 38.8 ..iv

∴ Both the discount schemes result in the same saving. Hence, both the discount schemes are equal.

Hence, the correct answer is option c.

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