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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 ratio of the number of boys and girls who appeared for the exam is 15:7. Out of the total number of boys and girls, the number of boys and girls who cleared their exams is in the ratio of 3:2. Find out the percentage of boys who passed in the exam if it is given that 65 % of the girls cleared their exams.

1. 40 %
2. 41.5 %
3. 45.5 %
4. 44.5 %
5. None of the above

Explanation:

According to the data given in the question,

The ratio of the number of boys and girls who appeared for the exam = 15:7 …..i

Hence, let the total number of boys = 15x …………..ii

And, the total number of girls = 7x ……………iii

It is also given that, the total % of girls who passed the exam = 65 % ……..iv

∴ Number of girls passing the examination = 7x * (65/100) = 4.55x …………v

It is also given that, the ratio of the number of boys and girls passing the exam = 3:2 ………….vi

∴ The number of boys who passed the exam = 3 * (4.55x) / 2 = 6.825x ………….vii

∴ % of boys passing the exam = (6.825x /15x) * 100 = 45.5 % ……..viii

Thus, 45.5% of the boys passed the examination.

Hence, the correct answer is option c.

2. Sam divides his income between his wife, son and two daughters in certain ratio. Sam gives 20 % to his son, 35 % to his wife and the remaining percentage of his savings is divided equally between his two daughters. Find the approximate amount that his wife receives if both of his daughters receive an equal amount of \$ 250.

1. \$ 250
2. \$ 350
3. \$ 450
4. \$ 460
5. None of the above

Explanation:

Let 'x' be the total amount that is saved by Sam and divided between his wife, son and the two daughters.

According to the data given in the question,

% of total amount received by son = 20 % ………i

∴ Amount received by his son = (20 * x)/100 = \$ x/5 …….ii

% of total amount received by his wife = 35 % …….ii

∴ Amount received by his wife = (35/100) * (x – (x/5)) = \$ 7x/4 ……..iii

% of total amount received by each of his daughter's = (1/2) * (x – (x/5) – (7x/4))……………iv

But, it is given that, each of the two daughters receive an amount of \$ 250.

∴ (1/2) * (x – (x/5) – (7x/4)) = 250

∴ 19x/20 = 250

∴ x = (250 * 20) / 19

∴ x = \$263.15 ………………v

∴ Amount received by his wife = (35/100) * (x – (x/5)) = \$ 7x/4 = (7 * 263.15) / 4

∴ Amount received by his wife = \$460.5125

Hence, the correct answer is option d.

3. Which of the following statements is false with respect to the values used to represent Roman Numbers?

1. The alphabet M is used to represent the numeric value of 1000
2. The alphabet I is used to represent the numeric value of 1
3. The alphabet C is used to represent the numeric value of 100
4. The alphabet L is used to represent the numeric value of 50

1. All of them are true
2. All of them are false
3. Only i and ii are true
4. Only ii and iii are true
5. Only i and iv are true

Explanation:

According to the rules established for writing the roman numbers,

Letter I represents a value of 1

Letter V represents a value of 5

Letter X represents a value of 10

Letter L represents a value of 50

Letter C represents a value of 100

Letter D represents a value of 500

Letter M represents a value of 1000

Hence, the correct answer is option a

4. How will you represent the term 140 with the help of roman numbers?

1. CXXXX
2. LCD
3. DCL
4. CXL
5. None of the above

Explanation:

According to the rules used for writing the roman numbers,

Letter I represents a value of 1

Letter V represents a value of 5

Letter X represents a value of 10

Letter L represents a value of 50

Letter C represents a value of 100

Letter D represents a value of 500

Letter M represents a value of 1000

∴ 140 can be written as 100 + 40

For 100 we can use the symbol C.

But, 40 cannot be written as XXXX, because we cannot the same symbol more than 3 times consecutively.

∴ We can write 40 as XL

Hence, we can write 140 as CXL in terms of roman numbers.

Hence, the correct answer is option d.

5. What is 12.5 % of 3565?

1. 12.5
2. 120.5
3. 30.5
4. 40.5
5. None of the above

Explanation:

We have to find out 12.5 % of 3565. Let the answer be equal to 'x'.

∴ (12.5 * 3565) / 100 = x

∴ x = 445.625

But, none of the options represent this value.

Hence, the correct answer is option e.

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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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