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GMAT Sample Questions » GMAT Sample Problem Soving Ability

# Quantitative Section : GMAT Sample Problem Solving Ability

Solve the following quantitative questions and then choose the correct answer from the given five options.

1. At the St. Mary's high school, all the 200 students of the class 9 are divided into two houses, namely red house and the blue house. There are 50 students in red house as well as there are 35 students in the blue house. 150 students are still not assigned into any of the two houses because some of the students are assigned both the houses by mistake. Find out the total number of students who are assigned both red as well as blue house by mistake.

1. 200
2. 50
3. 35
4. 115
5. None of the above

Explanation:

According to the data given in the question,

Total number of students in class 9 of St. Mary's high school = 200

Total Number of students in red house = 50

Total number of students in blue house = 35

Total Number of students who are not assigned any of the two houses yet = 150

We have to find out the total number of students who are assigned to both the houses.

Let these number = x

There is a standard formula to solve such problems. This formula is stated as follows:

Total students = students in red house + students in blue house + students in neither of the houses – students belonging to both the houses

Substituting the respective values in the above formula we get,

200 = 50 + 35 + 150 - x

∴ x = -200 + 235

∴ x = 35

Hence, there are 35 students who are assigned both the red and the blue house.

Hence, the correct answer is option c.

2. There are 10 members in a committee. Out of these 10 members, 6 are women and the remaining members are men. But, now the society has fixed the number of female members to 3 and the number of male members to only 1. In how many ways can this combination be formed which results in a committee of exactly 4 members out of which 3 are female and 1 is men from a total of 10 members.

1. 20
2. 40
3. 60
4. 80
5. None of the above

Explanation:

According to the data given in the question,

Condition 1:

Total number of members originally = 10 Total number of female members = 6 Total number of male members = 4

Condition 2:

Total number of members newly = 4 Total number of female members = 3 Total number of male members = 1

Now, total possible outcomes for 6 females in 3 places = 6*5*4/3*2*1 = 120/6

∴ Total possible outcomes for 6 females in 3 places = 20

Similarly, possible outcomes for 4 males in 1 place = 4/1 = 4.

∴ The total number of combinations is equivalent to the product of the above two results = 20*4 = 80

Hence, the correct answer is option d.

3. Calculate the total number of ways to arrange 7 chairs in a row.

1. 120
2. 216
3. 420
4. 5040
5. None of the above

Explanation:

As per the data given in the question we have to arrange, 7 chairs in 7 places in a row.

∴ The total number of possible combinations = 7! = 7*6*5*4*3*2*1 = 5040

Hence, the correct answer is option d.

4. The given triangle is a right angled triangle. You have to find out the length of the third side which is unknown i.e. side LN.

1. 12
2. 15
3. 37
4. 14
5. None of the above

Explanation:

Since, the given triangle is a right angled triangle we have the standard formula to find the length of the hypotenuse. This formula is stated as follows,

(Hypotenuse)2 = (one side)2 + (other side)2

i.e. (LN)2 = (LM)2 + (MN)2

∴ (LN)2 = (144) + (225)

∴ (LN)2 = 369

Now, taking square roots on both sides of the equation, we get,

LN = 19.2093

But, none of the options represents this value.

Hence, the correct answer is option e.

5. Find the value of tanΘ with the help of the details given in the adjoin figure.

1. 16/9
2. 25/9
3. 9/16
4. 9/25
5. 16/25

Explanation:

We know that tanΘ = opposite side/adjacent side

Side LM is the adjacent side and side MN is the opposite side

∴ tanΘ = 9/16

Hence, the correct answer is option c.

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