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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. How will you represent the number 786 with the help of roman numbers?

1. XXXX
2. MDC
3. CMD
4. DMC
5. None of the above

Explanation:

According to the roman number representation scheme,

Letter I represents a value of 1.

Letter X represents a value of 10.

Letter V represents a value of 5.

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.

We have to find the roman symbol for number 786.

786 = 700 + 80 + 6 = DCCLVI

But, none of the given options represent this value.

Hence, the correct answer is option e.

2. It is given that 2:3 is the value of the sub triplicate ratio of the variables 'p' and 'q' respectively. Find out the value of the variables 'p' as well as 'q' and also find out the triplicate ratio of these two variables.

1. p:q = 2:3 and p3:q3 = 8:27
2. p:q = 2:3 and p3:q3 = 4:9
3. p:q = 8:27 and p3:q3 = 512:19683
4. p:q = 3:2 and p3:q3 = 4:8
5. p:q = 512:19683 and p3:q3 = 8:27

Explanation:

According to the data given in the question, value of the sub triplicate ratio of the variables 'p' and 'q' respectively = 8:27 ....(i)

We have to find the values of 'p' as well as 'q' i.e. p:q

We also to have to find the value of the triplicate ratio of p:q i.e. p3:q3

Sub triplicate ratio = p1/3:q1/3 = (2):(3) ....(ii)

∴To find p:q, we will have to take cubes on both the sides.

∴ p:q = 8:27 .....(ii)

Now, to find the triplicate ratio we will have to again take cubes on both sides of the equation (ii).

∴ p3:q3 = 83:273 = 512:19683 ..........(iii)

Hence, the correct answer is option c.

3. The radius of two concentric circles is in the ratio 2:5, then find out the ratio between their areas.

1. 2:5
2. 5:2
3. 4:25
4. 25:4
5. None of the above

Explanation:

According to the data given in the question, the radius of two concentric circles is in the ratio 2:5.

The standard formula to calculate the area of a circle (A) = Πr2, where r is the radius of the circle.

Since, p is a constant, we can say that A is directly proportional to the square of the radius.

∴ A1 : A2 = r12 : r22 = (2)2 : (5)2 = 4 : 25

Hence, the correct answer is option c.

4. How much are 16.66% of 420?

1. 50
2. 60
3. 70
4. 80
5. None of the above

Explanation:

We have to find 16.665 of 420.

We know that 16.66% is equivalent to 1/6.

∴ Multiplying on 420 by 1/6, we will get the correct answer.

∴ 420 * 1 / 6 = 420 / 6 = 70

Hence, the correct answer is option c.

5. The price of 1 kg of beans was \$15 in the month of June. The price of beans increased to \$17 by the month of July. Calculate the percentage increase in the cost of beans from June to July.

1. 13%
2. 12%
3. 10%
4. 13.33%
5. None of the above

Explanation:

According to the data given in the question,

Price of 1kg of beans in the month of June = \$15

Price of 1kg of beans in the month of July = \$17

Total increase in the price of beans from June till July in terms of \$ = \$2

We have to increase in terms of percentage.

Let this value be 'x'.

∴ x% of 15 = 2

∴ 15 * x/100 = 2

∴ 15 * x = 100 * 2 = 200

∴ x = 200/15

∴ x = 13.33

Hence, the correct answer is option d.

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