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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 following five options.

1. If x* = (3x + 2)/6, and x = 6x + 1, then what will be the value of x*?

1. 3x + 5/6
2. 2x + 6/5
3. 6/5 + 2x
4. 5/6 + 2x
5. None of the above

Explanation:

According to the data given in the question,

x* = (3x + 2)/6.....(i)

and x = 6x + 1......(ii)

Substituting the value of x from equation ii in equation i, we get,

x* = (3(6x + 1) + 2)/6

∴ x* = (18x + 3 + 2)/6

∴ x* = (18x + 5)/6

∴ x* = 3x + 5/6

Hence, the correct answer is option a.

2. What will be the digit in the unit's place of a single digit which belongs to the set of natural numbers, when this number is raised to the power 5?

1. The number itself
2. Number + 1
3. Number – 1
4. Number / 1
5. None of the above

Explanation:

In order to answer this question, let us find out the values of the different natural numbers in the ascending order of their powers upto the power 5.

For the natural number 2:

2, 4, 8, 16, 32

For the natural number 3:

3, 9, 27, 81, 243

For the natural number 4:

4, 16, 64, 256, 1024

For the natural number 5:

5, 25, 125, 625, 3125

From the above results we can come to a conclusion that the digit in the unit's place when any single digit natural number is raised to the power 5 is equal to the digit itself.

Hence, the correct answer is option a.

3. If f(x) = x + 9 / 3, then find the value of f(2).

1. 3
2. 6
3. 9
4. 12
5. None of the above

Explanation:

According to the data given in the question,

f(x) = (x + 9)/3……. (i)

We have to find the value of f(2).

Thus, substituting, x=2 in equation (i), we get,

f(2) = (2 + 9)/3

∴ f(2) = 11/3 = 3.6667

But, none of the given options represent this value.

Hence, the correct answer is option e.

4. Find the dividend if it is given that the dividend when divided by 6 gives the remainder as half of the divisor and the quotient is 2 more than the perfect square of the divisor.

1. 123
2. 321
3. 345
4. 123
5. 231

Explanation:

According to the data given in the question,

Divisor = 6..... (i)

Quotient = 2 + perfect square of the divisor

Thus, quotient = 2 + 36 = 38.....(ii)

Remainder = half of the divisor

Thus, remainder = 6/2 = 3.....(iii)

According to the standard mathematical formula for division:

Dividend = divisor * quotient + remainder

Substituting the values from equation (i), (ii) as well as (iii) in this formula, we get,

Dividend = 6 * 38 + 3

∴ Dividend = 228 + 3

∴ Dividend = 231

Hence, the correct answer is option e.

5. Find the difference between 'm and 'n', if it is given that, (m)2 – (n)2 = 81 and the sum of these two variables is equal to 50.

1. 1.5
2. 2.5
3. 1.62
4. 1.75
5. None of the above

Explanation:

According to the data given in the question,

(m)2 – (n)2 = 81….(i)

Sum of these two variables = sum of 'm' and 'n' = 50.....(ii)

We have to find the difference between 'm' and 'n' i.e. (m-n)

According to the standard mathematical formula,

(m)2 – (n)2 = (m + n) (m - n)

On substituting the values from equations (i) and (ii) in this formula we get,

81 = 50 (m - n)

∴ (m – n) = 81/50 = 1.62

Hence, the correct answer is option c.

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