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GMAT Sample Questions » GMAT Sample Problem Soving Ability

# Quantitative Section : GMAT Sample Problem Solving Ability

Choose the correct answer form the given five options by solving the quantitative questions.

1. What will be the value of (am)n for the value of a = 3, m = 2 and n = 4 respectively.

1. 9
2. 16
3. 81
4. 6561
5. None of the above

Explanation:

According to the data in the question, the value of a = 3, m = 2 and n = 4 respectively.

We have to find the value of (am)n

Substituting the given values in (am)n we get,

(am)n  = (32)4

∴(am)n = 32*4 = 38

∴ (am)n = 6561

Hence, the correct answer is option d.

2. Find out which of the following number is not a perfect square.

1. 2187
2. 78125
3. 16284
4. 3125
5. None of the above

Explanation:

According to the standard properties of square numbers, all perfect square numbers must end in either 0, 1, 4, 5, 6 or 9.

Now, looking at the given options, we find that options b, c and d have 4 and 5 as the digit in the unit's place. Hence, these numbers belong to the set of perfect squares.

Thus, we are left only with the option a. this number has 7 as the digit in the unit's place. Hence, it 2187 is not a perfect square.

Hence, the correct answer is option a.

3. Which of the following statements are true with respect to the properties of squares of any number?

1. The square of even numbers is always even
2. The square of odd number is always odd
3. When you divide a perfect square by 3, the remainder is either 0 or 1
4. The total number of zeroes at the end of a perfect square is not odd at all

1. i and ii only
2. ii and iii only
3. i, ii and iii
4. ii, iii and iv
5. all the statements are true

Explanation:

All the statements represent some or the other property that is possessed by the square numbers.

Hence, the correct answer is option e.

4. What will be the square of x + 1/x, if it is given that x2+1/x2 = 34?

1. ±7
2. -7
3. ±6
4. -6
5. None of the above

Explanation:

According to the data given in the question, x2+1/x2 = 34

We have to find the value of x+1/x

We have the standard algebraic formula for the square of addition of two numbers as follows:

(a + b)2 = a2 + 2ab + b2

∴ (a + b)2 – 2ab = a2 + b2

Now substituting a =x and b = 1/x in the above formula, we get,

(x + 1/x)2 = 34 + 2*x*1/x

∴ (x + 1/x)2 = 34 + 2 = 36

Now taking square root on both the sides we get,

x + 1/x = ± 6

Hence, the correct answer is option c.

5. If (m + n) = 24, and the product of m and n is equal to 15, then find the value of the sum of the squares of the two variables 'm' and 'n'. Also find the value of (m-n)2.

1. 500, 550
2. 516, 546
3. 546, 516
4. 600, 500
5. None of the above

Explanation:

According to the data given in the question,

(m + n) = 24.....(i)

m*n = 15......(ii)

We have to find the sum of the squares of the two variables 'm' and 'n' i.e. m2 + n2

According to the standard mathematical formula,

(m + n)2 = m2 + 2mn + n2......(iii)

∴ (m + n)2 – 2mn = m2 + n2........(iv)

Substituting the value of m + n from equation (i) and (ii), in equation (iv), we get

(24)2 – 2(15) = m2 + n2

∴ 576 – 30 = m2 + n2

∴ m2 + n2 = 546

We also have to find the value of (m - n)2

Now, according to the standard mathematical formula,

(m - n)2 = m2 - 2mn + n2

∴ (m - n)2 = 546 – 2(15)

∴ (m - n)2 = 546 – 30 = 516

Hence, the correct answer is option c.

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