1. If thearithmetic mean of x, 2x + 3 and 4x is 8, then the value of ‘x’ is?

Show me the answers!

**Correct answer is option - 3**

**Explanation:**

Arithmetic mean = (Sum of the numbers)/ (Number of numbers present)

Arithmetic mean of x, 2x + 3 and 4x is (x + 2x + 3 + 4x)/ 3 = 8

This gives: (7x + 3)/ 3 = 8 ==> 7x + 3 = 24 ==> 7x = 24 – 3 ==> 7x = 21.

This implies: x = 21/7 which gives x = 3.

2. In a bag there are oranges and apples, and the ratio of their weights is 3: 2. If the bag weighs 12 pounds, then how much do the oranges weigh in the bag?

Show me the answers!

**Correct answer is option - 1**

**Explanation: **The ratio of their weights is 3: 2.

Therefore we can say that the oranges weigh 3x and apples weigh 2x and the total weight of the bag is 3x + 2x = 5x.

Since the total weight of the bag is 12 pounds, hence we get: 5x = 12 ==> x = 12/5.

Hence the oranges weigh = 3x = 3 * 12/5 = 36/5 pounds.

3. What is the value of ‘x’ in the expression, |2x + 5| = 3?

Show me the answers!

**Correct answer is option - 4**

**Explanation: **The absolute value equation always splits into 2 possibilities.

The given equation also splits in two ways: (2x + 5) = 3 or (2x + 5) = -3.

If (2x + 5) = 3, then 2x = 3 – 5 ==> 2x = -2 which gives x = -1.

If (2x + 5) = -3, then 2x = -3 – 5 ==> 2x = -8 which gives x = -4.

Since -1 is not in the options, therefore the answer is x = -4.

4. If 2^{a} = 4^{b} = 8^{c}, then what is the sum, (a + b + c) only in terms of ‘c’?

Show me the answers!

**Correct answer is option - 3**

**Explanation:**

If 2^{a} = 4^{b} = 8^{c}, then this can also be written as: 2^{a} = (2^{2})^{b} = (2^{3})^{c}.

This gives: 2^{a} = 2^{2b} = 2^{3c} and since the bases are the same, the exponents can be equated.

This implies: a = 2b = 3c ==> a = 3c and 2b = 3c which gives b = 3c/2.

The sum, (a + b + c) = 3c + 3c/2 + c. Now we can take the common denominator.

Hence we get: (6c + 3c + 2c)/2 = 11c/2.

5. The point where the graph of the function, f(x) = 2x^{2} + 4x - 6 cuts the Y-axis is?

Show me the answers!

**Correct answer is option - 5**

**Explanation: **In order to find the point where the function cuts the Y-axis, we should first plug-in x = 0.

This gives: f(x) = y = 2(0)^{2} + 4(0) – 6.

This gives: y = -6.

Hence the point on the Y-axis is (0, -6).

6. In the figure as shown below, ABCD is a square and the length of DE is 10. If the measure of the angle BED is 60°, then the area of the square ABCD is?

Show me the answers!

**Correct answer is option - 4**

**Explanation: **From the figure we can see that triangle BDE is a right angled triangle.

Hence we can use the appropriate trigonometric function to get the other side length.

tan(60°) = (opposite side)/ (adjacent side) ==> tan(60°) = BD/ DE

This gives: BD = DE * tan(60°) ==> BD = 10 * √3 = 10√3.

Area of the square = (side length)^{2} = (10√3)^{2} = 300.

7. In the figure shown below, the measure of angle BAC is 120° and all the other angles are mentioned. If the angle BDC is 2k as shown in the figure, then what is the value of ‘k’?

Show me the answers!

**Correct answer is option - 3**

**Explanation: **In the triangle ABC, the measure of angle BAC is 120°.

Sum of all the angles in a triangle = 180°.

Hence in triangle ABC, 120° + 3m + 3n = 180° ==> 3(m + n) = 180° - 120°.

This gives: (m + n) = 60°/3 ==>(m + n) = 20°

Now, similarly in triangle BDC, 2k + 2m + 2n = 180° ==> 2k + 2(m + n) = 180°.

Hence 2k + (2 * 20°) = 180° ==>2k = 180° - 40° = 140°.

This gives: k = 140°/2 ==> k = 70°.