1. In triangle ABC, angle C is 12 less than twice of angle A and angle B is 16 more than angle A. What is the measure of angle C?

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**Correct answer is option - 2**

**Explanation: **Let angle A be = x

Then angle B = x + 16

And angle C = 2x – 12

Sum of the angles of triangle = 180°.

This gives: x + x + 16 + 2x - 12 = 180° ==> 4x + 4 = 180° ==> 4x = 180° - 4

This implies: 4x = 176° ==> x = 176°/4 ==> x = 44°

Therefore angle A = x = 44°, angle B = 44° + 16 = 60°.

Angle C = 2(44°) – 12 = 76°.

2. Andrew has enough money to buy 30 apples, however if the cost of each apple was 10 cents less, then Andrew could buy 40 apples. How much money is Andrew carrying with himself to buy the apples?

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**Correct answer is option - 2**

**Explanation: **Let the money carried by Andrew be = m

Let the price of each apple be = p

Since he can buy 30 apples, it would cost him 30 * p = m ==> m = 30p.

Now if the price of each apple was 10 cents less which gives, (p – 10) then Andrew could buy 10 more apples which means 30 + 10 = 40 apples.

This implies: 40 (p – 10) = m ==> 40p – 400 = 30p.

This gives: 40p – 30p = 400 ==> 10p = 400 ==> p = 40 cents.

This gives: total money = m = 30p = 30 * 40 = 1200 cents.

$1 = 100 cents ==> 1200 cents means $12.

3. Which of the following is equivalent to i^{450}, where ‘i’ is the imaginary number?

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**Correct answer is option - 3**

**Explanation: **Given i^{450} can also be written in terms as i^{4}, the advantage being i^{4} = 1.

Hence 450 can be split as 450 = 448 + 2, since 448 is exactly divisible by 4.

This gives: i^{450} = i^{448 + 2} ==> i^{448} * i^{2} ==> (i^{4})^{112} * i^{2} ==> (1)^{112} * i^{2}

Hence we get: i^{2} which is equal to -1 as the answer.

4. Laura has few books and among them she wants to sell some of the books. She sold 20% more number of books than she kept with herself. If the number of books she sold is 18, then how many books did she keep with her without selling?

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**Correct answer is option - 3**

**Explanation: **Let the number of books she kept with herself = x.

Then the number of books sold = 20% more than x = x + (20/100)x ==> x + 0.2x = 1.2x.

This gives 1.2x = 18 ==> x = 18/1.2 ==> x = 15.

Hence she kept 15 books with herself without selling.

5. If [1/ (5 – x)] + 2 = 3, then the value of ‘x’ is?

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**Correct answer is option - 1**

**Explanation: **Taking the common denominator as (5 – x), we get: [1 + 2(5 – x)]/ (5 – x) = 3.

This implies: (1 + 10 – 2x)/ (5 – x) = 3 ==> (11 – 2x)/ (5 – x) = 3.

Cross-multiplying we get: 11 – 2x = 3 (5 -x) ==> 11 – 2x = 15 – 3x.

This gives: 3x – 2x = 15 – 11 ==> x = 4.

6. Midpoint of a line segment is (-4, 6). If one of the end points of the line is (2, 1), then what is the other end point?

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**Correct answer is option - 4**

**Explanation: **Midpoint of a line segment joining the points (x_{1}, y_{1}) and (x_{2}, y_{2}) is = [(x_{1} + x_{2})/2, (y_{1} + y_{2})/2].

Let the other unknown endpoint be (x, y).

Then [(2 + x)/ 2, (1 + y)/ 2] = (-4, 6)

Now taking each coordinate separately we get: (2 + x)/2 = -4 ==> 2 + x = -8 ==> x = -10.

Similarly, (1 + y)/ 2 = 6 ==> 1 + y = 12 ==> y = 11.

This gives the other endpoint (x, y) = (-10, 11).

7. Which of the following is the solution for the equation: |5x - 2| + 1 = 9?

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**Correct answer is option - 3**

**Explanation: **In order to solve for x, we have to split this absolute value equations in two ways.

(5x - 2) + 1 = 9 ==> (5x – 2) = 9 – 1 ==> 5x – 2 = 8 ==> 5x = 10 ==> x = 10/5 = 2.

Similarly, (5x - 2) + 1 = -9 ==> 5x – 2 = -9 -1 ==> 5x – 2 = -10 ==> 5x = -8 ==> x = -8/5.

Since x = 2 is not in the given options, hence the answer is x = -8/5.