1. If 12/k = 4/7, then what is the value of ‘k’ for the given equation to be true?

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**Correct answer is option - 1**

**Explanation:**

We can cross- multiply the numbers to the other side of the equation sign.

This gives: 12 * 7 = 4 * k which implies 84 = 4k.

Dividing 4 on both sides gives k = 84/4 = 21.

2. The value of ‘x’ from the given expression, 2(4x – 4) – 5(4x + 8) = 12 is:

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**Correct answer is option - 4**

**Explanation:**

First distribute the numbers on the outside to numbers inside the parenthesis.

8x – 8 – 20x – 40 = 12 which gives -12x – 48 = 12.

This implies: -12x = 60 and hence x = 60/-12 = -5.

3. In a certain store, every item is on a discount of 20%. Laura wants to buy a bag of original price $40. Since she is an employee, she gets an additional employee discount of 10% on the reduced item. How much does she pay for the bag?

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**Correct answer is option - 3**

**Explanation: **

The original price of the bag = $40.

The 20% discount on the bag gives $40 – ($40 * 0.2) = $32.

Additional 10% discount on the reduced price of bag = $32 – ($32 * 0.1) = $28.80.

4. What is the value of i^{3602}?

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**Correct answer is option - 4**

**Explanation: **3602 can be written as 3600 + 2. This gives: i^{3602} = i^{(300 + 2) }= i^{3600} * i^{2}

This implies: (i^{4})^{900} * i^{2} and i^{4} = (i^{2})^{2} = (-1)^{2} = 1

Therefore we get: (1)^{900} * -1 = -1.

5. If p^{2} – 14p + c = (p – 7)^{2} then the value of c is:

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**Correct answer is option - 5**

**Explanation: **According to the formula, (a –b)^{2} = a^{2} – 2ab + b^{2}.

Therefore, (p – 7)^{2} = p^{2} -14p + 7^{2}

Hence, p^{2} – 14p + 49 implies c = 49.

6. In the square shown below, the length of PR is 6cm. The length of the side PQ is:

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**Correct answer is option - 4**

**Explanation: **Since it’s a square, all the side lengths are equal.

Let the side PQ = QR = s

Here, triangle PQR is a right triangle and hence we can use the Pythagorean Theorem.

This gives: s^{2} + s^{2} = 6^{2} which implies 2s^{2} = 36.

Therefore s^{2} = 18 which gives s = √18 = 3√2.

7. The sum of the two solutions of the equation x^{2}– 9x – 36 = 0 is:

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**Correct answer is option - 2**

**Explanation: **The above given quadratic equation can be factored as (x – 12)(x + 3)= 0.

This gives (x – 12) = 0 and (x + 3) = 0.

Hence x = 12 and x = -3.

Therefore the sum of the two solutions is 12 + (– 3) = 9.