1. What is the greatest common factor of 21, 49 and 91?

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**Correct answer is option - 3**

**Explanation:**In order to find the GCF, we can first find their prime factors.

Prime factorization of 21 = 3 * 7

Prime factorization of 49 = 7 * 7

Prime factorization of 91 = 7 * 13

Since GCF is the greatest common factor of the given numbers, we can see that here the common factor is 7.

Therefore GCF of 21, 49 and 91 is 7.

2. If 2x + y = 3 and 3x + 2y = 4, then what is the value of (x + y)?

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**Correct answer is option - 2**

**Explanation: **To find the value of (x + y), we can first solve the system of linear equation.

From the first equation we get: y = 3 – 2x.

Substitute this ‘y’ value in the second equation. This gives: 3x + 2(3 – 2x) = 4.

So, 3x + 6 – 4x = 4 ==> 6 – x = 4 ==> x = 6 – 4 ==> x = 2.

Now y = 3 – 2x ==> y = 3 – 2(2) ==> y = 3 – 4 ==> y = -1.

Therefore, (x + y) = 2 – 1 = 1.

3. Given ‘a’ and ‘b’ are positive numbers and (a + b)^{2} = 196 and (a^{2} – b^{2}) = 28, then what is the value of b?

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**Correct answer is option - 4**

**Explanation: **If (a + b)^{2} = 196, then (a + b) = √196 ==> a + b = 14 (the value of (a + b) cannot be -14 cause ‘a’ and ‘b’ are supposed to be positive numbers).

Then expanding (a^{2} – b^{2}) = (a + b) (a – b), we can say 14 * 2 = 28.

Since (a + b) = 14, hence (a – b) should be = 2.

Solving the above two equations we have: 2a = 16 ==> a = 8.

Since (a + b) = 14 ==> b = 14 – 8 ==> b = 6.

4. What is the slope of the line perpendicular to 3x – 7y + 16 = 0?

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**Correct answer is option - 1**

**Explanation: **The given line can be rearranged as: 7y = 3x + 16.

This gives: y = (3/7)x + (16/7).

This is in the form of y = mx +b where ‘m’ is the slope of the line.

Therefore slope of the given line = 3/7.

If two lines are perpendicular, then the product of their slopes is = -1.

This gives (3/7) * m = -1 ==> m = -7/3 is the slope of the perpendicular line.

5. The factor of the polynomial expression: -3x^{2} + 2x + 8is?

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**Correct answer is option - 4**

**Explanation: **The given polynomial expression can be factored by first splitting its middle term.

Since -3 * 8 = = -24, we need to find two numbers which would add and give the middle term number 2.

This gives: -3x^{2} + 6x – 4x + 8.

Now we can group the first two and the last two terms: -3x (x – 2) – 4 (x – 2).

This gives: (x – 2) (-3x – 4).

Since (x – 2) is not in the options, (-3x – 4) is the answer.

6. If a, b, and c are three consecutive numbers and their sum is 21, then what is the value of ‘b’?

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**Correct answer is option - 5**

**Explanation: **Let a = n, b = (n + 1) and c = (n + 2) as they are three consecutive numbers.

Sum ==> n + n + 1 + n + 2 = 21 ==> 3n + 3 = 21 ==> 3n = 21 – 3.

This gives: 3n = 18 ==> n = 18/3 ==> n = 6.

Hence the value of b = (n + 1) is 6 + 1 ==> b = 7.

7. The sum of ‘p’ numbers is 7 more than thrice the numbers. If the arithmetic mean of all the ‘p’ numbers is 4, then the value of ‘p’ is?

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**Correct answer is option - 4**

**Explanation: **Sum of ‘p’ numbers = 3p + 7.

Arithmetic mean = (Sum of all the numbers)/(number of numbers)

This gives: (3p + 7)/ p = 4 ==> When we cross-multiply we get: 3p + 7 = 4p.

Solving for ‘p’ gives 4p – 3p = 7 ==> p = 7.