**1.) **If the sum of a number and its square is 182, what is the number?

**A.** 13 **B.** 26

**C.** 52 **D.** 91

**View Answer**

**Answer:** Option **A**

**Explanation:**

Let the number be x.

Then, x + x^{2} = 182

==> x^{2 }+ x - 182 = 0

==> (x+14) (x-13) = 0

==>** X=13**

**2.)** Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:

**A.** 11 **B.** 15

**C.** 21 **D.** 29

**View Answer**

**Answer:** Option **B**

**Explanation:**

Let the three integers be x, x + 2 and x + 4.

Then, 3x = 2(x + 4) + 3

==> x = 11.

Third integer = x + 4 = **15.**

**3.) **Twenty times a positive integer is less than its square by 96. What is the integer?

**A.** 20 **B.** 24

**C.** 24 **D.** None of these

**View Answer**

**Answer:** Option **C**

**Explanation:**

Let the integer be x

Then, x^{2}-20x=96

==> X^{2 }- 20x – 96 =0

==> (x+4)(x-24) = 0

==> **X=24**

**4.)** The sum of two numbers is 25 and their difference is 13. Find their product.

**A.** 99 **B.** 177

**C.** 255 **D.** 114

**View Answer**

**Answer:** Option **D**

**Explanation:**

Let the numbers be x and y.

Then, x + y = 25 and x - y = 13.

4xy = (x + y)^{2} - (x- y)^{2}

= (25)^{2} - (13)^{2}

= (625 - 169)

= 456

**xy = 114.**

**5.)** Thrice the square of a natural number decreased by 4 times the number is equal to 50 more than the number. The number is:

**A.** 4 **B.** 5

**C.** 6 **D.** 10

**View Answer**

**Answer:** Option **B**

**Explanation:**

Let the number be x

Then, 3x^{2 }- 4x = x + 50

==> 3x^{2 }- 5x-50 = 0

==> (3x+10)(x-5)=0

==>** X = 5**