**Question 1 :**

If 2000/2x = 10, then what is √x?

(A) √10 (B) 10 (C) √1000 (D) 100 (E) 1000

**Solution :**

2000/2x = 10

1000/x = 10

x = 1000/10

x = 100

Taking square roots on both sides, we get

√x = √100

√x = 10

**Question 2 :**

If x = 9, y = -9 and z = -1, what is the value of yz + √x + yz - √x ?

(A) -24 (B) -18 (C) 0 (D) 18 (E) 24

**Solution :**

First let us simplify

yz + √x + yz - √x

= 2yz

By applying the value of y and z, we get

= 2(-9) (-1)

= 18

**Question 3 :**

1 dollar = 0.5 pillets

4 coss = 1 dollar

Lindsey has $20 to spend. She needs to buy exactly 2 pillets. She spends the remaining amount buying coss. How many coss does Lindsey purchase ?

(A) 4 (B) 5 (C) 64 (D) 72 (E) 76

**Solution :**

1 dollar = 0.5 pillets ----(1)

2 pillets = 4 dollar

She is spending 4 dollar to purchase 2 pillets. So, the remaining amount that she has = 20 - 4 = 16 dollar

For this 16 dollars, she has to buy coss.

Give n that :

1 dollar = 4 coss

16 dollar = 4 (16) coss

16 dollar = 64 coss

Hence, she has to purchase 64 coss.

**Question 4 :**

√100 ÷ √25 =

(A) √2 (B) 2 (C) 4 (D) 10 (E) 1/2

**Solution :**

** = √100 ÷ √25**

** = **√(100/25)

= √4

= 2

**Question 5 :**

If x = -8, what is the value of (1/2) |4x - 4|?

(A) -18 (B) -14 (C) -8 (D) 14 (D) 14 (E) 18

**Solution :**

** = (1/2) |4x - 4|**

**Applying the value of x in the expression, we get**

** = (1/2) |4(-8) - 4|**

** = (1/2) |-32-4|**

** = (1/2) (36)**

** = 18**

**Hence the answer is 18.**

**Question 6 :**

Triangle NPQ is an equilateral triangle. If its perimeter is 27, what is the length of NP + NQ ?

(A) 16 (B) 18 (C) 4 (D) 32 (E) 0

**Solution :**

To find the perimeter of the triangle, we have to find the sum of all the sides.

NP + NQ + PQ = 27

x + x + x = 27

3x = 27

x = 27/3 = 9

NP + PQ = 9 + 9 = 18

**Question 7 : **

If 40% of x is 160, what is x ?

(A) 0.0025 (B) 4 (C) 64 (D) 360 (E) 400

**Solution :**

40% of x = 160

(40/100) ⋅ x = 160

x = 160 (100/40)

x = 400

**Question 8 :**

When d is divided by 7, the remainder is 5, what is the remainder when d + 1 is divided by 7 ?

(A) 0 (B) 1 (C) 4 (D) 5 (E) 6

**Solution :**

Let d = 12

Here we choose 12, because it is greater than 7, when we divide 12 by 7, we get the remainder 5.

Then d + 1 = 12 + 1 = 13

By dividing this d + 1 by 7, we get 6(5 + 1) as remainder.

Hence the answer is 6.

Note : The number chosen should be 5 more than the multiple of 7.

**Question 9 :**

In the figure above, O is the center of the square. What is the area of the square ?

(A) 8 (B) 16 (C) 32 (D) 64 (E) 256

**Solution :**

Side length of square is 8 units.

Area of square = a^{2}

= 8^{2}

= 64 square units.

**Question 10 :**

If O is the midpoint of PW, then what is the distance of OE ?

(A) 10 (B) 11 (C) 12 (D) 13 (E) 17

**Solution :**

P (-13, 0) W (-3, 0)

O is the midpoint of PW

= (x_{1} + x_{2})/2, (y_{1} + y_{2})/2

= (-13-3)/2, (0+0)/2

= O (-8, 0)

E (3, 0)

OE = **√(x _{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}**

**OE = √(-8-3)^{2} + (0-0)^{2}**

**OE = √(-11)^{2}**

** = 11**

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