**Question: 41 The ancient Arabs calculated the area of a circle by subtracting 1/7th diameter of the circle from the diameter and then squaring the result. If d represents the diameter and A the area, which of the following represents a formula for this method?**

Option: (a) A = (d - 1/7)

*(b) A= (d -(1/7)d)*

^{ 2}*(c) A = 2(d - (1/7)d)*

^{ 2}*(d) A = d - ((1/7)d)*

^{ 2}*(e) A = d*

^{ 2}*-(1/7)*

^{ 2}

^{ 2}Answer : (b) is the formula described in the problem. So, the answer is (b)

**Question: 42 Which of the following information is alone sufficient to find out the value of 4x**

*+ 12xy + 9y*^{ 2}*?*^{ 2}Option: (a) x = 4 (b) y = 9 (c) 2x = 3y (d) 2x + 3y = 2 (e) None of these

Explore: Note that, 4x

^{ 2}*is not an equation, but an expression here. So, the information given in (a), (b) or, (c) will not help us. But if you observe that*

^{ 2}*= (2x)*

^{ 2}*+ 2(2x)(3y) + (3y)*

^{ 2}*= (2x + 3y)*

^{ 2}*,*

^{ 2}We can easily say, using (d), that

(2x + 3y)

*= 2*

^{ 2}*= 4*

^{ 2}Answer : (d)

**Question: 43 In ΔABC, AB = 4cm, AC = 6 cm& BD = 3 cm. If ∠BAD =∠DAC, what is the length of BC?**

Option: (a) 7 (b) 7.5 (c) 9 (d) 9.5 (e) None of those

Try this yourself.

**Question: 44 Suppose, you have $ 500 to spend on beef and chicken. Beef costs $ 110 per KG and chicken cost $ 85 per kg. Write an expression that must be satisfied if you are to consumer X kg beef and Y kg chicken.**

Option: (a) 110x + 85y >50 (b) 110X + 85Y < 500 (c) 110x + 85y ≤ 500 (d) 110x

Explore:

1 kg beef costs $ 110

:. X kg beef cost $(110 x X) = $110X

1 kg chicken costs $ 85

:. y kg chicken costs $ (85 x Y) = $85y

Total cost can't exceed $ 500

:. 110x + 85y ≤500

Answer : (c)

**Question: 45 If x is above y and z, and y is above z and below w, which one of the following statements is correct?**

Option: (a) z is above y (b) w is above z (c) x is not above z & w (d) z is above w (e) None

Explore: First we will write all the inequalities in mathematical form. So,

x>y, x>z, w>y>z

We can see that only (b) is true.

Answer : (b)

**Question: 46 Mr. X purchased some pens for $ 120. If the price of per piece of pen was $ 3 less, he would have received 2 more pens. How many pens did he purchase?**

Option: (a) 6 (b) 8 (c) 10 (d) 12 (e) 16

Explore:

Let, Mr. X bought p pens with cost $c/piece.

:. pc = 120=> c = 120/P

According to the problem,

(p + 2)(c -3) = 120

:. (p + 2)(120/p - 3) = 120

:. (p + 2)((120 - 3p)/p) = 120

=> (p+2)(120 -3p) = 120p