Thursday, September 26, 2013

Home Books Problem Discussion Table Of Contents Self Test Exercise Problem and Solution Part: 6 (Equation, Solving Equations, Systems of liner equations, Quadratic equations, Inequalities)

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) 2 (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
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 2 + 12xy + 9y 2 ?
Option: (a) x = 4 (b) y = 9 (c) 2x = 3y (d) 2x + 3y = 2 (e) None of these
Explore: Note that, 4x 2 +12xy + 9y 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 
4x + 12xy + 9y 2 = (2x) 2 + 2(2x)(3y) + (3y) 2 = (2x + 3y) 2,
We can easily say, using (d), that
(2x + 3y) 2 = 2  2 = 4
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 +85y ≥ 500
   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
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

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