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The sides of rectangle X are each multiplied by a to form re [#permalink]
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27 Feb 2014, 12:50
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The sides of rectangle X are each multiplied by a to form rectangle Y and by b to form rectangle Z. a times the area of X is 10, and b times the area of X is 5. If the difference in area between Y and Z is 300, what is a  b? A. 5 B. 20 C. 30 D. 50 E. 60 Set sides of rectangle X are L and W Area of X: = LW Area of Y = (aL)(aW) = a^2 * LW Area of Z = (bL)(bW) = b^2 * LW a times area X = aLW = 10 b times area X = bLW = 5 Which means that difference between Y and Z = aaLW – bbLW = 300. And since you're looking to solve for a  b, you can try to get a and b alone by factoring out the common LW terms: LW(a^2  b^2) = 300 Which gives you the Difference of Squares setup that allows you to get (a  b) alone: LW(a + b)(a  b) = 300 Then you should see that if you distribute LW across the first set of parentheses, you can get aLW and bLW, for which you have actual values: (aLW + bLW)(a  b) = 300 (10 + 5)(a  b) = 300 15(a  b) = 300 (a  b) = 20 Hi, I want to know if we have the simpler solution, please
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Re: The sides of rectangle X are each multiplied by a to form re [#permalink]
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27 Feb 2014, 20:35
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goodyear2013 wrote: The sides of rectangle X are each multiplied by a to form rectangle Y and by b to form rectangle Z. a times the area of X is 10, and b times the area of X is 5. If the difference in area between Y and Z is 300, what is a  b? 5 20 30 50 60 Set sides of rectangle X are L and W Area of X: = LW Area of Y = (aL)(aW) = a^2 * LW Area of Z = (bL)(bW) = b^2 * LW a times area X = aLW = 10 b times area X = bLW = 5 Which means that difference between Y and Z = aaLW – bbLW = 300. And since you're looking to solve for a  b, you can try to get a and b alone by factoring out the common LW terms: LW(a^2  b^2) = 300 Which gives you the Difference of Squares setup that allows you to get (a  b) alone: LW(a + b)(a  b) = 300 Then you should see that if you distribute LW across the first set of parentheses, you can get aLW and bLW, for which you have actual values: (aLW + bLW)(a  b) = 300 (10 + 5)(a  b) = 300 15(a  b) = 300 (a  b) = 20 Hi, I want to know if we have the simpler solution, please Assume the side of rectangle X is s. X (side s, area s^2) Y (side as, area (as)^2) Z (side bs, area (bs)^2) Given: \(as^2 = 10\), \(bs^2 = 5\) ..........(I) \((as)^2  (bs)^2 = 300\) \(s^2 (a+b)(ab) = 300\) ...........(II) We need to find (ab). From (I), \(as^2 + bs^2 = 15 = s^2(a+b)\) (you do this because you need to get rid of s^2 and (a+b) in equation (II) above) Substitute this in (II) to get \(15*(ab) = 300\) (ab) = 20
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Re: The sides of rectangle X are each multiplied by a to form re [#permalink]
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27 Feb 2014, 23:02
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VeritasPrepKarishma wrote: goodyear2013 wrote: The sides of rectangle X are each multiplied by a to form rectangle Y and by b to form rectangle Z. a times the area of X is 10, and b times the area of X is 5. If the difference in area between Y and Z is 300, what is a  b? 5 20 30 50 60 Set sides of rectangle X are L and W Area of X: = LW Area of Y = (aL)(aW) = a^2 * LW Area of Z = (bL)(bW) = b^2 * LW a times area X = aLW = 10 b times area X = bLW = 5 Which means that difference between Y and Z = aaLW – bbLW = 300. And since you're looking to solve for a  b, you can try to get a and b alone by factoring out the common LW terms: LW(a^2  b^2) = 300 Which gives you the Difference of Squares setup that allows you to get (a  b) alone: LW(a + b)(a  b) = 300 Then you should see that if you distribute LW across the first set of parentheses, you can get aLW and bLW, for which you have actual values: (aLW + bLW)(a  b) = 300 (10 + 5)(a  b) = 300 15(a  b) = 300 (a  b) = 20 Hi, I want to know if we have the simpler solution, please Assume the side of rectangle X is s. X (side s, area s^2) Y (side as, area (as)^2) Z (side bs, area (bs)^2) Given: \(as^2 = 10\), \(bs^2 = 5\) ..........(I) \((as)^2  (bs)^2 = 300\) \(s^2 (a+b)(ab) = 300\) ...........(II) We need to find (ab). From (I), \(as^2 + bs^2 = 15 = s^2(a+b)\) (you do this because you need to get rid of s^2 and (a+b) in equation (II) above) Substitute this in (II) to get \(15*(ab) = 300\) (ab) = 20 Did you consider a rectangle as a square? Because if it is a rectangle then the sides may or may not be equal. Please clarify.



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Re: The sides of rectangle X are each multiplied by a to form re [#permalink]
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28 Feb 2014, 01:23
Every square is a rectangle however every rectangle need not be a square. Considering the same, the answer comes up correct = 20 = Answer = B
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Re: The sides of rectangle X are each multiplied by a to form re [#permalink]
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28 Feb 2014, 06:56
it doesn't matter here if its a square o rectanlge value gets replaced later. take it as s^2 or a*b



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Re: The sides of rectangle X are each multiplied by a to form re [#permalink]
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28 Feb 2014, 09:54
b2bt wrote: it doesn't matter here if its a square o rectanlge value gets replaced later. take it as s^2 or a*b Agreed, it gets cancelled, sorry for the trouble



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Re: The sides of rectangle X are each multiplied by a to form re [#permalink]
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01 Mar 2014, 18:41
Fantabulous wrote: Did you consider a rectangle as a square? Because if it is a rectangle then the sides may or may not be equal. Please clarify. I have assumed that the rectangle is a square since square is also a type of rectangle (but I see I missed writing it). It is a PS question so it will have a unique answer. This means a  b will be the same for every such group of rectangles. So we can easily take one such group such that the rectangles are squares to make our calculations easier.
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Re: The sides of rectangle X are each multiplied by a to form re [#permalink]
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27 Apr 2015, 18:32
Could you please let me know why you do not distribute the s^2 through the parenthesis? I asked this in my own topic but it has since been locked and no further information was provided to me except to link to this thread. \(s^2(a+b)(a−b)=300\) ...........(II) Why does this not simplify to: \(15∗s^2a−s^2b)\) veritasprepthesidesofrectanglexareeachmultipliedbyatofor196927.html



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Re: The sides of rectangle X are each multiplied by a to form re [#permalink]
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27 Apr 2015, 19:30
willowtree2 wrote: Could you please let me know why you do not distribute the s^2 through the parenthesis? I asked this in my own topic but it has since been locked and no further information was provided to me except to link to this thread. \(s^2(a+b)(a−b)=300\) ...........(II) Why does this not simplify to: \(15∗s^2a−s^2b)\) veritasprepthesidesofrectanglexareeachmultipliedbyatofor196927.html\((a+b)*(ab) = a^2  b^2\) You can simplify this to \(s^2a^2  s^2b^2 = 300\) but how will that take you to the answer? You need the value of \((a  b)\) so you need to get rid of only \(s^2(a+b)\).
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Re: The sides of rectangle X are each multiplied by a to form re [#permalink]
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Let rectangle X length=l width=w => Area = l*w So now: rectangle Y length=a*l width=a*w => Area =a^2* l*w rectangle Z length=b*l width=b*w => Area =b^2* l*w
given: a* Area of X = 10 = a*l*w b* Area of X = 5 = b*l*w
so we can write a*l*w+b*l*w=10+5 => l*w(a+b)=15
Also given => Area of Y  area of Z = 300 = a^2*l*w b^2*l*w
so lw(a^2b^2)=300 => l*w(a+b)(ab)=300 => 15 (ab)=300 => (ab)= 20
Answer: B



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Re: The sides of rectangle X are each multiplied by a to form re [#permalink]
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14 Nov 2017, 04:11
VeritasPrepKarishma wrote: goodyear2013 wrote: The sides of rectangle X are each multiplied by a to form rectangle Y and by b to form rectangle Z. a times the area of X is 10, and b times the area of X is 5. If the difference in area between Y and Z is 300, what is a  b? 5 20 30 50 60 Set sides of rectangle X are L and W Area of X: = LW Area of Y = (aL)(aW) = a^2 * LW Area of Z = (bL)(bW) = b^2 * LW a times area X = aLW = 10 b times area X = bLW = 5 Which means that difference between Y and Z = aaLW – bbLW = 300. And since you're looking to solve for a  b, you can try to get a and b alone by factoring out the common LW terms: LW(a^2  b^2) = 300 Which gives you the Difference of Squares setup that allows you to get (a  b) alone: LW(a + b)(a  b) = 300 Then you should see that if you distribute LW across the first set of parentheses, you can get aLW and bLW, for which you have actual values: (aLW + bLW)(a  b) = 300 (10 + 5)(a  b) = 300 15(a  b) = 300 (a  b) = 20 Hi, I want to know if we have the simpler solution, please Assume the side of rectangle X is s. X (side s, area s^2) Y (side as, area (as)^2) Z (side bs, area (bs)^2) Given: \(as^2 = 10\), \(bs^2 = 5\) ..........(I) \((as)^2  (bs)^2 = 300\) \(s^2 (a+b)(ab) = 300\) ...........(II) We need to find (ab). From (I), \(as^2 + bs^2 = 15 = s^2(a+b)\) (you do this because you need to get rid of s^2 and (a+b) in equation (II) above) Substitute this in (II) to get \(15*(ab) = 300\) (ab) = 20 Another way of doing this.. Let the original sides be x and y  area = \(xy\) For Rectangle X  ax and ay  area = \(a^2xy\) For Rectangle Y  bx an by  area = \(b^2xy\) Now, it's given that \(axy = 10\) Thus \(a = \frac{10}{(xy)}\) Similarly we can write for Z as \(bxy = 5\) Thus \(b = \frac{5}{(xy)}\) It can clearly be seen that \(a = 2b\) Substituting "axy" in the original area equation..we can see that the area of X can be written as = 10a Similarly for B it can be written as = 5b Difference in areas \(10a  5b = 300\) Using value of a as 2b, we get b = 20 a = 40 Thus ab = 20 (B)
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