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# The length of rectangle B is x percent less than the length of rectang

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Re: The length of rectangle B is x percent less than the length of rectang [#permalink]
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Bunuel wrote:

FRESH GMAT CLUB TESTS QUESTION

The length of rectangle B is x percent less than the length of rectangle A, and the width of rectangle B is y percent, greater than the width of rectangle A (where both x and y are greater than 0 and less than 100). Is the area of rectangle A greater than the area of rectangle B?

(1) x = y
(2) x + y = 20

#1
let l of A = 10 and w= 5
area = 50
x=y ; 2=2
so B ;l = 8 and w ; 6
area of b ; 48
sufficient
#2
x+y=20 now value of x & y would vary over ranges 1,19 , 2,18 , 3,17 so the relation of area of A wont be > than B always..
IMO A
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Re: The length of rectangle B is x percent less than the length of rectang [#permalink]
Bunuel wrote:

FRESH GMAT CLUB TESTS QUESTION

The length of rectangle B is x percent less than the length of rectangle A, and the width of rectangle B is y percent, greater than the width of rectangle A (where both x and y are greater than 0 and less than 100). Is the area of rectangle A greater than the area of rectangle B?

(1) x = y
(2) x + y = 20

Rectangle A: L=a, W=b; Rectangle B: L=c=a(1-x/100), W=d=b(1+y/100)

$$Question:ab>a(1-x/100)b(1+y/100)?…ab>(ab/100^2)(100-x)(100+y)…$$
$$Question:100^2>(100-x)(100+y)?$$

(1) x = y sufic.

$$Question: 100^2>(100-x)(100+x)…100^2>(100^2-x^2)…0>-x^2…0<x^2…x>0?$$
$$0<(x,y)<100…x>0?…Answer:yes$$

(2) x + y = 20 insufic.

$$if:x=y…Answer:yes$$
$$if:x≠y…Answer:yes/no$$

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Re: The length of rectangle B is x percent less than the length of rectang [#permalink]
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Re: The length of rectangle B is x percent less than the length of rectang [#permalink]
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