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Quantitative Question

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Intern
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Quantitative Question [#permalink] New post 14 Sep 2006, 08:42
I can't figure the following questions out:


1) For all real numbers v, the operation V* is defined by the equation V*=V-V/3. If (V*)*=8, the v=

A)15
B)18
C)21
D)24
E)27

The answer happens to be B)18

2) A rectangular tabletop consists of a pice of laminated wood bordered by a thin metal strip along its four edges. The surface area of the tabletop is x square feet, and the total length of the strip before it was attached was x feet. If the tabletop is 3 feet wide, what is its approximate length, in feet?

A)12
B)10
C)9
D)8
E)6

The answer is B)10

Can someone explain these answers to me.

Thanks!
SVP
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 [#permalink] New post 14 Sep 2006, 09:03
For the first one My ANSWER IS B

fisrst simplifyv* = v-v/3 = 2/3v name it b thus v* = b =2/3v

(v*)* = b* = 2/3b = 2/3(2/3v) = 4/9v

given that (v*)* = 8

thus 4/9v = 8 therfore v = 18

for the second one

i think

area of table top = circomference = x

ie 2l+2w = lw = x and given w=3

thus 2l+3*2 = 3l ie l =6

it is not 10 as mentioned but this is the best i could get
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 [#permalink] New post 14 Sep 2006, 11:33
hmmm
for #2 I get E)6:

w=3 so l had to be x/3 for area to = x

2x3 + 2(x/3) = x (perimetar is also x)

x/3 = 6
x=18

length = 18/3 = 6
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 [#permalink] New post 14 Sep 2006, 11:56
Is it just me? Cause I think some of these problem solving questions are just poorly worded. I didn't understand the problem until I saw how above posters tried to solve it.

So basically, it's asking for what value of the length(x/3) does the perimeter equal the area?

If so, it clearly can't be 10 because A=30 and P=26, not a very good approximation.
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Quantitative Question [#permalink] New post 14 Sep 2006, 12:48
Thanks for all your help!
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 [#permalink] New post 14 Sep 2006, 13:02
[quote="EconGirl"]hmmm
for #2 I get E)6:

w=3 so l had to be x/3 for area to = x

2x3 + 2(x/3) = x (perimetar is also x)

x/3 = 6
x=18

length = 18/3 = 6[/quote]


I am also getting 6.

Area = x
Length of strip = x
Width = 3


Perimeter = 2L + 2W
2W = 6
L = (Length of metal strip - 2W) / 2
= (x - 6 ) / 2

Area = width * length
x = 3 * (x-6)/2
2x = 3(x-6)
2x = 3x - 18
x = 18

Since area is 18 and we know width is 3
Length = x / 3
= 18/3
= 6
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 [#permalink] New post 14 Sep 2006, 20:13
Agree with Yezz and others on the second one - the answer is 6 E
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 [#permalink] New post 14 Sep 2006, 20:20
Try and simplify the problem first

V* = V-V/3 = (3V-V)/3
= 2V/3

Now,

(V*)* = (2V/3)*
=2V/3 - (2V/3)/3
=2V/3 - 2V/9
= 6V/9 - 2V/9
= 4V/9 = 8

=> V = 18.


Second one is 6 too... so OA is wrong.
  [#permalink] 14 Sep 2006, 20:20
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