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Need Help in DS problems - 5

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by phoenix9801 » Thu Jun 10, 2010 2:31 am
Would you please use Picking Numbers and/or Straightforward Math to solve these questions Please be simple. (not Algebra). Thanks.




Note for number 10 I can not replicate the image In GMAT Book but the image is a retangle box and top represented by L (as length) and on the side represented by W (as With)



10 - If L and W represents the length and with, respectively, of the rectangle above, what is the perimeter?

(1) 2L + w = 40

(2) L + W = 25
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by Rich@VeritasPrep » Thu Jun 10, 2010 3:07 am
Perimeter is given by the formula 2L+2W, so you need either the individual values of L and W or the value of the sum itself.

(1) is insufficient, because you can't locate either of these.

(2) is sufficient, because you are given L+W, and if you multiply it by 2, you get 2L+2W, which is the perimeter.
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by phoenix9801 » Thu Jun 10, 2010 3:35 am
raz1024 wrote:Perimeter is given by the formula 2L+2W, so you need either the individual values of L and W or the value of the sum itself.

(1) is insufficient, because you can't locate either of these.

(2) is sufficient, because you are given L+W, and if you multiply it by 2, you get 2L+2W, which is the perimeter.

I understand that the Perimeter = 2 (base + height) = 2 (b + h) and you must be give 2 values either L and W or the sum itself to be sufficient.

I kinda understand but I can not get the full grasp of it, would you please be willing to explain the statements 1 and 2 by using picking numbers.

I would greatly appreciated it. Thanks
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by Rich@VeritasPrep » Thu Jun 10, 2010 4:31 am
10 - If L and W represents the length and with, respectively, of the rectangle above, what is the perimeter?

(1) 2L + w = 40

L=10, W=20
L=5, W=30

Each of these two possibilities produces a different perimeter. INSUFFICIENT

(2) L + W = 25

L=13, W=12
L=10, W=15
L=5, W=20

Plug into 2L+2W, and you always get 50. This is because you can manipulate the equation as such:

L + W = 25
2(L + W) = 25(2)
2L+2W = 50

Since 2L+2W is perimeter, you now know the perimeter will always be 50. SUFFICIENT

Another way to look at it is that L+W is half the perimeter, because you have one of the two lengths and one of the two widths. L+W gives you half of the perimeter, so if you know half the perimeter, you can certainly find the whole perimeter.
Rich Zwelling
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