Online Lab # 7 DS Rephrasing, Q52

[sarora]

Is the permeter of square S greater than the perimeter of equilateral triangle T?

(1) The ratio of the length of a side of S to the length of a side of T is 4:5

(2) The sum of the lengths of a side of S and a side of T is 18


< Standard DS Sufficiency Choices >

My Solution:

Let side of the square = a
Let side of the triangle = l

Q Rephrase: Is 4a > 3l or a/l > 3/4 ?

(1) a/l=4/5 = 0.8 > 3/4. That is, perimeter of square is greater than triangle. Therefore, (1) is sufficient.

(2) a+l = 18
l = 18 - a
4a / 3l = 4a / 3(18-a) = 4a / 54-3a

Suppose 4a /3l > = 1 or 4a / 54-3a > = 1
4a >= 54 - 3a
7a >= 54
a >= 22 ... (a)
Since l = 18 - a and cannot be -ve, a < 18. Intersection with (a) gives No solution. Hence, the above is UNTRUE.


Suppose 4a/3l <= 1 or 4a / 54-3a <= 1
4a <= 54 - 3a
7a <= 54
a <= 22 ... (b)

Since l = 18 - a and cannot be -ve, a < 18. Intersection with (b) gives solution a < 18. Or , according to statement (2) , as long as a < 18, the condition of 4a < 3l is met. Hence, the above supposition is TRUE.

That is, 4a / 3l < 1 or 4a < 3l or Perimeter of square is greater than perimeter of triangle.
Therefore, (2) is sufficient.


MY ANSWER = (C) , Either of the two is sufficient to answer the question.

The online lab says the answer is (A) - Statement 1 only is sufficient.

[StaceyKoprince]

Hi - please make sure to cite the author's name. I'm assuming you got this from MGMAT's online lab, but don't forget to mention that! :)

Also, you say above:

MY ANSWER = (C) , Either of the two is sufficient to answer the question.

Perhaps that's just a typo, but please note that D is the "either is sufficient" answer choice. C says that they must be used together and cannot work separately.

In evaluating statement 2, you say:

7a >= 54
a >= 22 ... (a)

54/7 is not 22 - check your math here. Try this one again from here (and let us know if you still have a question).

[dbernst]

Sarora, I became a bit confused with your algebra for statement (2). To me, these are two completely independent geometric figures, as nothing in the statement provides a relationship between the two. Thus, the only given fact for statement (2) is that The sum of the lengths of a side of S and a side of T is 18 .

As this is our only constraint, we could potentially have a triangle with a side length of 17 and a square with a side length of 1. In this case, the perimeter of the triangle is 54 and the perimeter of the square is 4. However, we could just as easily have a square with a side length of 17 and a triangle with a side length of 1. Here, the perimeter of the square (68) is significantly larger than the perimeter of the triangle (3). Since we have no idea of the relationship between the two figures, statement two is Insufficient to definitively answer the question.

-dan

ps. Don't forget that answer choice C signifies that neither statement alone is sufficient but both statements together are sufficient. I think you meant to choose D in your initial post.