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# Is the length of a side of square S greater than the length of a side

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Is the length of a side of square S greater than the length of a side [#permalink]

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27 Dec 2015, 09:48
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Is the length of a side of square S greater than the length of a side of equilateral triangle T ?

(1) The sum of the lengths of a side of S and a side of T is 22.
(2) The ratio of the perimeter of square S to the perimeter of triangle T is 5 to 6.
[Reveal] Spoiler: OA

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Re: Is the length of a side of square S greater than the length of a side [#permalink]

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29 Dec 2015, 16:06
Let the side of the Square S = x and side of the equilateral triangle T = y.

Question : x>y? or can be rephrased to say $$\frac{x}{y} > 1$$ (x and y cant be neg).

Statement 1:

x + y = 22.

Lets test values:

11 + 11 = 22, in this case the answer to the question is NO
12 + 10 = 22. in this case the answer to the question is YES.

2 different answers and hence Statement 1 is insufficient.

Statement 2:
Perimeter of the square = 4x
Perimeter of the triangle = 3y

$$\frac{4x}{3y} = \frac{5}{6}$$

$$\frac{x}{y} = \frac{5}{6} * \frac{3}{4}$$ This is clearly less than 1.

Hence $$\frac{x}{y} < 1$$ or x<y. Sufficient.

Answer B.
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Re: Is the length of a side of square S greater than the length of a side [#permalink]

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03 Jan 2016, 03:54
Statement 1: s+t =22
insufficient
Statement 2: 4S/3T = 5/6
S/T = 5/8 which is less than 1
thus
S<T
Sufficient

Ans: B
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Re: Is the length of a side of square S greater than the length of a side [#permalink]

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04 Jan 2016, 03:25
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is the length of a side of square S greater than the length of a side of equilateral triangle T ?

(1) The sum of the lengths of a side of S and a side of T is 22.
(2) The ratio of the perimeter of square S to the perimeter of triangle T is 5 to 6.

In general, when you suppose a:b=2:3 when it comes to ratio, you don't know how big 'b' is but you know that b>a. That is, you can compare a size with the ratio. Also, when one con is number and the other con is ratio(percent), percent is most likely to be an answer.
In the question, it asks if the length a side of square is greater than the length of a side of equilateral triangle. In 2), the question asks the ratio. So, suppose the sum of the lengths of a side of square 5k and the sum of the lengths of a side of equilateral triangle 6k. Then the length of one side of square is 5k/4=1.25k and the length of one side of equilateral triangle is 6k/3=2k, which is 1.25k<2k. So, it is no and sufficient. Therefore, the answer is B. Just like this question, when one con is number and the other conis ratio, you have to pay attention to ratio.

 from con 1) and con 2), if one of the conditions is given by numbers and the other is given by ratio (percent,fraction), then the condition with ratio (percent,fraction) value has higher chance of being the answer.
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Re: Is the length of a side of square S greater than the length of a side [#permalink]

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09 Mar 2017, 16:46
Bunuel wrote:
Is the length of a side of square S greater than the length of a side of equilateral triangle T ?

(1) The sum of the lengths of a side of S and a side of T is 22.
(2) The ratio of the perimeter of square S to the perimeter of triangle T is 5 to 6.

statement 1 alone doesn't give much info...
say side of square is "s", and side of triangle is "a"
we have: 4s+3a=22. we can't solve any further.

statement 2, on the contrary...gives sufficient information.
4s/3a = 5/6
8s=3a
we can find the ratio for s/a and see which one is bigger, but clearly, it says that side of the triangle is much bigger.

statement 2 is sufficient.
Re: Is the length of a side of square S greater than the length of a side   [#permalink] 09 Mar 2017, 16:46
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# Is the length of a side of square S greater than the length of a side

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