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Is the length of the diagonal of the rectangle bigger than

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by fskilnik@GMATH » Fri Nov 02, 2018 4:54 pm

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BTGmoderatorLU wrote:Source: GMAT Paper Tests

$$\text{Is the length of the diagonal of the rectangle bigger than }\sqrt{6}?$$

1) The shorter side of the rectangle is 2.
2) The longer side of the rectangle is 3.
$$a \ge b > 0\,\,\,\,\,\left[ {{\rm{rectangle}}\,\,{\rm{dimensions}}} \right]$$
$${a^2} + {b^2}\,\,\mathop > \limits^? \,\,6$$
$$\left( 1 \right)\,\,a > b = 2\,\,\,\, \Rightarrow \,\,\,{a^2} + {b^2} > {2^2} + {2^2} = 8\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle $$
$$\left( 2 \right)\,\,3 = a > b > 0\,\,\,\, \Rightarrow \,\,\,{a^2} + {b^2} > {3^2} = 9\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle $$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by Jay@ManhattanReview » Sun Nov 04, 2018 11:59 pm

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BTGmoderatorLU wrote:Source: GMAT Paper Tests

$$\text{Is the length of the diagonal of the rectangle bigger than }\sqrt{6}?$$

1) The shorter side of the rectangle is 2.
2) The longer side of the rectangle is 3.

The OA is D
Question: Is the length of the diagonal of the rectangle bigger than √6?

Let's take each statement one by one.

1) The shorter side of the rectangle is 2.

Since the shorter side is 2, the longer side must be greater than 2.

Assuming that both the sides are 2 each, thus, the length of the diagonal of the rectangle > 2√2 > √6. Sufficient.

You may compare 2√2 and √6 by squaring them. (2√2)^2 = 8 and (√6)^2 = 6; thus, 8 > 6.

2) The longer side of the rectangle is 3.

Note that the diagonal of the rectangle is greater than the longer side. Thus, the diagonal of the rectangle > 3 > √6. Sufficient

The correct answer: D

Hope this helps!

-Jay
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