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555-605 (Medium)|   Geometry|      
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Bunuel
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Does the area of a certain square greater than the area of a certain 26 Dec 2014, 08:49
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Tough and Tricky questions: Geometry.



Does the area of a certain square greater than the area of a certain rectangle?

(1) One side of the rectangle equals to the side of the square.

(2) One side of the rectangle is twice greater than the side of the square.

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C
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littlewarthog
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Does the area of a certain square greater than the area of a certain 26 Dec 2014, 10:16
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Statement 1: Insufficient. While one side of the rectangle is equal to the side of the square, the other could be either longer or shorter than the sides of the square, so the area could be either greater or smaller.

Statement 2: Insufficient. With the same logic, we can conclude that statement 2 is insufficient. The remaining side of the rectangle could over- or under-compensate the longer side.

Together/None: Taken together, the statements are sufficient. Statement 1 says that one side of the rectangle is equal to the square's sides and statement 2 says that one side is much longer. The statements therefore need to refer to the two different sides and we can conclude that the area of the square is NOT greater than that of the square.

Answer C.
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Does the area of a certain square greater than the area of a certain 26 Dec 2014, 16:23
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Bunuel

Tough and Tricky questions: Geometry.



Does the area of a certain square greater than the area of a certain rectangle?

(1) One side of the rectangle equals to the side of the square.

(2) One side of the rectangle is twice greater than the side of the square.

Kudos for a correct solution.
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1. One side of the rectangle equals to the side of the square - WE are not sure whether it is larger or smaller side of the rectangle - Insufficient
2. Again no information about the other side - Insufficient

Combining Both: We can say area of the rectangle is larger

ANS C
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Does the area of a certain square greater than the area of a certain 27 Dec 2014, 10:49
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Bunuel

Tough and Tricky questions: Geometry.



Does the area of a certain square greater than the area of a certain rectangle?

(1) One side of the rectangle equals to the side of the square.

(2) One side of the rectangle is twice greater than the side of the square.

Kudos for a correct solution.
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We need to remember all sides of a square are the same - and their area is
For a rectangle's area to be bigger than that of the square we just need to one side of the rectangle to be bigger while the other side remains the same OR we need one side of the rectangle be a square of the sides of the square.

A) Insufficient because if one side is equal to the rectangle, we have no info on the rectangle's other side which could be bigger or smaller

B) Insuff Because we have no info on other side of rect - it could be as small as 1.

C is correct. If we know one side of Rectangle is equal to squre and the other side is bigger, then area's can be compared
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Does the area of a certain square greater than the area of a certain 09 Jan 2015, 06:05
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Bunuel

Tough and Tricky questions: Geometry.



Does the area of a certain square greater than the area of a certain rectangle?

(1) One side of the rectangle equals to the side of the square.

(2) One side of the rectangle is twice greater than the side of the square.

Kudos for a correct solution.
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OFFICIAL SOLUTION:

(C) The area of a square is a², where a is the side of a square. The area of a rectangle is bc, where b and c are the sides of a rectangle.

Statement (1) tells us that the figures have one equal side. Clearly, that is not enough. If the smaller side of the rectangle is equal to the side of the square, then the area of the rectangle is greater. If the bigger side of the rectangle is equal to the side of the square, then the area of the square is greater. If the rectangle is a square as well, then their areas equal. Therefore statement (1) by itself is NOT sufficient.

Statement (2) tells us that one side of the rectangle is twice greater than the side of the square. If the other side of the rectangle is greater as well, then the area of the rectangle is greater. However if the other side of the rectangle is less than half the side of the square, then the area of the square is greater. Statement (2) by itself is NOT sufficient.

If we use the both statements together the area of the rectangle is greater, because in this case the sides of the rectangle must be a and 2a. So the area of the rectangle is 4a². The correct answer is C.
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Does the area of a certain square greater than the area of a certain 09 Jan 2015, 20:49
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(1) All squares are rectangles.

The rectangle may be a congruent square, in which case the areas are equal.

The rectangle may also be non-square, in which case we need the other dimension (length or width) to meet sufficiency.

Strike A/D.

(2) We again only know one dimension. NOT sufficient.

Strike B.

(1/2) We know know the relative dimensions for both length and width of each of the two rectangles. Sufficient.

The answer is C.
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