题目信息
Is the perimeter of a certain rectangular garden greater than 50 meters?
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B:Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D:EACH statement ALONE is sufficient.
E:Statements (1) and (2) TOGETHER are NOT sufficient.
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A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Geometry Quadrilaterals; Perimeter
Let W represent the length of the shorter side (that is, the width) of the rectangular garden, and let L represent the length of the longer side (that is, the length). The perimeter is then 2(L + W). Determine if 2(L + W) > 50 is true, or equivalently, if L +W > 25 is true.
It is given that W = 15, from which it follows that L > 15. Then, L + W > 15 + 15 > 25; SUFFICIENT. It is given that L = W + 5, from which it follows that L + W = 2W + 5. If, for example, W = 1, then 2W + 5 is not greater than 25, but if W = 11, then 2W + 5 is greater than 25; NOT sufficient.
The correct answer is A;statement 1 alone is sufficient.
Tip When determining whether a certain condition holds for an expression involving two variables, avoid assuming that the values of both variables must be known. In (1), knowing that L represents the length of the longer side and knowing the value of W, the length of the shorter side, is enough information to determine whether L + W meets the given condition.
Let W represent the length of the shorter side (that is, the width) of the rectangular garden, and let L represent the length of the longer side (that is, the length). The perimeter is then 2(L + W). Determine if 2(L + W) > 50 is true, or equivalently, if L +W > 25 is true.
It is given that W = 15, from which it follows that L > 15. Then, L + W > 15 + 15 > 25; SUFFICIENT. It is given that L = W + 5, from which it follows that L + W = 2W + 5. If, for example, W = 1, then 2W + 5 is not greater than 25, but if W = 11, then 2W + 5 is greater than 25; NOT sufficient.
The correct answer is A;statement 1 alone is sufficient.
Tip When determining whether a certain condition holds for an expression involving two variables, avoid assuming that the values of both variables must be known. In (1), knowing that L represents the length of the longer side and knowing the value of W, the length of the shorter side, is enough information to determine whether L + W meets the given condition.
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