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28 Jul 2010, 05:45
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
50% (01:51) correct
50%
(01:45)
wrong
based on 275
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Does rectangle A have a greater perimeter than rectangle B?
(1) The length of a side of rectangle A is twice the length of a side of rectangle B
(2) The area of rectangle A is twice the area of rectangle B
(1) The length of a side of rectangle A is twice the length of a side of rectangle B
(2) The area of rectangle A is twice the area of rectangle B
28 Jul 2010, 06:09
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Does rectangle A have a greater perimeter than rectangle B?
Let the sides of rectangle A be \(s\) and \(t\) and the side of rectangle B \(m\) and \(n\).
Question: is \(2(s+t)>2(m+n)\)? --> or is \(s+t>m+n\)?
(1) The length of a side of rectangle A is twice the length of a side of rectangle B --> \(s=2m\), clearly insufficient as no info about the other side of rectangles.
(2) The area of rectangle A is twice the area of rectangle B --> \(st=2mn\), also insufficient as if \(s=t=2\), \(m=1\) and \(n=2\) then the answer would be YES, but if \(s=t=2\), \(m=\frac{1}{2}\) and \(n=4\) then the answer would be NO.
(1)+(2) \(s=2m\) and \(st=2mn\) --> substitute \(s\): \(2m*t=2mn\), so \(t=n\). Thus as \(s=2m\) and \(t=n\): \(s+t=2m+n\) which is obviously more than \(m+n\). Sufficient.
Answer: C.
Let the sides of rectangle A be \(s\) and \(t\) and the side of rectangle B \(m\) and \(n\).
Question: is \(2(s+t)>2(m+n)\)? --> or is \(s+t>m+n\)?
(1) The length of a side of rectangle A is twice the length of a side of rectangle B --> \(s=2m\), clearly insufficient as no info about the other side of rectangles.
(2) The area of rectangle A is twice the area of rectangle B --> \(st=2mn\), also insufficient as if \(s=t=2\), \(m=1\) and \(n=2\) then the answer would be YES, but if \(s=t=2\), \(m=\frac{1}{2}\) and \(n=4\) then the answer would be NO.
(1)+(2) \(s=2m\) and \(st=2mn\) --> substitute \(s\): \(2m*t=2mn\), so \(t=n\). Thus as \(s=2m\) and \(t=n\): \(s+t=2m+n\) which is obviously more than \(m+n\). Sufficient.
Answer: C.
General Discussion
28 Jul 2010, 06:04
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Hi,
Statement one provides information about one side only. This is not enough since one side of rect A can be greater than one side of rect B while the second side of rectangle A can be either less or greater than the second side of rectangle B. Remember Perimeter = 2(L+W).
Consider:
Rect A: 20*20
Rect B: 1*2
or
Rect A: 20*1
Rect B: 1*40
Statement 2 is not sufficient as well. Consider:
Rect A: 20*1, P=42
Rect B: 1*10, P=22
or
Rect A: 2*2, P=8
Rect B: 20:0.1, P=40.2
Taking both conditions, the answer will be sufficient.
You can also solve this problem by equations.
regards,
Jack
Statement one provides information about one side only. This is not enough since one side of rect A can be greater than one side of rect B while the second side of rectangle A can be either less or greater than the second side of rectangle B. Remember Perimeter = 2(L+W).
Consider:
Rect A: 20*20
Rect B: 1*2
or
Rect A: 20*1
Rect B: 1*40
Statement 2 is not sufficient as well. Consider:
Rect A: 20*1, P=42
Rect B: 1*10, P=22
or
Rect A: 2*2, P=8
Rect B: 20:0.1, P=40.2
Taking both conditions, the answer will be sufficient.
You can also solve this problem by equations.
regards,
Jack
