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16 Sep 2014, 00:37
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If Richard is 3 years younger than his sister, how old is Richard?
(1) Two years ago, Richard's sister was twice as old as Richard.
(2) If Richard's sister had been born 2 years earlier, she would currently be twice as old as Richard.
(1) Two years ago, Richard's sister was twice as old as Richard.
(2) If Richard's sister had been born 2 years earlier, she would currently be twice as old as Richard.
16 Sep 2014, 00:37
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Official Solution:
If Richard is 3 years younger than his sister, how old is Richard?
Let's assume Richard's age is \(r\) and his sister's age is \(s\). We are given that \(r = s - 3\) and asked to find the value of \(r\).
(1) Two years ago, Richard's sister was twice as old as Richard.
Given: \(s-2 = 2(s - 3 - 2)\). Solving for \(s\), we get \(s = 8\). Therefore, \(r = s - 3 = 8 - 3 = 5\). Sufficient.
(2) If Richard's sister had been born 2 years earlier, she would currently be twice as old as Richard.
If Richard's sister were born 2 years earlier, her age would be \(s + 2\) years now. So, \(s + 2 = 2(s - 3)\). Solving for \(s\), we get \(s = 8\). Therefore, \(r = s - 3 = 8 - 3 = 5\). Sufficient.
Answer: D
If Richard is 3 years younger than his sister, how old is Richard?
Let's assume Richard's age is \(r\) and his sister's age is \(s\). We are given that \(r = s - 3\) and asked to find the value of \(r\).
(1) Two years ago, Richard's sister was twice as old as Richard.
Given: \(s-2 = 2(s - 3 - 2)\). Solving for \(s\), we get \(s = 8\). Therefore, \(r = s - 3 = 8 - 3 = 5\). Sufficient.
(2) If Richard's sister had been born 2 years earlier, she would currently be twice as old as Richard.
If Richard's sister were born 2 years earlier, her age would be \(s + 2\) years now. So, \(s + 2 = 2(s - 3)\). Solving for \(s\), we get \(s = 8\). Therefore, \(r = s - 3 = 8 - 3 = 5\). Sufficient.
Answer: D
23 Oct 2023, 12:38
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I've revised the question and solution, incorporating additional details for improved clarity. I trust this makes it more comprehensible.
