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Bunuel
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Thank you for the solution. Just a quick question on the first formula. Why is it 2(s-3-2)? Wondering where that -2 comes from. Thank you.
Bunuel
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
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Thank you for the solution. Just a quick question on the first formula. Why is it 2(s-3-2)? Wondering where that -2 comes from. Thank you.
Bunuel
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

The "-2" comes from the fact that the scenario in statement (1) refers to "two years ago." At that time, Richard was not only 3 years younger than his sister, but also 2 years younger than his current age. Therefore, his age two years ago is expressed as s - 3 - 2.

Let me know if you need further clarification!
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That's extremely helpful, thank you!
Bunuel
TaremyLunsil
Thank you for the solution. Just a quick question on the first formula. Why is it 2(s-3-2)? Wondering where that -2 comes from. Thank you.
Bunuel
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

The "-2" comes from the fact that the scenario in statement (1) refers to "two years ago." At that time, Richard was not only 3 years younger than his sister, but also 2 years younger than his current age. Therefore, his age two years ago is expressed as s - 3 - 2.

Let me know if you need further clarification!
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