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25 Oct 2021, 08:29
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If \(a\), \(b\), and \(c\) are positive integers, what is the value of \(a\)?
(1) \(a*b*c = c!\)
(2) \(a! + b! = 3\)
(1) \(a*b*c = c!\)
(2) \(a! + b! = 3\)
25 Oct 2021, 08:29
Kudos
Bookmarks
Official Solution:
If \(a\), \(b\), and \(c\) are positive integers, what is the value of \(a\)?
Before moving to the statements notice that we are NOT told that \(a\), \(b\), and \(c\) are distinct, so any two or all three unknows can be equal to each othrer.
(1) \(a*b*c = c!\)
Many cases are possible. For example:
\(a=b=c=1\)
\(a=b=1\) and \(c=2\)
\(a=1\), \(b=2\) (or vise-versa) and \(c=3\)
\(a = 3\), \(b = 2\) (or vise-versa) and \(c = 4\)
...
Not sufficient.
(2) \(a! + b! = 3\)
3 is a small number so we can easily test numbers:
Only \(a=1\) and \(b=2\) or vise-versa works.
Not sufficient.
(1)+(2) When combining we get that \(2c=c!\), which gives \(c=3\). Unfortunately we need the value of \(a\) and \(a\) still can be 1 or 2. Not sufficient.
Answer: E
If \(a\), \(b\), and \(c\) are positive integers, what is the value of \(a\)?
Before moving to the statements notice that we are NOT told that \(a\), \(b\), and \(c\) are distinct, so any two or all three unknows can be equal to each othrer.
(1) \(a*b*c = c!\)
Many cases are possible. For example:
\(a=b=c=1\)
\(a=b=1\) and \(c=2\)
\(a=1\), \(b=2\) (or vise-versa) and \(c=3\)
\(a = 3\), \(b = 2\) (or vise-versa) and \(c = 4\)
...
Not sufficient.
(2) \(a! + b! = 3\)
3 is a small number so we can easily test numbers:
Only \(a=1\) and \(b=2\) or vise-versa works.
Not sufficient.
(1)+(2) When combining we get that \(2c=c!\), which gives \(c=3\). Unfortunately we need the value of \(a\) and \(a\) still can be 1 or 2. Not sufficient.
Answer: E
