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03 Dec 2018, 05:43
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
75% (01:20) correct
25%
(01:12)
wrong
based on 292
sessions
History
Date
Time
Result
Not Attempted Yet
If a, b, and c are positive integers, what is the value of a?
(1) a*b*c = c!
(2) a! + b! = 3
M36-41
(1) a*b*c = c!
(2) a! + b! = 3
M36-41
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25 Oct 2021, 08:30
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Bunuel
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
General Discussion
Archit3110
Major Poster
Updated on: 03 Dec 2018, 09:45
Originally posted by Archit3110 on 03 Dec 2018, 06:08.
Last edited by Archit3110 on 03 Dec 2018, 09:45, edited 1 time in total.
Last edited by Archit3110 on 03 Dec 2018, 09:45, edited 1 time in total.
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Bunuel
from 1
a*b*c=c!
means that c>b>a and a,b,c are all consective integers
so value of a at best can be 1 only
1*2*3=3! or 2*3*4=4!
not sufficient
From 2:
a!+b!=3
only possible if
a=1 and b=2 or a=2 ., b=2
Not sufficient
IMO E ..
