DS question from princeton

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rakaisraka: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Mon Jul 06, 2015 2:46 am

by rakaisraka » Sat Aug 29, 2015 11:15 am

#m = ((m!)!). lf m is a positive integer, what is the
value of m ?
(1) 2! : (m - 1)!
(2 #m is six times the value of 5!

Can we cancel out the factorial from both sides?

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Source: Beat The GMAT — Data Sufficiency | Sat Aug 29, 2015 11:15 am

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Sun Aug 30, 2015 12:06 am

Did you write Statement 1 correctly?

Is Statement 1 what you are referring to with your question?

Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
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rakaisraka: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Mon Jul 06, 2015 2:46 am

by rakaisraka » Sun Aug 30, 2015 2:51 am

Hi, Actually this is a DS question and this was the only info given. It is from princeton. I can get the answer but im not sure if we can cancel out factorials from both side. ?Thanks

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Aug 30, 2015 6:44 am

rakaisraka wrote:Hi, Actually this is a DS question and this was the only info given. It is from princeton. I can get the answer but im not sure if we can cancel out factorials from both side. ?Thanks

In MOST cases, you can cancel out the factorials.
That is, if k! = j!, then k = j
So, if 2! = (m - 1)!, then we can conclude that 2 = m-1, which means m = 3

HOWEVER, there is one proviso, which is based on the fact that 0! = 1! = 1
If either factorial is 0! or 1!, then the above rule does not apply.

For example, if we have (n - 2)! = 1!, then there are two possible solutions: n = 3 and n = 2

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Aug 30, 2015 6:50 am

I's assuming that statement 1 should read as follows:

rakaisraka wrote:#m = ((m!)!). lf m is a positive integer, what is the
value of m ?
(1) 2! = (m - 1)!
(2 #m is six times the value of 5!

Target question: What is the value of m?

Statement 1: 2! = (m - 1)!
This means that 2 = m-1, which means m = 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: #m is six times the value of 5!
So, (m!)! = (6)(5!)
(m!)! = (6)(5)(4)(3)(2)(1)
(m!)! =6!
So, m! = 6, which means m = 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Mon Aug 31, 2015 6:17 am

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

#m = ((m!)!). lf m is a positive integer, what is the
value of m ?
(1) 2! = (m - 1)!
(2) #m is six times the value of 5!

==> In the original condition we have 1 variable (m) and we need 1 equation to match the number of variables and equations. Since we have 1 each in 1) and 2), D is likely the answer.

In actual calculation,

In case of 1), 2=m-1, m=3 sufficient and in case of 2), (m!)!=6(5!)=6!, m!=6=3*2*1, m=3 therefore is sufficient. Thus the answer is D.

For 95% of the questions that have 1) =2), D is the answer.

If you know our own innovative logics to find the answer, you don't need to actually solve the problem.
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