Questions about the world of GMAT Math from other sources and general math related questions.
elawyer8
 
 

Challenge Problem this week

by elawyer8 Mon Jul 30, 2007 12:26 pm

Dear Manhattan GMAT:

There appears to be a typo error in this week's challenge problem (currently displayed on the Home page of this site). The answer choice C: (7! - 5!3!) is "visually" closest to the answer that I think is correct (7! - (5 x 3!)) , but not quite correct, I think.

Regards,
cindyqtran
 
 

by cindyqtran Mon Jul 30, 2007 7:24 pm

wow, i thought it was either A or B. not sure. I am not sure if the position of the women matter here.

How did u get (5!) in answer choice C?
shaji
 
 

Re: Challenge Problem this week

by shaji Mon Jul 30, 2007 11:21 pm

C is the correct answer. GMAT sometimes not too good at extrasensory deceptions. Visually close answers are often correct, hence the 'challenge'.

elawyer8 Wrote:Dear Manhattan GMAT:

There appears to be a typo error in this week's challenge problem (currently displayed on the Home page of this site). The answer choice C: (7! - 5!3!) is "visually" closest to the answer that I think is correct (7! - (5 x 3!)) , but not quite correct, I think.

Regards,
StaceyKoprince
ManhattanGMAT Staff
 
Posts: 9360
Joined: Wed Oct 19, 2005 9:05 am
Location: Montreal
 

by StaceyKoprince Tue Jul 31, 2007 1:27 am

Answer choice C is presented correctly: (7! - 5!3!). I won't go into whether this is the right answer right now, since this question is still "open" - see if you can figure it out and check back next week when the answer is posted. :)
Stacey Koprince
Instructor
Director, Content & Curriculum
ManhattanPrep
shaji
 
 

Re: Challenge Problem this week

by shaji Thu Aug 02, 2007 11:39 am

A quick fix for GMAT problems !!!

Having elliminated the impossible, then whatever is left, however improbable it may seem, has to be the correct answer!!!

Since the problem is still open, I shall post a complete mathematical analysis of this problem exhausting all possibilities next Monday.


shaji Wrote:C is the correct answer. GMAT sometimes not too good at extrasensory deceptions. Visually close answers are often correct, hence the 'challenge'.

elawyer8 Wrote:Dear Manhattan GMAT:

There appears to be a typo error in this week's challenge problem (currently displayed on the Home page of this site). The answer choice C: (7! - 5!3!) is "visually" closest to the answer that I think is correct (7! - (5 x 3!)) , but not quite correct, I think.

Regards,
GMAT 2007
 
 

by GMAT 2007 Thu Aug 02, 2007 9:16 pm

The answer is (C) and it is stated correctly too. Here is the solution: -

We are looking for the cases when three men will not sit in the three adjacent seats: -

Desired cases when men will not sit adjacent to each other = Total no. of ways of seating arrangement - No. of ways men will sit at the three adjacent seats

Total no. of ways men & women can be seated= 7!

Now lets go through the possible ways men can be seated in the three adjacent seats: -

1 2 3 4 5 6 7 No of Ways
M1 M2 M3 W W W W = 4!3!
W M1 M2 M3 W W W = 4!3!
W W M1 M2 M3 W W = 4!3!
W W W M1 M2 M3 W = 4!3!
W W W W M1 M2 M3 = 4!3!

So desired cases = 7! - 5X4!3! = 7! -5!3!

So the correct answer is (C)

Hope it helps

GMAT 2007
SHAJI
 
 

by SHAJI Fri Aug 03, 2007 12:15 am

Precisely!!! C is the correct answer as stated and it was never in doubt. However, a complete audit of all 7! possibilities from the man's point of view and and the women's point of view independantly would be an interesting exercise. Dealing with similar situations on the GMAT would then be a 30 second job.

GMAT 2007 Wrote:The answer is (C) and it is stated correctly too. Here is the solution: -

We are looking for the cases when three men will not sit in the three adjacent seats: -

Desired cases when men will not sit adjacent to each other = Total no. of ways of seating arrangement - No. of ways men will sit at the three adjacent seats

Total no. of ways men & women can be seated= 7!

Now lets go through the possible ways men can be seated in the three adjacent seats: -

1 2 3 4 5 6 7 No of Ways
M1 M2 M3 W W W W = 4!3!
W M1 M2 M3 W W W = 4!3!
W W M1 M2 M3 W W = 4!3!
W W W M1 M2 M3 W = 4!3!
W W W W M1 M2 M3 = 4!3!

So desired cases = 7! - 5X4!3! = 7! -5!3!

So the correct answer is (C)

Hope it helps

GMAT 2007
dbernst
ManhattanGMAT Staff
 
Posts: 300
Joined: Mon May 09, 2005 9:03 am
 

by dbernst Fri Aug 03, 2007 12:59 am

Just a little word to the wise about the challenge problems. The challenge problems are great fun, and they are also excellent practice for those scoring in the 95th+ percentile on their Quant sections. However, most of the challenge problems are somewhere between 750 and 900 in terms of difficulty (that is not a typo - many of the challenge problems are more difficult than any problem you will see on your official GMAT). Thus, though I encourage you to continue to work through the challenge problems, do not do so at the expense of truly solidifying your fundamentals.

Unlike Stacey K and Emily S and Jad L, who score in the 99th percentile on their Quant, I only score in the 90-93 percentile range (I like to think that I return the favor on the verbal, but they all score exceptionally on it as well!) Thus, I rarely see problems on my quant sections that are as difficult as the challenge problems. Because I am aware of the types of problems I am most likely to see (at least in terms of difficulty), I prepare for my GMAT accordingly. Whereas my colleagues might do challenge problems galore, I rarely look at them. For me, it's all about the fundamentals (and I mean FUNdamentals!).

Just my 2 cents. Hope it helps!
-dan
GMAT 2007
 
 

by GMAT 2007 Fri Aug 03, 2007 1:16 am

Thanks for your 2 cents :) Dan
shaji
 
 

by shaji Mon Aug 06, 2007 7:31 am

Its Monday, and the correct answer is posted for all to see. Now the rest of the story!!!

# of ways that each of the three men are flanked by women on both sides=144
#of ways that two women are together while the other two are seperated by men=1728
#of ways that the women sit in pairs seperated by men=2592
# of ways the all four women are together =576

This is the complete audit of the 7! ways.



SHAJI Wrote:Precisely!!! C is the correct answer as stated and it was never in doubt. However, a complete audit of all 7! possibilities from the man's point of view and and the women's point of view independantly would be an interesting exercise. Dealing with similar situations on the GMAT would then be a 30 second job.

GMAT 2007 Wrote:The answer is (C) and it is stated correctly too. Here is the solution: -

We are looking for the cases when three men will not sit in the three adjacent seats: -

Desired cases when men will not sit adjacent to each other = Total no. of ways of seating arrangement - No. of ways men will sit at the three adjacent seats

Total no. of ways men & women can be seated= 7!

Now lets go through the possible ways men can be seated in the three adjacent seats: -

1 2 3 4 5 6 7 No of Ways
M1 M2 M3 W W W W = 4!3!
W M1 M2 M3 W W W = 4!3!
W W M1 M2 M3 W W = 4!3!
W W W M1 M2 M3 W = 4!3!
W W W W M1 M2 M3 = 4!3!

So desired cases = 7! - 5X4!3! = 7! -5!3!

So the correct answer is (C)

Hope it helps

GMAT 2007
Rustic Myth
 
 

A Reply Too Late

by Rustic Myth Wed Aug 27, 2008 3:24 pm

Hi I do not know the question but by going through the discussion the simple way would be.

MMMWWWW ----------- 7 people

total no of ways =7P7 = 7!

As three men should be together MMM = X

the can be seated as 3P3 = 3!

XWWWW ----------- 5 Seats considering MMM = X

so total no of ways = 5P5 = 5!

so the number of ways possible = 7! - 5!3!

:)

i think some time grouping similar things helps in probablity......... !!! :oops: :oops: