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flying acrobats raring to go!

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by ashish1354 » Fri Sep 18, 2009 11:12 pm
The flying acrobatic team is made up of 120 airplanes. The team wants to form a rectangular formation with X planes in a row and Y planes in a column. If the number of airplanes in a row is no less than 4 and no more than 30, how many different combinations of rectangular shapes are possible?

(a) 4.
(b) 5.
(c) 6.
(d) 8.
(e) 10.

can someone show a fast way to solve this
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Re: flying acrobats raring to go!

by Brent@GMATPrepNow » Mon Sep 21, 2009 8:21 am
ashish1354 wrote:The flying acrobatic team is made up of 120 airplanes. The team wants to form a rectangular formation with X planes in a row and Y planes in a column. If the number of airplanes in a row is no less than 4 and no more than 30, how many different combinations of rectangular shapes are possible?

(a) 4.
(b) 5.
(c) 6.
(d) 8.
(e) 10.

can someone show a fast way to solve this
For the formation to be a rectangle, we can see that X and Y must be factors (divisors) of 120.
Once we select the value of X (# of planes in a row), the value of Y follows (e.g., if X=20, then Y must equal 6).
So, how many values of X can we have?
Well, let's list all of the factors of 120.
120: {1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120}
Given the conditions for the values of X in the question, we see that X can equal 4,5,6,8,10,12,15,20,24,and 30
So, the answer is E

As far as a "quick" way to find divisors is concerned, we could use a nice rule involving the prime factorization (see below), but the restrictions regarding the value of X prevent this from being as useful as usual. For this question, listing the divisors might be the fastest way.

Aside:
Finding the total number of divisors of positive integer N:
- Write the prime factorization of N
- If the prime factorization of N = (W^a)(X^b)(Y^c). . ., then the total number of divisors of N=(a+1)(b+1)(c+1)...
Brent Hanneson - Creator of GMATPrepNow.com
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interpretation problem

by vivekjaiswal » Mon Sep 21, 2009 8:19 pm
Hi,

I somehow (mis)interpreted the statements 'no less than 4' and 'no greater than 30' as 4<x<30 :(

Any tips to watch out for such word translations?


Cheers,
Vivek
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Master | Next Rank: 500 Posts
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interpretation problem

by vivekjaiswal » Mon Sep 21, 2009 8:52 pm
Hi,

I somehow (mis)interpreted the statements 'no less than 4' and 'no greater than 30' as 4<x<30 :(

Any tips to watch out for such word translations?


Cheers,
Vivek
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Re: interpretation problem

by mohitsharda » Mon Sep 21, 2009 9:18 pm
vivekjaiswal wrote:Hi,

I somehow (mis)interpreted the statements 'no less than 4' and 'no greater than 30' as 4<x<30 :(

Any tips to watch out for such word translations?


Cheers,
Vivek
For this you need to ask the question.
i.e. is 4 less than 4? Ans: No.
=> 4 is no less than 4.
same for upper limit:
is 30 greater than 30? Ans: No.
=> 30 is no greater than 30.
MS
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