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Dots

by Lattefah84 » Tue Jan 19, 2010 8:14 am
Each dot in the mileage table above represents an entry indicating the distance between a pair of the five cities. If the table were extended to represent the distances of 30 cities and each distance were to be represented by only one entry, how many entries would the table then have?

(A) 60
(B) 435
(C) 450
(D) 465
(E) 900


The answer is B 900-30=870

870/2=435

The part I don't understand is - why dividing by 2? And if have to put only one dot for one pair of cities, wouldn't it extremely decrease the number of dots (entries). So, my question is why dividing by 2?
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by Pharo » Tue Jan 19, 2010 9:06 am
There are two ways to represent the distance information. You either represent it by putting a dot in A(row)B(column) or you put a dot in B(row)A(column). Since the question wants only one half of the table full, you divide 870 by 2; meaning you choose to fill only one half of the table and represent each distance by only one entry, as the question asks.

Dividing by 2 decreases the number of dots significantly but does not take away anything from the information of the table.
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by Lattefah84 » Tue Jan 19, 2010 10:36 am
Pharo wrote:There are two ways to represent the distance information. You either represent it by putting a dot in A(row)B(column) or you put a dot in B(row)A(column). Since the question wants only one half of the table full, you divide 870 by 2; meaning you choose to fill only one half of the table and represent each distance by only one entry, as the question asks.

Dividing by 2 decreases the number of dots significantly but does not take away anything from the information of the table.
Does this mean that in column for city E (example) it would be two dots instead of four. Or it would me only one dot? I am not sure about this term "only one entry" - does it mean only one distance between one and other cities (one distance from city E to all other cities)?
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by mmslf75 » Tue Jan 19, 2010 11:03 am
Pharo wrote:There are two ways to represent the distance information. You either represent it by putting a dot in A(row)B(column) or you put a dot in B(row)A(column). Since the question wants only one half of the table full, you divide 870 by 2; meaning you choose to fill only one half of the table and represent each distance by only one entry, as the question asks.

Dividing by 2 decreases the number of dots significantly but does not take away anything from the information of the table.
@latte

Distance between E and A , for example, will be same as distance between A to E
The question asks us to find ONLY ONE entry for the same

hope that helps
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by Lattefah84 » Tue Jan 19, 2010 11:07 am
mmslf75 wrote:
Pharo wrote:There are two ways to represent the distance information. You either represent it by putting a dot in A(row)B(column) or you put a dot in B(row)A(column). Since the question wants only one half of the table full, you divide 870 by 2; meaning you choose to fill only one half of the table and represent each distance by only one entry, as the question asks.

Dividing by 2 decreases the number of dots significantly but does not take away anything from the information of the table.
@latte

Distance between E and A , for example, will be same as distance between A to E
The question asks us to find ONLY ONE entry for the same

hope that helps
:)

I see, and only one distance for example A-E is found in the first table isn't it? There are no few distances from the same cities - so I just ask what's the difference when we look at the first table?
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by ksundar » Wed Jan 20, 2010 2:39 am
Its a simple sum of AP...

Sn = n/2(2a+(n-1)d)
= 29/2(2+28)
=435

IMO B
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by Lattefah84 » Wed Jan 20, 2010 7:54 am
ksundar wrote:Its a simple sum of AP...

Sn = n/2(2a+(n-1)d)
= 29/2(2+28)
=435

IMO B
Can you please explain to me the difference between this first table and the table that is to make (except additional it is 30x30 and not 5x5) ? There is already one entry for every city...?
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by ksundar » Thu Jan 21, 2010 9:05 pm
Lattefah84 wrote:
ksundar wrote:Its a simple sum of AP...

Sn = n/2(2a+(n-1)d)
= 29/2(2+28)
=435

IMO B
Can you please explain to me the difference between this first table and the table that is to make (except additional it is 30x30 and not 5x5) ? There is already one entry for every city...?
There is no difference except for extending the table to be 30X30.
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by Apple3-14 » Sun Mar 29, 2015 2:43 pm
I was working on this question in the GMAT Official Guide, and there's a way to get this question right in about 30 seconds with almost no math, so I thought I'd share. I've been training to be aware of the answer options as I'm breaking the question down, and here, as is so often the case, it's clutch:

(A) 60
(B) 435
(C) 450
(D) 465
(E) 900

So, if our 30 city table has 900 cells, is there any way all 900 cells would have an entry (dot)? No way, right?
Then, we can even use the example table as a reference. Notice about half of the cells have dots, but is it exactly half? No. So C is out. In fact, we can see from both the description and the table that there are no entries from a town to itself. I mean do we care about the distance from Town A to Town A? 0? No. So notice, that we're talking just a little bit less than a half. Which option is the only option that's a little bit less than a half of 900. B. This is not guessing. It's guaranteed that logically, option B has to be correct.
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by Brent@GMATPrepNow » Sun Mar 29, 2015 4:20 pm
More on this question here https://www.beatthegmat.com/og-13th-q124-t278241.html

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by [email protected] » Sun Mar 29, 2015 4:30 pm
Hi Apple3-14,

You've described an aspect to this question that you'll see on several questions in the Quant section of the GMAT - the answer choices provide a BIG clue as to how to find the fastest way to get to the correct answer. Many Test Takers assume that the Quant section of the GMAT should be treated as if it were a "math test", but that is NOT what the Quant section is about. While there are plenty of calculations that will need to be done, many of the Quant questions you'll face are designed primarily to test your critical thinking skills. In that way, paying attention to the ENTIRE prompt (including how the answers are written and organized) is a must when attempting to maximize your performance and optimize your pacing. Keep on the lookout for these opportunities and you'd be amazed how many "thick" looking questions are actually fairly straight-forward.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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