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2 problems on GMAT Prep - help needed

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2 problems on GMAT Prep - help needed

by sanjana » Tue Aug 25, 2009 8:13 am
Can someone please help me solve these 2 problems?

(1)On her way back home from work,Janet drives through several tollbooths.Is there any pair of tollbooths that are less than 10miles apart?

(a)The 1st and last tollbooth are 25 miles apart

(b)Janet drives through 4 tollbooths.

(2)When a tree was 1st planted it was 4 feet tall and increased by a constant amount each year for 6 years.At the end of the 6th year the tree was 1/5 taller than it was at the end of the 4th year.By what amount did its height increase every year?

Any help would be great!
Thanks.
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by winsome_vagabond » Tue Aug 25, 2009 9:04 am
1) Using both

2)2/3
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by sanjana » Tue Aug 25, 2009 9:51 am
winsome_vagabond wrote:1) Using both

2)2/3
I have the answers,I need the explaination please
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by LFalken » Tue Aug 25, 2009 10:41 am
sanja,

in response to your first problem....

from (1) we know that the FIRST and LAST tollbooth are 25 miles apart. However, we have no idea whether there are more tollbooths in between or not. Insufficent.

from (2) we know that Janet drives through 4 tollbooths, however, we have absolutely no idea of any of the distances bewtweent these four tollbooths, they could be 100 miles apart each, or 1 mile apart each. We do not know. Insuffcient.

Together: We know that the distance between the First and Last tollbooth is 25 miles, and we know janet drives through 4 tollbooths. Thus the first (#1) two more (#2 and #3) and the last (#4), and all in a distance of 25 miles. 4 tollbooths means we have THREE distances. (distance 1= the distance between the first and second tollboth), (distance 2= distance between 2nd and 3rd tollbooth), and finally (distance 3= distance between third and last tollbooth)...

If all distances are equal 25 miles/3 distances = 8.3 miles between tollbooths, which is less than 10. NOW, if we make any of the distances greater than 10 miles then at LEAST 1 of the remaining distances will then be shorter than 10 miles and WE KNOW that there IS A PAIR of tollbooths less than 10 miles apart. Sufficient.
LFAL
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by LFalken » Tue Aug 25, 2009 10:44 am
sanja,

in response to your first problem....

from (1) we know that the FIRST and LAST tollbooth are 25 miles apart. However, we have no idea whether there are more tollbooths in between or not. Insufficent.

from (2) we know that Janet drives through 4 tollbooths, however, we have absolutely no idea of any of the distances bewtweent these four tollbooths, they could be 100 miles apart each, or 1 mile apart each. We do not know. Insuffcient.

Together: We know that the distance between the First and Last tollbooth is 25 miles, and we know janet drives through 4 tollbooths. Thus the first (#1) two more (#2 and #3) and the last (#4), and all in a distance of 25 miles. 4 tollbooths means we have THREE distances. (distance 1= the distance between the first and second tollboth), (distance 2= distance between 2nd and 3rd tollbooth), and finally (distance 3= distance between third and last tollbooth)...

If all distances are equal 25 miles/3 distances = 8.3 miles between tollbooths, which is less than 10. NOW, if we make any of the distances greater than 10 miles then at LEAST 1 of the remaining distances will then be shorter than 10 miles and WE KNOW that there IS A PAIR of tollbooths less than 10 miles apart. Sufficient.
LFAL
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by sbasha » Tue Aug 25, 2009 11:04 am
Lets say the height of the tree will be as follows:

1 year = 4+x
2 year = 4+2x
3 year = 4+3x
4 year = 4+4x
5 year = 4+5x
6 year = 4+6x

"At the end of the 6th year the tree was 1/5 taller than it was at the end of the 4th year"

Height of the tree at the end of 6 year = 4+6x
Height of the tree at the end of 4 year = 4+4x

so the eq will be

4+6x = 4+4x +1/5 (4+4x) Basically ( 4 years + 1/5 of 4th year)

Leads to

20+30x = 20+20x+4+4x Solving we get x = 2/3
Regards

Syed Basha
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by shootingforstars » Tue Aug 25, 2009 8:02 pm
Hi Lfal,

how do you know there is equal distance between the tollboths ?
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by sanjana » Wed Aug 26, 2009 7:19 am
shootingforstars wrote:Hi Lfal,

how do you know there is equal distance between the tollboths ?
He doesnt know that there is equal distance,he is just trying see if he can answer the question assuming the distances are equal.
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by mohitsharda » Wed Aug 26, 2009 9:33 am
sanjana wrote:
shootingforstars wrote:Hi Lfal,

how do you know there is equal distance between the tollboths ?
He doesnt know that there is equal distance,he is just trying see if he can answer the question assuming the distances are equal.
He is not trying to see it he can answer by assuming the distances are equal.
By doing this, he proves that at max 8.3 miles is the distance between all three. So, the distance is less than 10 miles.
However, if they are unequal, say two are 10.1 (>10 miles), then third will automatically be less than 10.

So, by using both the statements together, we can be sure that there would be at least one pair of toll boooths that are within 10 miles.
MS
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