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Hey guys another question which I think needs more opinions about:

If a lumberjack crew needs to secure a safety zone for cutting down the trees, how far from a given tree should the safety barrier be put up so that it is at least 5 meters away from the danger area, and the barrier perimeter is minimized? The first tree is the highest one.

1. The height of the first tree is 50m. 2. Currently the distance from the barrier to the top of the tree is 70 meters.

A) Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient B) Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient D) EACH statement ALONE is sufficient E) Statements (1) and (2) TOGETHER are NOT sufficient -------

So, should'nt the answer be "D" ?

From statement (1) , it is straight forward, it is sufficient.

From statement (2) alone we can say --> x^2 + (x + 5)^2 = 70^2 , and solve for x. (Pythagorus theorem). ** Please see the attached image of the triangle. **

AB = x = tree height. BC = x+5 = distance of the barrier from base of the tree. AC = 70 = the distance from the barrier to the top of the tree is 70 meters.

And hence, get x + 5 , which will give us ~=17.95. Hence statement (2) is sufficient.

If a lumberjack crew needs to secure a safety zone for cutting down the trees, how far from a given tree should the safety barrier be put up so that it is at least 5 meters away from the danger area, and the barrier perimeter is minimized? The first tree is the highest one.

1. The height of the first tree is 50m. 2. Currently the distance from the barrier to the top of the tree is 70 meters.

I received a PM asking for comment. This is one of those questions that tests whether you can guess what the question designer was thinking, rather than testing any mathematical ability. I frankly have no idea what the question means, and if I list the problems with the question, it's a pretty long list:

* GMAT test takers aren't, by and large, lumberjacks, so the question needs to define what it means by 'safety zone' and 'danger area'.

* The question talks first about a 'given tree' and then about a 'first tree'; are these the same tree? That's not clear, and it's crucially important.

* If I have a group of trees, there is no particular tree which I could logically call the 'first' tree. Trees aren't in some kind of sequence.

* The question talks about the 'perimeter' of the barrier. This suggests that the barrier is some kind of polygon (if it were a circle, the question should discuss its 'circumference'). It's then not altogether clear what's meant when the question asks 'how far' the polygonal barrier should be from the circular(?) 'danger area'; we're not measuring the distance between points but rather between shapes.

* The solution seems to assume that only the tallest tree matters. But if I have three trees in a line, where T is the tallest tree and measures 50 meters in height, and A and B both measure 40 meters in height:

---A-----T-----B-----

and I erect a barrier enclosing these trees, then if A and B are far enough from T, then they are certainly relevant here: I need to position my barrier 45 meters from A and B to ensure I have 5 meters of leeway as the question requires. It's only if you assume that by 'first tree' they mean 'tree closest to the barrier' that you can ignore the other trees.

* Statement 2 says that "Currently the distance from the barrier to the top of the tree is 70 meters" whereas the stem asks where the barrier should be 'put up'. Statement 2 suggests that the barrier has already been put up. That makes no sense.

It's rare that I read a question and simply have no understanding of what it's asking, but that's the case here. It's pretty much pointless to attempt to answer it, since you'd really need to have some psychic ability to work out what the question designer intended.
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If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

I think your solution with statement 2 assumes that the barrier is already exactly at the minimum safe distance, where it isn't indicated to be that way. So currently, the barrier could be anywhere.

Statement (1) by itself is sufficient. S1 tells us that the tree, if cut down, will hit the ground no farther than 50 meters away from its origin. Therefore, the barrier has to be at least 55 meters away.

Statement (2) by itself is insufficient. S2, without the height of the tree, is insufficient.

So, it says "height of the tree", which tree? Cannot we conclude that the answer speaks about height of the first tree?

I would agree with brandy96 if the answer said:

"Statement (2) by itself is insufficient. Since distance from the barrier to the top of *which* tree is unknown."

I don't understand why the information about the first tree is so emphasized. Although there is indeed some part of the question that's not totally clear, I tend to agree with oster here.

The barrier is 70m away from THE given tree's top won't help us determine how far we should put our barrier . The tree could be a 2m tall tree whose base is \(\sqrt{(70)^2-2^2}\) away from the barrier's base, in which case it is already secured but the perimeter needs to be minimized OR it could be a 65m tall tree whose base is \(\sqrt{(70)^2-(65)^2}\) away from the barrier's base, in which case the barrier will need to be moved further. In both cases, the only information required is the height of the tree to decide how far the barrier should be.

Will wait for IanStewart's comment.
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I think the sentence - ''how far from a given tree should the safety barrier be put up so that it is at least 5 meters away from the danger area''

and the Option 2 - ''Currently the distance from the barrier to the top of the tree is 70 meters''

Make it clear that the current distance is not the right distance and so the hypotenuse of 70 Mts is not that of the triangle whose base would be the actual barrier length that needs to be set.

If a lumberjack crew needs to secure a safety zone for cutting down the trees, how far from a given tree should the safety barrier be put up so that it is at least 5 meters away from the danger area, and the barrier perimeter is minimized? The first tree is the highest one.

1. The height of the first tree is 50m. 2. Currently the distance from the barrier to the top of the tree is 70 meters.

I received a PM asking for comment. This is one of those questions that tests whether you can guess what the question designer was thinking, rather than testing any mathematical ability. I frankly have no idea what the question means, and if I list the problems with the question, it's a pretty long list:

* GMAT test takers aren't, by and large, lumberjacks, so the question needs to define what it means by 'safety zone' and 'danger area'.

* The question talks first about a 'given tree' and then about a 'first tree'; are these the same tree? That's not clear, and it's crucially important.

* If I have a group of trees, there is no particular tree which I could logically call the 'first' tree. Trees aren't in some kind of sequence.

* The question talks about the 'perimeter' of the barrier. This suggests that the barrier is some kind of polygon (if it were a circle, the question should discuss its 'circumference'). It's then not altogether clear what's meant when the question asks 'how far' the polygonal barrier should be from the circular(?) 'danger area'; we're not measuring the distance between points but rather between shapes.

* The solution seems to assume that only the tallest tree matters. But if I have three trees in a line, where T is the tallest tree and measures 50 meters in height, and A and B both measure 40 meters in height:

---A-----T-----B-----

and I erect a barrier enclosing these trees, then if A and B are far enough from T, then they are certainly relevant here: I need to position my barrier 45 meters from A and B to ensure I have 5 meters of leeway as the question requires. It's only if you assume that by 'first tree' they mean 'tree closest to the barrier' that you can ignore the other trees.

* Statement 2 says that "Currently the distance from the barrier to the top of the tree is 70 meters" whereas the stem asks where the barrier should be 'put up'. Statement 2 suggests that the barrier has already been put up. That makes no sense.

It's rare that I read a question and simply have no understanding of what it's asking, but that's the case here. It's pretty much pointless to attempt to answer it, since you'd really need to have some psychic ability to work out what the question designer intended.

Great postmortem for the question is already dead. thanks.
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