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# What are the lengths of 3 sides of a right triangle? (1)

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Manager
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What are the lengths of 3 sides of a right triangle? (1) [#permalink]  11 Dec 2003, 15:18
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Question Stats:

0% (00:00) correct 100% (01:40) wrong based on 3 sessions
What are the lengths of 3 sides of a right triangle?

(1) Difference of hypotenuse and base is 6 inches.
(2) Difference of hypotenuse and perpendicular is 3 inches.
Senior Manager
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For this problem can we substitute numbers.

(1) - insufficient
(2) - insufficient

But when i combine them together I am getting a ratio which is 4:5:6.
Can this be an answer to this question ?
Manager
Joined: 26 Aug 2003
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I say D

What we know:
h = hyp
b = base
p = perpendicular
p┬▓ + b┬▓ = h┬▓

(1) So we know that p = h - 6, using this information we get:
(h - 6)┬▓ + b┬▓ = h┬▓
h┬▓ - 12h + 36 + b┬▓ = h┬▓
b┬▓ = 12h - 36
b = 12, b = (h - 3) .... b = (h - 3) is what's given in statement 2, we can use this information to figure out h = 15 and so p = 9

(2) We know b = h - 3, using this information we can use the substitution like the one in Statement 1 to figure out h = 15 and b = 12

So the triangle ends up being (9, 12, 15). For sanity check if you use both statements you'll see that h = 15 and h = 3. But we can't use h = 3 because that doesn't satisfy out conditions given in the DS statements.
Manager
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Good job wonder_gmat!

But if you use b = h-3 in step (1), arent you using information from (2) in the question, making your answer C instead of D?
Manager
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bluefox420 wrote:
Good job wonder_gmat!

But if you use b = h-3 in step (1), arent you using information from (2) in the question, making your answer C instead of D?

Not exactly, because you got this information on your own by using information provided only in current statement. The other thing is, in GMAT end information has to be agreed on by both statements so by that virtue you can still get away with having the same information that would be provided in the other statement.

BTW, good problem!
Senior Manager
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wondergmat ....

b = 12, b = (h - 3) .... b = (h - 3) is what's given in statement 2, we can use this information to figure out h = 15 and so p = 9
above you say that you are using the info from statement 2 and then you say .... "Not exactly, because you got this information on your own by using information provided only in current statement."

in GMAT end information has to be agreed on by both statements what does it mean. Please give an example.

Also us say
What we know:
h = hyp
b = base
p = perpendicular
p┬▓ + b┬▓ = h┬▓

but then while solving you interchange b and h; eg. statement 1 says "Difference of hypotenuse and base is 6 inches. " but in your solution you have "(1) So we know that p = h - 6, using this information we get: "

I have just come back from office after a long day ... so ....am I going crazy or just missing the point here?
Manager
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Cannot be D.. [#permalink]  12 Dec 2003, 16:30
WonderGmat wrote:

b┬▓ = 12h - 36
b = 12, b = (h - 3) .... b = (h - 3) is what's given in statement 2, we can use this information to figure out h = 15 and so p = 9

Vow!!

b*b = 12*(h-3) => b = 12 or b=h-3?

why not b =4 or b= 3(h-3)???

Without solving, I am thinking the answer is C.

3 unknowns and three equations.
CEO
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Quote:
I say D

What we know:
h = hyp
b = base
p = perpendicular
p┬▓ + b┬▓ = h┬▓

(1) So we know that p = h - 6, using this information we get:
(h - 6)┬▓ + b┬▓ = h┬▓
h┬▓ - 12h + 36 + b┬▓ = h┬▓
b┬▓ = 12h - 36
b = 12, b = (h - 3) .... b = (h - 3) is what's given in statement 2, we can use this information to figure out h = 15 and so p = 9

wonder , p = h -6 is wrong ... in 1. b= h -6 is the correct relationship.

Also, you need to check how you get b = 12 , b = h-3?

Quote:
(2) We know b = h - 3, using this information we can use the substitution like the one in Statement 1 to figure out h = 15 and b = 12

So the triangle ends up being (9, 12, 15). For sanity check if you use both statements you'll see that h = 15 and h = 3. But we can't use h = 3 because that doesn't satisfy out conditions given in the DS statements.

here again..you switch it... we need p =h-3.

Wonder, you want to take a look now... if you get a different answer?

Thanks
Praetorian

Last edited by Praetorian on 12 Dec 2003, 22:46, edited 2 times in total.
CEO
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Re: DS : Sides of a right triangle [#permalink]  12 Dec 2003, 22:40
bluefox420 wrote:
What are the lengths of 3 sides of a right triangle?

(1) Difference of hypotenuse and base is 6 inches.
(2) Difference of hypotenuse and perpendicular is 3 inches.

heres my solution.

We know. .. h- b = 6

also, we know that p^2 + b^2 = h^2

h^2 - b^2 = p^2
(h - b) ^2 + 2 hb = p^2
36 + 2hb = p^2 ................................................(a)

(1) ..clearly not sufficient .

Similarly from (2) => h - p = 3

a simplification gives....9 + 2 hp = p ^2 ...............(b)

Again, clearly insufficient

Combine..from (a) and (b).... 36 + 2 hb = 9 + 2hp
27 = 2h (p - b)
b = h - 6 , p = h- 3
p - b = 3
27 = 6h get h = 27 .. the rest can be calculated one hyp is known

addendum : i think this problem can be solved easily if we see that we have three unknowns and each of the choices only gives us information about two. so we might want to skip directly to the "combine" step.

thanks
praetorian
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praetorian123 wrote:
Quote:
I say D

What we know:
h = hyp
b = base
p = perpendicular
p┬▓ + b┬▓ = h┬▓

(1) So we know that p = h - 6, using this information we get:
(h - 6)┬▓ + b┬▓ = h┬▓
h┬▓ - 12h + 36 + b┬▓ = h┬▓
b┬▓ = 12h - 36
b = 12, b = (h - 3) .... b = (h - 3) is what's given in statement 2, we can use this information to figure out h = 15 and so p = 9

wonder , p = h -6 is wrong ... in 1. b= h -6 is the correct relationship.

Also, you need to check how you get b = 12 , b = h-3?

Quote:
(2) We know b = h - 3, using this information we can use the substitution like the one in Statement 1 to figure out h = 15 and b = 12

So the triangle ends up being (9, 12, 15). For sanity check if you use both statements you'll see that h = 15 and h = 3. But we can't use h = 3 because that doesn't satisfy out conditions given in the DS statements.

here again..you switch it... we need p =h-3.

Wonder, you want to take a look now... if you get a different answer?

Thanks
Praetorian

Yes, I switched the variables by mistake. Sorry about that. But that shouldn't matter, the answer is still the same.
CEO
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Posts: 3469
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Kudos [?]: 702 [0], given: 781

wonder_gmat wrote:
praetorian123 wrote:
Quote:
I say D

What we know:
h = hyp
b = base
p = perpendicular
p┬▓ + b┬▓ = h┬▓

(1) So we know that p = h - 6, using this information we get:
(h - 6)┬▓ + b┬▓ = h┬▓
h┬▓ - 12h + 36 + b┬▓ = h┬▓
b┬▓ = 12h - 36
b = 12, b = (h - 3) .... b = (h - 3) is what's given in statement 2, we can use this information to figure out h = 15 and so p = 9

wonder , p = h -6 is wrong ... in 1. b= h -6 is the correct relationship.

Also, you need to check how you get b = 12 , b = h-3?

Quote:
(2) We know b = h - 3, using this information we can use the substitution like the one in Statement 1 to figure out h = 15 and b = 12

So the triangle ends up being (9, 12, 15). For sanity check if you use both statements you'll see that h = 15 and h = 3. But we can't use h = 3 because that doesn't satisfy out conditions given in the DS statements.

here again..you switch it... we need p =h-3.

Wonder, you want to take a look now... if you get a different answer?

Thanks
Praetorian

Yes, I switched the variables by mistake. Sorry about that. But that shouldn't matter, the answer is still the same.

it should be C , not D

what did i do wrong ..could you check my post in this thread.
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