What are the lengths of 3 sides of a right triangle? (1) : DS Archive
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 22 Jan 2017, 01:09

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
Manager
Joined: 06 Jun 2003
Posts: 59
Followers: 1

Kudos [?]: 1 [0], given: 0

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

### Show Tags

11 Dec 2003, 15:18
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (01:40) wrong based on 3 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
Joined: 05 May 2003
Posts: 424
Location: Aus
Followers: 2

Kudos [?]: 10 [0], given: 0

### Show Tags

11 Dec 2003, 22:04
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
Posts: 233
Location: United States
Followers: 1

Kudos [?]: 13 [0], given: 0

### Show Tags

12 Dec 2003, 06:03
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
Joined: 06 Jun 2003
Posts: 59
Followers: 1

Kudos [?]: 1 [0], given: 0

### Show Tags

12 Dec 2003, 07:22
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
Joined: 26 Aug 2003
Posts: 233
Location: United States
Followers: 1

Kudos [?]: 13 [0], given: 0

### Show Tags

12 Dec 2003, 07:45
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!
Manager
Joined: 12 Oct 2003
Posts: 247
Location: USA
Followers: 1

Kudos [?]: 6 [0], given: 0

### Show Tags

12 Dec 2003, 15:04
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
Joined: 11 Oct 2003
Posts: 102
Location: USA
Followers: 1

Kudos [?]: 0 [0], given: 0

### Show Tags

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
Joined: 15 Aug 2003
Posts: 3460
Followers: 67

Kudos [?]: 862 [0], given: 781

### Show Tags

12 Dec 2003, 22:22
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
Joined: 15 Aug 2003
Posts: 3460
Followers: 67

Kudos [?]: 862 [0], given: 781

Re: DS : Sides of a right triangle [#permalink]

### Show Tags

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
Manager
Joined: 26 Aug 2003
Posts: 233
Location: United States
Followers: 1

Kudos [?]: 13 [0], given: 0

### Show Tags

22 Dec 2003, 10:42
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
Joined: 15 Aug 2003
Posts: 3460
Followers: 67

Kudos [?]: 862 [0], given: 781

### Show Tags

22 Dec 2003, 10:47
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.
22 Dec 2003, 10:47
Display posts from previous: Sort by