Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 10 Jul 2006
Posts: 10

A ladder 25 feet long is leaning against a wall that is perp [#permalink]
Show Tags
21 Jul 2006, 03:57
3
This post was BOOKMARKED
Question Stats:
62% (02:42) correct
38% (01:43) wrong based on 138 sessions
HideShow timer Statistics
A ladder 25 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 7 feet from the base of the wall. If the top of the ladder slips down 4 feet, how many feet will the bottom of the ladder slip? (A) 4 (B) 5 (C) 8 (D) 9 (E) 15 OPEN DISCUSSION OF THIS QUESTION IS HERE: aladder25feetlongisleaningagainstawallthatis130364.html
Official Answer and Stats are available only to registered users. Register/ Login.



Intern
Joined: 17 Jul 2006
Posts: 26

I cannot think of any faster way to do it.
However, here are some tips when dealing with phthagorus theorem and in general, problems involving sqauring numbers.
1. Finding the sqaure of a number ending in 5 (such as 15, 25,35,45, etc).
The answer has two parts, Part A and Part B
Step a: Take whatever is there to the left 5 in the original number and multiply it by one more. the product is part A.
Step b: Take 5^2 = 25 and write it down on the right hand side, this is part B.
eg: 15^2 = (1*2) 25 = 225
25^2 = (2*3) 25 = 625
35^2 = (3*4) 25 = 1225
45^2 = (4*5) 25 = 2025
etc.
95^2 = (9*10)25 = 9025
115^2 = (11*12) 25 = 13225
2. Finding sqaures of any two digit number
Note that (x+y)^2 = x^2 + 2xy + y^2
This is a very powerful algebric formula and can be effectively used to find the sqaure of any two digit number.
for example, 32^2
it has three parts  part A, part B, part C
part A  x^2 which is 3^2 = 9
part B  2xy = 2*3*2 =12
part C  y^2 = 2^2 = 4
the answer is (9)(12)(4) = 1024
when putting together ABC, you need to add from right to left with any carry forward.
eg: 56^2 = (25)(60)(36) = 3136
eg: Small numbers are very trivial, 12^2=(1)(4)(4) = 144, 13^2 = (1)(6)(9) = 169
eg: 43^2 = (16)(24)(9) = 1849
Now combing back to the original problem:
it is good to know some basic phthagorun triplets (integers that form the sides of a right triangle), 3,4,5, 5,12,13, 7,24,25, 9,40,41 etc..
the follow a specific pattern, 3^2 = 4+5, 5^2 = 12+13, 7^2=24+25, 9^2=40+41 and so on (next one is 11,60,61).
(Note that there are other types of phthagorun triplets which do not satisfy the above condition).
mathguru
_________________
http://www.askmathguru.com



GMAT Instructor
Joined: 04 Jul 2006
Posts: 1262
Location: Madrid

Quote: it is good to know some basic phthagorun triplets (integers that form the sides of a right triangle), 3,4,5, 5,12,13, 7,24,25, 9,40,41 etc..
This is precisely how to do the above question quickly! Don't forget 8:15:17



Intern
Joined: 10 Jul 2006
Posts: 10

Excellent tips! Thanks guys. BTW, the OA is C.



VP
Joined: 02 Jun 2006
Posts: 1260

Not really.. there are no tricks when it comes to unusual right angle triangles. The only thing that you can do is remember the usual ones
345 (and its multiples) etc. And use the quick computation techniques above...
As for this, it should be pretty quick to calculate.
62549 = 576 (has to be 24 or 16.. ends in 6).
which gives 625400 = 225 = 15 x 15.
15 = 7+8..
Answer : (C). 8
Last edited by haas_mba07 on 21 Jul 2006, 09:53, edited 1 time in total.



VP
Joined: 02 Jun 2006
Posts: 1260

Great information gmatmathguru... Thanks/
Could you clarify a little more as to how to get the sum after the x^2, 2xy, y^2 terms are calculated.
gmatmathguru wrote: the answer is (9)(12)(4) = 1024
when putting together ABC, you need to add from right to left with any carry forward.
eg: 56^2 = (25)(60)(36) = 3136
eg: Small numbers are very trivial, 12^2=(1)(4)(4) = 144, 13^2 = (1)(6)(9) = 169
eg: 43^2 = (16)(24)(9) = 1849
Now combing back to the original problem:
it is good to know some basic phthagorun triplets (integers that form the sides of a right triangle), 3,4,5, 5,12,13, 7,24,25, 9,40,41 etc..
the follow a specific pattern, 3^2 = 4+5, 5^2 = 12+13, 7^2=24+25, 9^2=40+41 and so on (next one is 11,60,61).
(Note that there are other types of phthagorun triplets which do not satisfy the above condition).
mathguru



Intern
Joined: 17 Jul 2006
Posts: 26

1
This post was BOOKMARKED
sure.
eg: 32^2
You write down (x^2)(2xy)(y^2) terms individually.
in this case, (9), (12), (4) respectively.
Once, you have this, the process is very simple. You add them from right to left with anything above 9 (10 or more) as a carry (that you do in addition).
Step1:
Start with the (y^2) term which is 4 to begin with. (9), (12), (4)
So, I start with 4 first. my answer looks like XXX4. Because 4 is less than 10, I do not have a carry.
Step2:
(9), ( 12), (4)
Next, take the 2xy term which is 12. Because 12 is more than 10, you put down 2 and take 1 as the carry.
So, up to now, you have XX24 and 1 as the carry to the next step.
(9), (1 2), (4)
Step 3:
I have a 9 and 1 as the carry from step 2. I add 9 and 1 to get 10.
(9), (1 2), (4)
PUtting all three steps together, I have 1024 as the answer.
when putting together ABC, you need to add from right to left with any carry forward.
eg: 56^2 = (25)(60)(36) = 3136
Step 1: (25)(60)(3 6) and 3 is the carry
Step 2: (25) (60+3) 6
which is (25) (6 3) 6 and 6 is the carry
Step 3: (25+6) 36 = 3136
eg: Small numbers are very trivial, 12^2=(1)(4)(4) = 144, 13^2 = (1)(6)(9) = 169
eg: 43^2 = (16)(24)(9) = 1849
mathguru
_________________
http://www.askmathguru.com



VP
Joined: 02 Jun 2006
Posts: 1260

Got it!! Thanks so much... This is a great way for quick squared computations...
gmatmathguru wrote: sure.
eg: 32^2
You write down (x^2)(2xy)(y^2) terms individually.
in this case, (9), (12), (4) respectively.
Once, you have this, the process is very simple. You add them from right to left with anything above 9 (10 or more) as a carry (that you do in addition).
Step1:
Start with the (y^2) term which is 4 to begin with. (9), (12), (4)
So, I start with 4 first. my answer looks like XXX4. Because 4 is less than 10, I do not have a carry.
Step2:
(9), (12), (4)
Next, take the 2xy term which is 12. Because 12 is more than 10, you put down 2 and take 1 as the carry.
So, up to now, you have XX24 and 1 as the carry to the next step.
(9), (1 2), (4)
Step 3:
I have a 9 and 1 as the carry from step 2. I add 9 and 1 to get 10.
(9), (1 2), (4)
PUtting all three steps together, I have 1024 as the answer.
when putting together ABC, you need to add from right to left with any carry forward.
eg: 56^2 = (25)(60)(36) = 3136
Step 1: (25)(60)(3 6) and 3 is the carry
Step 2: (25) (60+3) 6
which is (25) (6 3) 6 and 6 is the carry
Step 3: (25+6) 36 = 3136
eg: Small numbers are very trivial, 12^2=(1)(4)(4) = 144, 13^2 = (1)(6)(9) = 169
eg: 43^2 = (16)(24)(9) = 1849
mathguru



CEO
Joined: 20 Nov 2005
Posts: 2894
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD  Class of 2008

You guys may want to check this out for squares:
http://www.gmatclub.com/phpbb/viewtopic.php?t=25664
This is vedic mathematics. For who don't know about Vedic mathematics: Vedas are the ancient Indian books written thousands of years ago. These books contain many things that include quick mathematics tricks. The tricks in above link are just the tip of the iceberg.
_________________
SAID BUSINESS SCHOOL, OXFORD  MBA CLASS OF 2008



VP
Joined: 02 Jun 2006
Posts: 1260

I am actually reading a book on Vedic Mathematics. Recently brought it back on my trip to India... I am not sure how much it will help me on my GMAT but a great read on different techniques they devised...
ps_dahiya wrote: You guys may want to check this out for squares: http://www.gmatclub.com/phpbb/viewtopic.php?t=25664This is vedic mathematics. For who don't know about Vedic mathematics: Vedas are the ancient Indian books written thousands of years ago. These books contain many things that include quick mathematics tricks. The tricks in above link are just the tip of the iceberg.



CEO
Joined: 20 Nov 2005
Posts: 2894
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD  Class of 2008

haas_mba07 wrote: I am actually reading a book on Vedic Mathematics. Recently brought it back on my trip to India... I am not sure how much it will help me on my GMAT but a great read on different techniques they devised... ps_dahiya wrote: You guys may want to check this out for squares: http://www.gmatclub.com/phpbb/viewtopic.php?t=25664This is vedic mathematics. For who don't know about Vedic mathematics: Vedas are the ancient Indian books written thousands of years ago. These books contain many things that include quick mathematics tricks. The tricks in above link are just the tip of the iceberg.
They will help you only if you practice practice and practice using those tricks. During my graduation, I used to read vedic mathematics in my spare time and I became so proficient that I was able to calculate A/B in few seconds accurate to 3 decimal places, where A is any number upto 1000 and B any number upto 30.
They may help on GMAT a little but not that much. GMAT is not about tedious calculations but its all about tricks and techniques.
_________________
SAID BUSINESS SCHOOL, OXFORD  MBA CLASS OF 2008



SVP
Joined: 30 Mar 2006
Posts: 1728

I dont know any shorter method. But it took me less than a minute.
What you can do is memorize some important squares.
Height of wall till ladder = (25^2  7^2)^1/2 = (62549)^1/2 = 576^1/2 = 24
New height = 20
New distance from the wall to the base of the ladder
= (25^2  20^2)^1/2
= (225)^1/2
= 15



Senior Manager
Joined: 04 Mar 2007
Posts: 434

ps_dahiya,
Thank you very much. I have never heard about vedic mathematics before. It's very interesting to know.
gmatmathguru,
thank you for your explanations. Great shortcuts and really useful for GMAT.



Manager
Joined: 18 Apr 2007
Posts: 120

1
This post received KUDOS
I am reviving this message because I think it has a lot of useful info. Also, it is really simple if you know your pythagorean triplets.
The triplet called into play here is a 7:24:25 triangle.
The base is 7, the height up the wall is 24 and the length of the ladder is 25. Now, decrease the height by 4 feet and you get the new height of 20. The ladder length stays the same so you can set up and solve the follwing equation for the base:
20^2 + b^2 = 25^2 > 400 + b^2 = 625
b^2 = 225 > b=15
Now we subtract 7 from 15 and we find that the base moved 8 ft!
Answer: C



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15969

Re: PS: Ladder [#permalink]
Show Tags
17 Jun 2014, 23:46
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Math Expert
Joined: 02 Sep 2009
Posts: 39672

Re: A ladder 25 feet long is leaning against a wall that is perp [#permalink]
Show Tags
18 Jun 2014, 00:56




Re: A ladder 25 feet long is leaning against a wall that is perp
[#permalink]
18 Jun 2014, 00:56







