What IS Y IN TERMS OF X?

Expert replies

pkw209: Master | Next Rank: 500 Posts; Posts: 266; Joined: Mon Oct 19, 2009 9:46 pm; Thanked: 8 times; GMAT Score:690

by pkw209 » Fri Feb 19, 2010 5:32 pm

Sub-portion of a Manhattan GMAT Question:

(100 - y) / (100) = (100) / (100 + x)

What is y in terms of x?

Apparently, the answer is [spoiler](100) - ((10,000) / (100 + x )) [/spoiler]

Can someone please explain?

I tried cross-multiplying but I get a different answer.

I can get the answer if I multiple both sides by 100 but why can't I cross-multiply and get the same solution?

Thanks.

Like this post

Source: Beat The GMAT — Problem Solving | Fri Feb 19, 2010 5:32 pm

papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Fri Feb 19, 2010 6:19 pm

(100 - y) / (100) = (100) / (100 + x)

Cross-multiply 100,

100 - y = (10,000 / (100 + x))

100 - (10,000 / (100+x)) = y

I hope that this is what you are expecting.

Like this post

pkw209: Master | Next Rank: 500 Posts; Posts: 266; Joined: Mon Oct 19, 2009 9:46 pm; Thanked: 8 times; GMAT Score:690

by pkw209 » Fri Feb 19, 2010 6:26 pm

I see the solution when you multiply both sides by 100 but I don't understand why you can't cross multiply and get the same equation.

In other words:

(100 - y) / (100) = (100) / (100 + x)

--->(100-y) (100 + x) = (100) (100)

if you cross multiply as mentioned above, you will not get the solution mentioned in the original post.

Why?

Like this post

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Fri Feb 19, 2010 7:20 pm

pkw209 wrote:I see the solution when you multiply both sides by 100 but I don't understand why you can't cross multiply and get the same equation.

In other words:

(100 - y) / (100) = (100) / (100 + x)

--->(100-y) (100 + x) = (100) (100)

if you cross multiply as mentioned above, you will not get the solution mentioned in the original post.

Why?

100 - (10,000 / (100+x)) = y this is nothing but y=100x/(100+x) the exp which u are getting after cross multiplication

(100 - y) / (100) = (100) / (100 + x)

--->(100-y) (100 + x) = (100) (100)

=10^4+100(x-y)-xy=10^4
or 100x-y(100+x)=0
or y=100x/(100+x)

its the same

Like this post

harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Fri Feb 19, 2010 11:37 pm

will explain it to you step by step:-

1)[(100-y)/100] = [(100)/(100 + x)]
2)Since we want the value of y, we keep it in the L.H.S. numerator and x on the RHS and transpose 100.
3)(100-y) = [(100 x 100)/(100 + x)]
4)-y = [(100 x 100)/(100 + x)] -[100]
5)Multiplying by -1 on both sides to get positive value of y, we get
6)y = 100 - [(100 x 100)/(100 + x)]

I hope the explanation is clear now.

It takes time and effort to explain, so if my comment helped you please press Thanks button

Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker

Like this post

shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Sat Feb 20, 2010 12:49 am

pkw209 wrote:Sub-portion of a Manhattan GMAT Question:

(100 - y) / (100) = (100) / (100 + x)

What is y in terms of x?

Apparently, the answer is [spoiler](100) - ((10,000) / (100 + x )) [/spoiler]

Can someone please explain?

I tried cross-multiplying but I get a different answer.

I can get the answer if I multiple both sides by 100 but why can't I cross-multiply and get the same solution?

Thanks.

Its simple though ...
(100 - y) / (100) = (100) / (100 + x)
multiply 100 both sides , u will get
100-y = 100x100/(100 + x)
add y both side u will get
100 = [100x100/(100 + x) ] + y
--> 100 = 10000/(100 + x) ] + y
subtract [10000/(100 + x) ] both sides
100 - [10000/(100 + x) ] = y
--> y= 100 - [10000/(100 + x) ] = (100) - ((10,000) / (100 + x )) (isn't both looking similar rather equal

)

I tried to solve by simple steps ....just like layman ....hope u get it....

My Websites:
www.mba.webmaggu.com - India's social Network for MBA Aspirants

www.deal.webmaggu.com -India's online discount, coupon, free stuff informer.

www.dictionary.webmaggu.com - A compact free online dictionary with images.

Nothing is Impossible, even Impossible says I'm possible.

Like this post

pkw209: Master | Next Rank: 500 Posts; Posts: 266; Joined: Mon Oct 19, 2009 9:46 pm; Thanked: 8 times; GMAT Score:690

by pkw209 » Mon Feb 22, 2010 5:30 pm

Guys-

Appreciate the help but none of you are answering my original question.

I can figure this out by multiplying both sides by 100.

However, I cannot seem to do so when I cross multiply.

This is my step by step process after cross-multiplying:

(100-y) (100 + x) = (100) (100)

10000 + 100x - 100y - xy = 10000

100x = 100y + xy

100x = y(100 + x)

100x / 100 + x = y

THIS IS NOT THE ANSWER. What am I doing wrong?

ANSWER = (100) - ((10,000) / (100 + x ))

Like this post

DeepthiRajan: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Sat Feb 06, 2010 1:55 pm; Thanked: 5 times

by DeepthiRajan » Wed Feb 24, 2010 3:18 pm

100-y/100 = 100/100+x

dont cross multiply yet, instead multiply the RHS with denominator of the first fraction

(100-y) = 100 * (100/(100+x))

(100-y) = ((100*100)/(100+x))

(100-y) = ((100)^2)/(100+x))

[100- ((100)^2)]/(100+x))] = y

Hope this helps.

Like this post

pkw209: Master | Next Rank: 500 Posts; Posts: 266; Joined: Mon Oct 19, 2009 9:46 pm; Thanked: 8 times; GMAT Score:690

by pkw209 » Tue Mar 02, 2010 4:20 pm

Thanks, but why can't I cross-multiply in that first step?

It's always natural for me to cross-multiply so I'm just trying to figure out why I can't.

Like this post

stufigol: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Wed Feb 03, 2010 12:09 am; GMAT Score:540

by stufigol » Tue Mar 02, 2010 9:17 pm

100- 10000/(x+100) = 100x/100+x
if u do like u did u ll have to

100x + 10000 - 10000 / 100 + x add 10000 and minus 10000 so it stays the same
= 100 (x+100) / (x+100) - 10000 /(x+100)= 100 -10000 / (x+100)

i agree it s not evident to do but that s the trick...they know that u re gonna get stuck there so u better consider to try the second option
hope this helps

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review