100X + 200Y

Expert replies

pappueshwar: Master | Next Rank: 500 Posts; Posts: 234; Joined: Fri Oct 01, 2010 7:28 pmFollowed by: 4 members; Location: chennai; Thanked: 5 times

by pappueshwar » Wed Mar 14, 2012 6:32 am

If x, y are positive numbers and x+y=1, which of the following can be the value of 100x+200y?
I. 80 II. 140 III. 199

A. I only
B. â…¡ only
C. â… ,â…¡ only
D. â…¡,â…¢ only
E. â… ,â…¡ and â…¢

OA IS C WHICH COMBINATION OF X AND Y SHOULD BE TAKEN ?

Like this post

Source: Beat The GMAT — Problem Solving | Wed Mar 14, 2012 6:32 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Mar 14, 2012 7:07 am

pappueshwar wrote:If x, y are positive numbers and x+y=1, which of the following can be the value of 100x+200y?
I. 80 II. 140 III. 199

A. I only
B. â…¡ only
C. â… ,â…¡ only
D. â…¡,â…¢ only
E. â… ,â…¡ and â…¢

OA IS C WHICH COMBINATION OF X AND Y SHOULD BE TAKEN ?

Put 100x+200y in terms of one of the variables.

Rephrasing x+y=1 as y=1-x and substituting for y in 100x+200y, we get:
100x + 200(1-x) = 100x + 200 - 200x = 200-100x.

Since x+y=1 and both x and y are positive, 0<x<1.
To determine the viable range here, convert 0<x<1 to 200-100x:
0 < x < 1
0 > -100x > -100
200 > 200-100x > 100.

Thus, 200-100x -- which is the equivalent of 100x+200y -- can be any value between 100 and 200.

The correct answer is D.

II: 140
200-100x = 140
-100x = -60
x=.6, implying that y=.4.
100(.6) + 200(.4) = 60+80 = 140.

III: 199
200-100x = 199.
-100x = -1
x = .01, implying that y=.99.
100x + 200y = 100(.01) + 200(.99) = 1 + 198 = 199.

I: 80
200-100x = 80
-100x = -120
x = 1.2, implying that y=-.2.
Doesn't work, since y must be positive.

Only II and III are possible.

Last edited by GMATGuruNY on Wed Mar 14, 2012 7:14 am, edited 1 time in total.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

killer1387: Legendary Member; Posts: 581; Joined: Sun Apr 03, 2011 7:53 amFollowed by: 5 members; Thanked: 52 times

by killer1387 » Wed Mar 14, 2012 7:09 am

pappueshwar wrote:If x, y are positive numbers and x+y=1, which of the following can be the value of 100x+200y?
I. 80 II. 140 III. 199

A. I only
B. â…¡ only
C. â… ,â…¡ only
D. â…¡,â…¢ only
E. â… ,â…¡ and â…¢

OA IS C WHICH COMBINATION OF X AND Y SHOULD BE TAKEN ?

I doubt the OA
imo D
FOR X=3/5;Y=2/5
100X+200Y=140 HENCE II IS CORRECT.

FOR X=0.01 AND Y=0.99
100X+200Y=199
HENCE III IS CORRECT.

HENCE D

Like this post

icemanKK: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Mon Sep 20, 2010 5:58 pm

by icemanKK » Sat Mar 24, 2012 6:28 pm

Hi guys,

Do you think the following approach can be applied.

Multiplying 100 with x+y = 1
we get -> 100x+100y = 100 -----> 1

Multiplying 200 with x+y = 1
we get -> 200x+200y = 200 -----> 2

Now the question is 100x+200y = ?

Since the numbers are both positive, Using equations 1 and 2 the following can be applied.

100x+200y > 100
and
100x+200y < 200

The only 2 values in this range are 140 and 199. Hence D[/spoiler]

Like this post

jsfinol: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Thu Jul 10, 2014 1:19 pm

by jsfinol » Sat Jul 23, 2016 5:03 pm

Does anyone know is the score difficulty of this question?

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Jul 23, 2016 5:57 pm

Hi jsfinol,

Certain Quant questions are built around relatively simple short-cuts; this prompt has a great built-in logic shortcut that you can take advantage of (and avoid lots of unnecessary calculations). As such, instead of thinking of the 'level' of this question, you should try thinking in terms of whether you could have gotten it correct in a reasonable amount of time or not.

We're told that X and Y are POSITIVE. That is an important 'restriction' that impacts how the math 'works' and we can use it to our advantage. Next, we're told that X+Y = 1. With this information, we know that both X and Y will end up being positive fractions.

We're asked for what COULD be the value of 100X and 200Y.

To start, it helps to think about the 'extreme' possibilities.

IF.... X=1 and Y=0, then the sum would be 100(1) + 200(0) = 100
IF... X=0 and Y=1, then the sum would be 100(0) + 200(1) = 200

Now, neither of those is a possible outcome (remember that BOTH X and Y have to be positive, and 0 doesn't fit that restriction), but they do provide the limits to the possible sum.

If we made X really small, then the bulk of the total would be in Y (eg. X=0.01 and Y= 0.99), so the sum would be REALLY close to 200. In that same way, if we made Y really small, then the bulk of the total would in X (eg. X= 0.99 and Y=0.01), so the sum would be REALLY close to 100. Moving the values in tiny increments would give us every possible value between 100 and 200, but NOT 100 or 200. Thus, Roman Numerals II and III are possible, while Roman Numeral I is not.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Thu Aug 04, 2016 9:57 pm

It might be easier to say that

x + y = 1

so

100x + 100y = 100

and

100x + 200y = 100x + 100y + 100y = 100 + 100y

So we have everything in terms of one variable. Then we know that y > 0, so 100 + 100y > 100 + 100*0, meaning our solution must be greater than 100.

We also know that x > 0, so 1 > y. That means 100 + 100y < 100 + 100, so our answer must be less than 200.

From here, anything between 100 and 200 is fine, so we've got two possible answers of the three given.

Save $100 on any VP online course!

Like this post

Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Thu Aug 04, 2016 10:00 pm

jsfinol wrote:Does anyone know is the score difficulty of this question?

I'd need to see response data, but I'd guess it's around the 50th percentile of the current quant scale, maybe a little higher. (What'd be really interesting is the average time each test taker takes to complete it, though! I'd guess it's more than 2 minutes.)

Save $100 on any VP online course!

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 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