Last visit was: 19 Nov 2025, 15:00 It is currently 19 Nov 2025, 15:00
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
   1   2 
555-605 Level|   Algebra|   Inequalities|   Number Properties|                              
User avatar
suganyam
User avatar
Joined: 19 Jan 2019
Last visit: 01 Oct 2022
Posts: 40
Own Kudos:
9
 [1]
Given Kudos: 65
Products:
My Reviews
Posts: 40
Kudos: 9
 [1]
If x and y are positive numbers such that x + y = 1, which of the 04 Feb 2020, 05:46
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
x+y= 1 -->x=1-y --->100(x+2y) 100(1-y+2y)--> 100+100y so any value greater than 100 for sure
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,784
Own Kudos:
12,807
 [2]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,784
Kudos: 12,807
 [2]
If x and y are positive numbers such that x + y = 1, which of the 04 Feb 2020, 12:24
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
suganyam
x+y= 1 -->x=1-y --->100(x+2y) 100(1-y+2y)--> 100+100y so any value greater than 100 for sure
Show more

Hi suganyam,

Based on the way that the overall prompt is written, your deduction (above) is fine. However, it's not completely accurate - and on other types of questions, that type of generality could lead you to choose a wrong answer. There is an 'upper-limit' to how high 100+100Y can be in this question, meaning that it's more appropriate to say that that value is greater than 100 AND less than 200.

GMAT assassins aren't born, they're made,
Rich
User avatar
Target4bschool
User avatar
Joined: 29 Dec 2019
Last visit: 19 Nov 2025
Posts: 61
Own Kudos:
64
Given Kudos: 181
Schools: IE MiM (Sep 21 Start) (A)
Schools: IE MiM (Sep 21 Start) (A)
Posts: 61
Kudos: 64
If x and y are positive numbers such that x + y = 1, which of the 29 Oct 2020, 13:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
IanStewart please help if there is an easy solution for this category of que.
User avatar
IanStewart
User avatar
GMAT Tutor
Joined: 24 Jun 2008
Last visit: 18 Nov 2025
Posts: 4,145
Own Kudos:
10,989
 [1]
Given Kudos: 99
Expert
Expert reply
Posts: 4,145
Kudos: 10,989
 [1]
If x and y are positive numbers such that x + y = 1, which of the 29 Oct 2020, 16:37
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Target4bschool
IanStewart please help if there is an easy solution for this category of que.
Show more

The question is really identical to this one: x% of employees are men and the rest, y%, are women. If men make $100 per hour and women make $200 per hour, what could be the average hourly wage for all employees? Or at least it's identical if you think of your percentages as decimals (so you think of "10%" as "0.1"). So it's just a weighted average, and the answer can be anything between 100 and 200. That's the fastest way to look at the problem (but I'm really just saying exactly what Karishma already wrote at the top of this thread).

You can also use substitution (y = 1 - x, then plug that into 100x + 200y to get 200 - 100x) to quickly see what values are possible -- you just have to remember that the value of x is between 0 and 1.
avatar
WizakoVignesh
avatar
Joined: 03 Jan 2021
Last visit: 19 Apr 2021
Posts: 2
Own Kudos:
4
 [2]
Given Kudos: 1
Location: India
Posts: 2
Kudos: 4
 [2]
If x and y are positive numbers such that x + y = 1, which of the 04 Jan 2021, 02:35
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given Condition: x + y = 1
Therefore, the values of x and y lie between 0 and 1.
i.e., 0 < (x, y) < 1

100x + 200y
= 100(x + 2y)
= 100(x + y + y)
= 100(1 + y)

100x + 200y = 100(1 + y)
Because y lies between 0 and 1, the value of 1 + y is greater than 1 and lesser than 2.
From the above expression, it is evident that the value of 100(1 + y) is greater than 100 and lesser than 200. i.e., 100 < 100(1 + y) < 200

From the given answer options, II and III satisfy the above condition.

Choice E is the correct answer.
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 19 Nov 2025
Posts: 6,839
Own Kudos:
16,354
 [1]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,839
Kudos: 16,354
 [1]
If x and y are positive numbers such that x + y = 1, which of the 27 May 2021, 08:31
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
BrainLab
If x and y are positive numbers such that x + y = 1, which of the following could be the value of 100x + 200y?

I. 80
II. 140
III. 199

(A) II only
(B) III only
(C) I and II
(D) I and III
(E) II and III
Show more


Answer: Option E

Video solution by GMATinsight

User avatar
CrackverbalGMAT
User avatar
Major Poster
Joined: 03 Oct 2013
Last visit: 19 Nov 2025
Posts: 4,844
Own Kudos:
8,945
Given Kudos: 225
Affiliations: CrackVerbal
Location: India
Expert
Expert reply
Posts: 4,844
Kudos: 8,945
If x and y are positive numbers such that x + y = 1, which of the 30 Aug 2021, 11:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given that x and y are positive numbers such that x + y = 1 ==> x= 1 - y

100x + 200y = 100(1-y) + 200y

100-100y + 200y = 100 + 100y

Y could be any decimal between 0 and 1.
We can conclude that

100 < 100 + 100y < 200
==> 100 < 100x + 200y < 200

I. 80 Its not possible as 80 is not in the range
II. 140 Possible when y = .4
III. 199 Possible when y = .99

Option E is the right answer.

Thanks,
Clifin J Francis,
GMAT SME
User avatar
avigutman
User avatar
Joined: 17 Jul 2019
Last visit: 30 Sep 2025
Posts: 1,293
Own Kudos:
1,931
Given Kudos: 66
Location: Canada
Schools: NYU Stern (WA)
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert
Expert reply
Schools: NYU Stern (WA)
GMAT 3: 770 Q50 V45
Posts: 1,293
Kudos: 1,931
If x and y are positive numbers such that x + y = 1, which of the 20 Dec 2021, 05:31
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
User avatar
CrushTHYGMAT
User avatar
Joined: 06 May 2021
Last visit: 16 May 2023
Posts: 59
Own Kudos:
23
Given Kudos: 36
Location: India
GMAT 1: 680 Q48 V35
GMAT 1: 680 Q48 V35
Posts: 59
Kudos: 23
If x and y are positive numbers such that x + y = 1, which of the 23 Jan 2022, 03:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi,

Can someone please evaluate my approach? avigutman, ScottTargetTestPrep

We are given that x + y = 1. I can arrive at x = 1 - y, and plug 1- y for x in the equation:

100(1-y) + 200y
100-100y+200y
100+100y
100(1+y)

Now, if 100(1+y) were to equal to 80, then y's value would become negative. Since y is positive, we know that 80 can't be the possible value.

100(1+y)=80
1+y=80/100
1+y=.8
y=.8-1
y= -.2

However, if I set the equation 100(1+y) equal to 140 or 199, then the value that we get for y is positive, and hence, those two values work.

Please let me know if my logic is correct.
User avatar
avigutman
User avatar
Joined: 17 Jul 2019
Last visit: 30 Sep 2025
Posts: 1,293
Own Kudos:
1,931
 [1]
Given Kudos: 66
Location: Canada
Schools: NYU Stern (WA)
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert
Expert reply
Schools: NYU Stern (WA)
GMAT 3: 770 Q50 V45
Posts: 1,293
Kudos: 1,931
 [1]
If x and y are positive numbers such that x + y = 1, which of the 23 Jan 2022, 05:10
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
CrushTHYGMAT


We are given that x + y = 1. I can arrive at x = 1 - y, and plug 1- y for x in the equation:

100(1-y) + 200y
100-100y+200y
100+100y
100(1+y)

Now, if 100(1+y) were to equal to 80, then y's value would become negative. Since y is positive, we know that 80 can't be the possible value.

However, if I set the equation 100(1+y) equal to 140 or 199, then the value that we get for y is positive, and hence, those two values work.

Please let me know if my logic is correct.
Show more

Yes, your logic is sound. Just be careful, if there were options greater or equal to 200 you’d have to eliminate those as we can reason that y is less than 1.

Posted from my mobile device
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 19 Nov 2025
Posts: 21,716
Own Kudos:
26,996
 [2]
Given Kudos: 300
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,716
Kudos: 26,996
 [2]
If x and y are positive numbers such that x + y = 1, which of the 24 Jan 2022, 20:42
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
CrushTHYGMAT
Hi,

Can someone please evaluate my approach? avigutman, ScottTargetTestPrep

We are given that x + y = 1. I can arrive at x = 1 - y, and plug 1- y for x in the equation:

100(1-y) + 200y
100-100y+200y
100+100y
100(1+y)

Now, if 100(1+y) were to equal to 80, then y's value would become negative. Since y is positive, we know that 80 can't be the possible value.

100(1+y)=80
1+y=80/100
1+y=.8
y=.8-1
y= -.2

However, if I set the equation 100(1+y) equal to 140 or 199, then the value that we get for y is positive, and hence, those two values work.

Please let me know if my logic is correct.
Show more

It is a good approach, however, you must also take into account that simply having a positive value for y does not guarantee that the value you are testing is a possible value. What if y turns out to be 1.2, which leads to having x = -0.2? For instance, if 240 were one of the values you had to check, you would solve 100(1 + y) = 240, which gives you y = 1.4. In this case, x = -0.4, which does not work.

You could actually repeat the same process with y = 1 - x. If you did that, 100x + 200y would simplify to 100(2 - x), and any value that you were not able to eliminate in the previous case such as 240, you would be able to eliminate in this step. The values which work in both steps will be your answer.
User avatar
NEYR0N
User avatar
Joined: 12 Feb 2025
Last visit: 18 Nov 2025
Posts: 94
Own Kudos:
9
Given Kudos: 66
Posts: 94
Kudos: 9
If x and y are positive numbers such that x + y = 1, which of the 16 Mar 2025, 08:31
Kudos
Add Kudos
Bookmarks
Bookmark this Post
are there any similar harder questions to this, perhaps you can think of a way the test can trick you with negatives ?
KarishmaB
BrainLab
If x and y are positive numbers such that x + y = 1, which of the following could be the value of 100x + 200y?

I. 80
II. 140
III. 199

(A) II only
(B) III only
(C) I and II
(D) I and III
(E) II and III

There are many ways in which you can deal with this question. A very efficient method is using weighted average concept.

Note that \(100x + 200y = \frac{(100x + 200y)}{1} = \frac{(100x + 200y)}{(x + y)}\)

So the expression is the weighted average of 100 and 200 where x and y are the weights. The weighted average of 100 and 200 will lie between 100 and 200. So it could be 140 and 199 but it cannot be 80.

Answer (E)

Check out the post on weighted averages here:
https://anaprep.com/arithmetic-weighted-averages/
and this video: https://www.youtube.com/watch?v=_GOAU7moZ2Q
Show more
User avatar
findingmyself
User avatar
Joined: 06 Apr 2025
Last visit: 19 Nov 2025
Posts: 230
Own Kudos:
157
Given Kudos: 57
Posts: 230
Kudos: 157
If x and y are positive numbers such that x + y = 1, which of the 11 May 2025, 01:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
A very easy and simple method:

100X+200Y--> 100(X+2Y)---> 100(X+Y+Y)
Since we know X+Y=1--->100(1+Y).
No matter how small Y is, The answer will always be more than 100 with infinite possibilities between (100-200)
Note: If the answer choice had any value above 200, then it wouldn't have to be always true since Y cannot take value more than 1

BrainLab
If x and y are positive numbers such that x + y = 1, which of the following could be the value of 100x + 200y?

I. 80
II. 140
III. 199

(A) II only
(B) III only
(C) I and II
(D) I and III
(E) II and III
Show more
User avatar
HarshavardhanR
User avatar
Joined: 16 Mar 2023
Last visit: 19 Nov 2025
Posts: 426
Own Kudos:
461
Given Kudos: 59
Status:Independent GMAT Tutor
Affiliations: Ex - Director, Subject Matter Expertise at e-GMAT
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 426
Kudos: 461
If x and y are positive numbers such that x + y = 1, which of the 27 Jun 2025, 23:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
x and y are both positive numbers

=> x>0; y>0

x + y = 1

=> x<1; y<1

Neither x nor y can be 1. For example, if x = 1, to satisfy x+y = 1, y would have to be 0. But y is given to be "positive" (0 is not positive). Thus, both x and y <1.

So,

  • 0<x<1
  • 0<y<1

Given sum: 100x + 200y

We can use x+y = 1 to simplify this.

100x + 200y = 100x + 100y + 100y = 100(x+y) + 100y = 100(1) + 100y

So,
100x + 200y = 100 + 100y

(1) because y>0

100 + 100y has to be greater than 100.

So,

100x + 200y > 100.....................(1)

(2) because y<1

100 + 100y has to be lesser than 200.

Why?

If y = 1, then 100+100y = 100+100 = 200. But because y<1, the sum 100+100y has to be <200.

So,

100x + 200y < 200.........................(2)

From (1) and (2)

100 < 100x + 200y < 200

Thus,

(I) 80. Not possible.
(II) 140. Possible.
(III) 199. Also possible.

(II) and (III) only.

---
Harsha
   1   2 
Moderators:
Bunuel
Math Expert
105390 posts
Krunaal
Tuck School Moderator
805 posts