GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 07 Dec 2019, 04:47 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If x and y are positive numbers such that x + y = 1, which of the

Author Message
TAGS:

### Hide Tags

Senior Manager  B
Joined: 10 Mar 2013
Posts: 461
Location: Germany
Concentration: Finance, Entrepreneurship
Schools: WHU MBA"20 (A$) GMAT 1: 580 Q46 V24 GPA: 3.88 WE: Information Technology (Consulting) If x and y are positive numbers such that x + y = 1, which of the [#permalink] ### Show Tags 17 145 00:00 Difficulty:   55% (hard) Question Stats: 69% (01:58) correct 31% (02:23) wrong based on 2451 sessions ### HideShow timer Statistics 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 ##### Most Helpful Expert Reply Veritas Prep GMAT Instructor V Joined: 16 Oct 2010 Posts: 9850 Location: Pune, India Re: If x and y are positive numbers such that x + y = 1, which of the [#permalink] ### Show Tags 52 34 BrainLab wrote: 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) _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > ##### Most Helpful Community Reply Manager  Joined: 29 Jul 2015 Posts: 152 Re: If x and y are positive numbers such that x + y = 1, which of the [#permalink] ### Show Tags 47 1 15 BrainLab wrote: 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 Given that x + y = 1 or x= 1-y we need to find possible values of 100x + 200y plugging in x from above, 100(1-y) + 200y or 100 + 100 y Now check for each value 1) 100+100y=80 Not possible because y would become negative in this case 2) 100+100y=140 y=40/100 = 2/5 so x =3/5 Possible 3) 100+100y = 199 y=99/100 so x=1/100 Possible Answer:- E ##### General Discussion Senior Manager  B Joined: 10 Mar 2013 Posts: 461 Location: Germany Concentration: Finance, Entrepreneurship Schools: WHU MBA"20 (A$)
GMAT 1: 580 Q46 V24 GPA: 3.88
WE: Information Technology (Consulting)
Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

### Show Tags

1
Solved this one using min/max principle...

1. 80 < min 100*0,9=90 x
2. 100*0,99=99, 200*0,01=2 ok
3. 200*0,99=198 + 100*0,01=1 =>199 ok (E)
Intern  Joined: 08 Sep 2015
Posts: 2
Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

### Show Tags

2
1
100x+200y = 100(x+y) + 100y
Given X+Y =1,
100x+200y = 100 + 100y
And Y's range is 0<Y<1,
Only options II and III are correct.
Intern  Joined: 06 May 2015
Posts: 12
Location: United States
Concentration: Operations, Other
GPA: 3.39
If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

### Show Tags

9
5
given, x+y=1 [0<x,y<1]

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

100(1+y) can be of any value more than 100 and less than 200, only II and III match with this.

E
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9850
Location: Pune, India
Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

### Show Tags

15
3
BrainLab wrote:
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

Another method is to take extreme values of x and y to figure out the range

x + y = 1
Say x is almost 1 (infinitesimally smaller than 1) and y is almost 0 (infinitesimally greater than 0)
Then 100x + 200y = 100*1 + 100*0 = approx. 100

Say y is almost 1 (infinitesimally smaller than 1) and x is almost 0 (infinitesimally greater than 0)
Then 100x + 200y = 100*0 + 200*1 = approx. 200

Now if x = 1/2 and y is 1/2,
Then 100x + 200y = 100*(1/2) + 200*(1/2) = 150

So we see that value of the expression will vary from 100 to 200.

_________________
Karishma
Veritas Prep GMAT Instructor

Intern  Joined: 15 Mar 2016
Posts: 3
GMAT 1: 610 Q37 V37 GPA: 3.6
Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

### Show Tags

VeritasPrepKarishma

How did you know that the weighted average method applies to this problem?
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9850
Location: Pune, India
Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

### Show Tags

2
acomas wrote:
VeritasPrepKarishma

How did you know that the weighted average method applies to this problem?

It's a lot about familiarity achieved through practice. x and y are given to be positive and x + y = 1 is given. Then you are given (100x + 200y). In all, it reminds one of the weighted average formula terms.

But if it doesn't come to your mind, it is alright. That is why I have shown the other method too.
_________________
Karishma
Veritas Prep GMAT Instructor

Intern  Joined: 02 Jun 2015
Posts: 12
If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

### Show Tags

5
1
You can solve it pretty quickly using regular algebra and subtracting 2 equations to isolate a variable.

Keep in mind the given fact that both x and y are positive.

Eq 1: x + y = 1

Eq 2: 100x + 200y = ?

There are 3 possible solutions to Eq 2 given the question: I. 80; II. 140; III. 199

Plug in each scenario into Eq 2, reduce, then subtract Eq 1.

Scenario I: 100x + 200y = 80; or x + 2y = 0.8. Subtract Eq 1 (x+y=1) to isolate what y equals. This gives y = -0.2 which violates the given info.

Scenarios II and III yield solutions greater than 1, so when you subtract Eq 1 you get a positive value for y (edit: positive value that is less than 1). Therefore both II and III are valid.
Intern  Joined: 01 May 2015
Posts: 36
Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

### Show Tags

4
x + y = 1

So, x = 1-y

Substituting in 100x + 200y:
100(1-y) + 200y
100 +100y
100(1+y)

Since y is positive, so clearly 100(1+y) cannot be less than 100. Hence, it cannot be 80. 140 and 199 are possible. So, E.
Manager  Status: 2 months to go
Joined: 11 Oct 2015
Posts: 103
GMAT 1: 730 Q49 V40 GPA: 3.8
If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

### Show Tags

1
BrainLab wrote:
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

x+y=1
100x+100y=100
200x+200y=200

Since both values could be close to 0 (but not 0), we can safely assume that 100<100x+200y<200.
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15661
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

### Show Tags

11
1
Hi All,

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.

GMAT assassins aren't born, they're made,
Rich
_________________
Current Student D
Joined: 12 Aug 2015
Posts: 2548
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

### Show Tags

1
Here we need to get the value of 100x+200y
hmm..
Let us calculate the boundary for 100x+200y
x+y=1
100x+100y=100
hence 100x+200y>100
and 100x+200y<200
therefore 100x+200y=> (100,200)
clearly only 2 and third is true
Hence E
_________________
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4125
Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

### Show Tags

2
Top Contributor
1
BrainLab wrote:
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

Given: x + y = 1
Given: x and y are positive numbers. So, if x + y = 1, then x and y are each less than 1

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

Since y is a POSITIVE number and since y < 1, we know that: 0 < 100y < 100
So, 100 < 100 + 100y < 200
In other words 100 + 100y (aka 100x + 200y) can have any value between 100 and 200

NOTE: If anyone needs more convincing, consider these two cases:
case a: If x = 0.6 and y = 0.4, then 100x + 200y = 60 + 80 = 140 (value II)
case b: If x = 0.01 and y = 0.99, then 100x + 200y = 1 + 198 = 199 (value III)

RELATED VIDEO

_________________
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

### Show Tags

1
2
BrainLab wrote:
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

We are given that x and y are positive numbers and that x + y = 1. We must determine possible values of 100x + 200y. An easy way to determine whether 80, 140, or 199 could be values of 100x + 200y is to use the given fact that x + y = 1 to determine the possible range of 100x + 200y. Since 200 is greater than 100, the high end of our range will be when y is the largest, and the low end of our range will be when x is the largest.

High end of range:

y = 1 and x = 0

100x + 200y = 100(0) + 200(1) = 200

Low end of range:

y = 0 and x = 1

100(1) + 200(0) = 100

Finally we must remember that x and y both must be positive, which means neither x nor y can be zero. They must each be a decimal between zero and one. Thus, the low end of the range cannot actually be 100 and the high end of the range cannot actually be 200. Therefore, we can create the following inequality:

100 < 100x + 200y < 200

Only 140 and 199 are greater than 100 and less than 200.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern  Joined: 07 Oct 2015
Posts: 11
Location: United States
Concentration: Finance, Real Estate
GPA: 3.45
WE: Real Estate (Hospitality and Tourism)
Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

### Show Tags

Will someone confirm that my logic works for this question:

I wanted to find the range of numbers that x could be without testing as that would take a very long time. We know that since x & y are positive integers and together them sum to 1, individually they can range from 0 to 1 as long as the sum is 1. So x could be 1 and y would be 0 or x could be 0 and y would be 1. In order to determine the maximum of the range we would need to apply the largest value (1) to the 200 y. Therefore 100(0) + 200(1)=200. Again, this is the maximum of the range. Also, 100(1) and 200(0)=100, which is the low end of the range. So my answer choices will range from 100 to 200. This eliminates roman numeral 1.

Thoughts with my logic?
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9850
Location: Pune, India
Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

### Show Tags

schelljo wrote:
Will someone confirm that my logic works for this question:

I wanted to find the range of numbers that x could be without testing as that would take a very long time. We know that since x & y are positive integers and together them sum to 1, individually they can range from 0 to 1 as long as the sum is 1. So x could be 1 and y would be 0 or x could be 0 and y would be 1. In order to determine the maximum of the range we would need to apply the largest value (1) to the 200 y. Therefore 100(0) + 200(1)=200. Again, this is the maximum of the range. Also, 100(1) and 200(0)=100, which is the low end of the range. So my answer choices will range from 100 to 200. This eliminates roman numeral 1.

Thoughts with my logic?

Your logic is perfectly correct. This is nothing but weighted average in your own words. The weight from 0 to 1 has to be allotted to 100 and 200. You could allot the entire 1 to 100 in which case you get the minimum or you could allot the entire 1 to 200 in which case you get the maximum. The overall sum will lie between 100 and 200 only.
_________________
Karishma
Veritas Prep GMAT Instructor

Intern  S
Status: One more try
Joined: 01 Feb 2015
Posts: 37
Location: India
Concentration: General Management, Economics
WE: Corporate Finance (Commercial Banking)
Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

### Show Tags

BrainLab wrote:
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

x+y=1
100(x+y)=100
Hence i is ruled out
_________________
Believe you can and you are halfway there-Theodore Roosevelt
Director  G
Joined: 02 Sep 2016
Posts: 641
Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

### Show Tags

Only algebra comes to my mind while I come across such questions. x+y=1
100(x+2y)

100(2-x)

Option 1 will give positive x but negative y. Hence not correct. Only options 2 and 3 are correct. Re: If x and y are positive numbers such that x + y = 1, which of the   [#permalink] 09 Sep 2017, 23:17

Go to page    1   2    Next  [ 31 posts ]

Display posts from previous: Sort by

# If x and y are positive numbers such that x + y = 1, which of the  