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

 It is currently 19 Sep 2019, 14:17

### 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

# If x and y are positive numbers such that x + y = 2, then which of the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3024
If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

30 Jun 2018, 11:07
12
00:00

Difficulty:

55% (hard)

Question Stats:

65% (01:51) correct 35% (02:10) wrong based on 328 sessions

### HideShow timer Statistics

Question-1

If x and y are positive numbers such that x + y = 2, then which of the following could be the value of 300x+200y?
1. 156
2. 397
3. 533

Options

A. I only
B. II only
C. III only
D. I and II
E. II and III

_________________
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3024
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

04 Jul 2018, 03:23
6
2

Solution

Given:
• x and y are positive integers
• x + y = 2

To find:
• From the given options, which one could be the value of 300x + 200y

Approach and Working:
We can rewrite the given expression 300x + 200y in the following manner:
• 300x + 200y = 200x + 200y + 100x = 100x + 200 (x + y) = 100x + 200*2 = 100x + 400

Now, as x is positive, 100x > 0
• Hence, 400 + 100x > 400

Only one value is more than 400 (i.e. 533)

Hence, the correct answer is option C.

_________________
##### General Discussion
Senior Manager
Joined: 29 Dec 2017
Posts: 380
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33
GMAT 2: 690 Q47 V37
GMAT 3: 710 Q50 V37
GPA: 3.25
WE: Marketing (Telecommunications)
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

30 Jun 2018, 15:16
2
300x+200y =200*(3x+2y)=200(2x+2y+x)=200(2+x)=400+200x - so the value will depend on x only

We are given that x and y are positive numbers such that x + y = 2

x will be min = 0.00..1 when y=1.99...9
x will be max = 1.99...9 when y=0.00..1

Obviously 400<400+200x<800 . Only 533 is in that range

Answer C. III only
Manager
Joined: 07 Feb 2017
Posts: 180
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

30 Jun 2018, 16:07
2
1
300x+200(2-x)
400+100x
x>0
Answer C. Greater than 400

Posted from my mobile device
VP
Joined: 31 Oct 2013
Posts: 1456
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

30 Jun 2018, 18:55
2
EgmatQuantExpert wrote:

Question-1

If x and y are positive numbers such that x + y = 2, then which of the following could be the value of 300x+200y?
1. 156
2. 397
3. 533

Options

A. I only
B. I only
C. III only
D. I and II
E. II and III

This question is designed based on weighted average method. This question can be solved easily following few steps.

Given,

300x + 200y

= $$\frac{600x + 400y}{2}$$
=$$\frac{600x + 400y}{x+y}$$

Now we know that weighted average value must be between 400 to 600 where x and y are their weights.

533 falls between 400 to 600.

Only option match is C.
Manager
Status: Enjoying the Journey
Affiliations: ND
Joined: 26 Sep 2017
Posts: 114
Schools: Rotman '21
WE: Marketing (Consulting)
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

01 Jul 2018, 12:15
1
both x & y are positive numbers meanwhile their sum equals to 2
Therefore, x&y could be (1,1)or (0,2) or (2,0)

therefore 300x+200y= 300(1)+200(1)= 500
Or = 300(0)+200(2)= 400
Or = 300(2)+200(0)=600

Therefore, C is the correct answer, as all the answers are greater than 400
_________________
"it takes more time to fix a mistake than to avoid one"
"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

High achievement always takes place in the framework of high expectation Charles Kettering
If we chase perfection we can catch excellence Vince Lombardi

GMAT Club Live: 5 Principles for Fast Math: https://gmatclub.com/forum/gmat-club-live-5-principles-for-fast-math-251028.html#p1940045
YouTube sessions by GMATNinja: https://gmatclub.com/forum/verbal-live-with-gmat-ninja-sc-pronouns-that-parallelism-250568.html#p1936104
The Best SC strategies - Amazing 4 videos by Veritas: https://gmatclub.com/forum/the-best-sc-strategies-amazing-4-videos-by-veritas-250377.html#p1934575
Intern
Joined: 04 Jun 2018
Posts: 24
Location: Viet Nam
Concentration: International Business, Operations
GMAT 1: 610 Q47 V27
GMAT 2: 620 Q46 V29
WE: Supply Chain Management (Internet and New Media)
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

02 Jul 2018, 07:59
1
x + y = 2 => x = 2-y and y = 2-x

x, y are positive numbers => $$0\leq{x}$$ < 2 and $$0\leq{y}$$ <2

300x+200y = 300(2-y)+200y = 600-100y. Because $$0\leq{y}$$ <2 => 600-100y < 600 (1)

300x+200y = 300x+200(2-x)=400+100x. Because $$0\leq{x}$$ => 400 + 100x > 400 (2)

Combine (1) and (2), the answer falls between 400 and 600, hence the correct answer is 533 (Option C)
Manager
Joined: 29 Sep 2017
Posts: 115
Location: United States
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

02 Jul 2018, 09:15
NDND wrote:
both x & y are positive numbers meanwhile their sum equals to 2
Therefore, x&y could be (1,1)or (0,2) or (2,0)

therefore 300x+200y= 300(1)+200(1)= 500
Or = 300(0)+200(2)= 400
Or = 300(2)+200(0)=600

Therefore, C is the correct answer, as all the answers are greater than 400

IIRC, 0 is neither positive nor negative (it is however even) so you cannot set one of the variables to 0 as the stem states that x and y are positive numbers.
_________________
If this helped, please give kudos!
Manager
Status: Enjoying the Journey
Affiliations: ND
Joined: 26 Sep 2017
Posts: 114
Schools: Rotman '21
WE: Marketing (Consulting)
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

03 Jul 2018, 11:31
strivingFor800 wrote:
NDND wrote:
both x & y are positive numbers meanwhile their sum equals to 2
Therefore, x&y could be (1,1)or (0,2) or (2,0)

therefore 300x+200y= 300(1)+200(1)= 500
Or = 300(0)+200(2)= 400
Or = 300(2)+200(0)=600

Therefore, C is the correct answer, as all the answers are greater than 400

IIRC, 0 is neither positive nor negative (it is however even) so you cannot set one of the variables to 0 as the stem states that x and y are positive numbers.

I guess you are right, which means that the only option we have is (1,1), and this would save us at least half the time, right?

Thanks for correcting me
_________________
"it takes more time to fix a mistake than to avoid one"
"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

High achievement always takes place in the framework of high expectation Charles Kettering
If we chase perfection we can catch excellence Vince Lombardi

GMAT Club Live: 5 Principles for Fast Math: https://gmatclub.com/forum/gmat-club-live-5-principles-for-fast-math-251028.html#p1940045
YouTube sessions by GMATNinja: https://gmatclub.com/forum/verbal-live-with-gmat-ninja-sc-pronouns-that-parallelism-250568.html#p1936104
The Best SC strategies - Amazing 4 videos by Veritas: https://gmatclub.com/forum/the-best-sc-strategies-amazing-4-videos-by-veritas-250377.html#p1934575
Manager
Status: Enjoying the Journey
Affiliations: ND
Joined: 26 Sep 2017
Posts: 114
Schools: Rotman '21
WE: Marketing (Consulting)
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

04 Jul 2018, 09:00
EgmatQuantExpert wrote:

Solution

Given:
• x and y are positive integers
• x + y = 2

To find:
• From the given options, which one could be the value of 300x + 200y

Approach and Working:
We can rewrite the given expression 300x + 200y in the following manner:
• 300x + 200y = 200x + 200y + 100x = 100x + 200 (x + y) = 100x + 200*2 = 100x + 400

Now, as x is positive, 100x > 0
• Hence, 400 + 100x > 400

Only one value is more than 400 (i.e. 533)

Hence, the correct answer is option C.

Thanks

EgmatQuantExpert could you comment on the approach used on this post? https://gmatclub.com/forum/if-x-and-y-a ... l#p2088234

Is it ok?

Thx
_________________
"it takes more time to fix a mistake than to avoid one"
"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

High achievement always takes place in the framework of high expectation Charles Kettering
If we chase perfection we can catch excellence Vince Lombardi

GMAT Club Live: 5 Principles for Fast Math: https://gmatclub.com/forum/gmat-club-live-5-principles-for-fast-math-251028.html#p1940045
YouTube sessions by GMATNinja: https://gmatclub.com/forum/verbal-live-with-gmat-ninja-sc-pronouns-that-parallelism-250568.html#p1936104
The Best SC strategies - Amazing 4 videos by Veritas: https://gmatclub.com/forum/the-best-sc-strategies-amazing-4-videos-by-veritas-250377.html#p1934575
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3024
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

05 Jul 2018, 04:23
1
Manager
Status: Enjoying the Journey
Affiliations: ND
Joined: 26 Sep 2017
Posts: 114
Schools: Rotman '21
WE: Marketing (Consulting)
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

05 Jul 2018, 11:29
EgmatQuantExpert wrote:
NDND wrote:

Thanks

EgmatQuantExpert could you comment on the approach used on this post? https://gmatclub.com/forum/if-x-and-y-a ... l#p2088234

Is it ok?

Thx

Hey NDND,
can you specify which solution you are referring to? The link you have provided somehow reverts back to the above post only.

Here you go:

both x & y are positive numbers meanwhile their sum equals to 2
Therefore, x&y could be (1,1)or (0,2) or (2,0)

therefore 300x+200y= 300(1)+200(1)= 500
Or = 300(0)+200(2)= 400
Or = 300(2)+200(0)=600

Therefore, C is the correct answer, as all the answers are greater than 400
_________________
"it takes more time to fix a mistake than to avoid one"
"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

High achievement always takes place in the framework of high expectation Charles Kettering
If we chase perfection we can catch excellence Vince Lombardi

GMAT Club Live: 5 Principles for Fast Math: https://gmatclub.com/forum/gmat-club-live-5-principles-for-fast-math-251028.html#p1940045
YouTube sessions by GMATNinja: https://gmatclub.com/forum/verbal-live-with-gmat-ninja-sc-pronouns-that-parallelism-250568.html#p1936104
The Best SC strategies - Amazing 4 videos by Veritas: https://gmatclub.com/forum/the-best-sc-strategies-amazing-4-videos-by-veritas-250377.html#p1934575
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3024
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

06 Jul 2018, 04:14
1
NDND wrote:

Here you go:

both x & y are positive numbers meanwhile their sum equals to 2
Therefore, x&y could be (1,1)or (0,2) or (2,0)

therefore 300x+200y= 300(1)+200(1)= 500
Or = 300(0)+200(2)= 400
Or = 300(2)+200(0)=600

Therefore, C is the correct answer, as all the answers are greater than 400

Although the approach and final answer is absolutely correct, there is a very small error in the calculation part. In the question it was mentioned that both x and y are positive integers, hence they are always greater than 0.

• Non-negative integers (Whole Numbers) start from 0.
• Positive integers (Natural Numbers) start from 1.

As both x and y are positive integers, they can't be equal to 0, hence, the only possible case will be (1, 1). You have identified that also in one of your previous replies.
_________________
LBS Moderator
Joined: 04 Jun 2018
Posts: 634
Location: Germany
Concentration: General Management, Finance
GMAT 1: 730 Q47 V44
GPA: 3.4
WE: Analyst (Transportation)
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

23 Jul 2018, 14:03
EgmatQuantExpert wrote:

Question-1

If x and y are positive numbers such that x + y = 2, then which of the following could be the value of 300x+200y?
1. 156
2. 397
3. 533

Options

A. I only
B. I only

C. III only
D. I and II
E. II and III

Good question, but could you adjust the answer choices to reflect different statements for A. & B.?
_________________
Intern
Joined: 08 Jul 2018
Posts: 25
Location: India
Concentration: General Management, Marketing
GPA: 4
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

23 Jul 2018, 15:40
1
You don't have to solve for x&y or even suppose values.

given: that x + y = 2,
to find: possible values for 300x+200y?

Solution:
300x+200y = 100x + 200(x+y) = 100x + 200(2) = 100x + 400

Since x is a +ve value, so whatever it may be, it won't reduce the value of the equation from 400 in any case

So, any solution would have 2 be more than 400, which leaves us with just Option 3!
VP
Joined: 07 Dec 2014
Posts: 1233
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

23 Jul 2018, 22:01
EgmatQuantExpert wrote:

Question-1

If x and y are positive numbers such that x + y = 2, then which of the following could be the value of 300x+200y?
1. 156
2. 397
3. 533

Options

A. I only
B. I only
C. III only
D. I and II
E. II and III

if x+y=2,
then 300x+300y=600
testing options:
1. subtracting 300x+200y=156,
100y=600-156=444
y=4.44 NO, must be less than 2
2. subtracting 300x+200y=397,
100y=600-397=203
y=2.03 NO, must be less than 2
subtracting 300x+200y=533,
100y=600-533=67
y=.67 YES, less than 2
III only
C
Intern
Joined: 06 Dec 2016
Posts: 24
Location: India
Concentration: Technology, Sustainability
WE: Engineering (Energy and Utilities)
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

23 Jul 2018, 23:34
Given,

X+Y=2.................1)
300x+200Y=?

Multiplying Eqn 1) with 2 ,
200X+200Y=200x2=400..............2)
Add another 100X to the equation derived.
300X+200Y=400+100X
It is going to be greater than 400 since X is positive.

_________________
War with the clock!
Director
Joined: 27 May 2012
Posts: 852
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

17 Dec 2018, 06:41
1
EgmatQuantExpert wrote:

Question-1

If x and y are positive numbers such that x + y = 2, then which of the following could be the value of 300x+200y?
1. 156
2. 397
3. 533

Options

A. I only
B. I only
C. III only
D. I and II
E. II and III

Dear Moderator,
Came across this question, if you see the answer choices , option A and B have the same choices , making it look awkward. Hope we can do something about it. Thank you.
_________________
- Stne
Math Expert
Joined: 02 Sep 2009
Posts: 58117
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

### Show Tags

17 Dec 2018, 06:45
stne wrote:
EgmatQuantExpert wrote:

Question-1

If x and y are positive numbers such that x + y = 2, then which of the following could be the value of 300x+200y?
1. 156
2. 397
3. 533

Options

A. I only
B. I only
C. III only
D. I and II
E. II and III

Dear Moderator,
Came across this question, if you see the answer choices , option A and B have the same choices , making it look awkward. Hope we can do something about it. Thank you.

_________________
Edited. Thank you.
_________________
Re: If x and y are positive numbers such that x + y = 2, then which of the   [#permalink] 17 Dec 2018, 06:45
Display posts from previous: Sort by

# If x and y are positive numbers such that x + y = 2, then which of the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne