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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

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14 00:00

Difficulty:   55% (hard)

Question Stats: 64% (01:51) correct 36% (02:10) wrong based on 335 sessions

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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 V
Joined: 04 Jan 2015
Posts: 3158
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

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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  G
Joined: 29 Dec 2017
Posts: 374
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33 GMAT 2: 690 Q47 V37 GMAT 3: 710 Q50 V37 GPA: 3.25
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Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

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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

Manager  S
Joined: 07 Feb 2017
Posts: 175
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

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2
1
300x+200(2-x)
400+100x
x>0

Posted from my mobile device
VP  D
Joined: 31 Oct 2013
Posts: 1489
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]

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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  G
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Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

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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
Intern  B
Joined: 04 Jun 2018
Posts: 25
Location: Viet Nam
Concentration: Strategy, Operations
Schools: Rotman '22 (A\$)
GMAT 1: 610 Q47 V27 GMAT 2: 620 Q46 V29 GMAT 3: 680 Q47 V36 Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

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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  S
Joined: 29 Sep 2017
Posts: 114
Location: United States
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

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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.
Manager  G
Status: Enjoying the Journey
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Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

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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 Manager  G
Status: Enjoying the Journey
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WE: Marketing (Consulting)
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

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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
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

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1
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.
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Manager  G
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Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

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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
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

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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. _________________
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Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

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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  B
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Posts: 25
Location: India
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Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

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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  P
Joined: 07 Dec 2014
Posts: 1218
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

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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
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Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

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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  V
Joined: 27 May 2012
Posts: 945
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

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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 V
Joined: 02 Sep 2009
Posts: 59561
Re: If x and y are positive numbers such that x + y = 2, then which of the  [#permalink]

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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
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