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

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

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30 Jun 2018, 11:07
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Difficulty:

55% (hard)

Question Stats:

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

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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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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.

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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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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

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

Posted from my mobile device
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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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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.
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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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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
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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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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)
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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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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.
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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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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
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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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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
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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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05 Jul 2018, 04:23
1
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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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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
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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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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.
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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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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.?
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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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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!
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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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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
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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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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.

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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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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.
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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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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.

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Edited. Thank you.
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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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