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

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

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New post 22 Oct 2017, 07:14
I solved this question using a very simple technique.
you have an equation given which is x+y=1. Now your second equation would be 100x+200y= ? ( put in one of the answer choice and solve for either x or y)
for option A you will get -ve value which can not be true as the question clearly states that x and y are positive. try out for other options...
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If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

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New post 22 Oct 2017, 07:23
It's a simple one.

Given that x+y=1

100x+200y=?

Ans: 100(x+2y)
=100(x+y+y)
=100(1+y)
Now if x and y are positive numbers: 0<y<1

Hence II and III
-E

+1 for Kudos
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Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

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New post 26 Nov 2017, 03:10
VeritasPrepKarishma wrote:
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.

Hence answer will be (E)

karishma hello :) why are you multiplying by 0. Zero is neither negative nor positive. No ? :? and condition says that "x and y are positive numbers" :-) have a great day!
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Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

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New post 26 Nov 2017, 03:15
dave13 wrote:
VeritasPrepKarishma wrote:
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.

Hence answer will be (E)

karishma hello :) why are you multiplying by 0. Zero is neither negative nor positive. No ? :? and condition says that "x and y are positive numbers" :-) have a great day!



Since we know that x and y are positive numbers but may not be integers, we have assumed that x is very close to 0 but not 0 e.g. x = 0.000000001 (which is a positive number).
100 multiplied by this will become 0.0000001 which is almost 0.
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Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

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New post 14 Dec 2018, 04:45
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


Bunuel and VeritasKarishma

Can u guys post the links of few similar questions like this.. Please.
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Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

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New post 26 Mar 2019, 02:02
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


If 0<x, 0<y, & x+y=1, systematically breakdown possible scenarios where this is true:
.1 + .9 = 1
.2 + .8 = 1
.3 + .7 = 1
.4 + .6 = 1
.5 + .5 = 1

if you quickly apply this range of possible values to x & y, 100x + 200y cant possibly equal 80. If I am overgeneralizing, please let me know. But if my understanding is correct, this is probably the best approach to saving time and keeping things simple.
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Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

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New post 26 Mar 2019, 13:15
Hi aaronhew,

YES - thinking about the information in this prompt in this way IS a fast way to deal with the given information. In the broader sense, you're thinking in terms of the 'limits' of what's possible.

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 lower and upper "boundaries" to the possible sum.

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

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New post 26 Mar 2019, 17:56
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


if x+y=1,
then 100x+100y=100
thus, 100x+200y>100
ll and lll
E
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Re: If x and y are positive numbers such that x + y = 1, which of the  [#permalink]

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New post 12 May 2019, 01:17
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
=>x=1-y

Now,
100(1-y)+200y
=>100-100y+200y
=>100+100y
=>100(1+y)

Both x & y are positive
Now we test the value:
If y=.2
100*1.2=120 it means that the value must be greater than 100 but less than 200.

140 & 199 are the possible values

Answer is E

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

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New post 02 Jun 2019, 03:04
If x and y > 0 and x+y=1 (or x=1-y), then

100x+200y => 100(1-y)+200y => 100y+100, which means we won't end up with a result less than 100 -- so 80 is out

II and III are the answers => E
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Re: If x and y are positive numbers such that x + y = 1, which of the   [#permalink] 02 Jun 2019, 03:04

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