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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 &nbs [#permalink] 26 Nov 2017, 03:15

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