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# If y + | y | = 0, which of the following must be true? (A) y

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If y + | y | = 0, which of the following must be true? (A) y [#permalink]

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18 Aug 2008, 05:59
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If y + | y | = 0, which of the following must be true?
(A) y > 0
(B) y≥0
(C) y < 0
(D) y≤0
(E) y = 0
SVP
Joined: 30 Apr 2008
Posts: 1874
Location: Oklahoma City
Schools: Hard Knocks
Followers: 42

Kudos [?]: 590 [1] , given: 32

Re: Mod DS - confused with OA [#permalink]

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18 Aug 2008, 06:12
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Answer must be D. The absolute value of anything is going to be positive. If y were positive, adding another positive number to it would make the value greater than 1, so y must be negative. But, if y = 0, the 0 + |0| = 0 also. There actually seems to be multiple answers below that MUST be true.

rao_1857 wrote:
If y + | y | = 0, which of the following must be true?
(A) y > 0 y = 2...2 + |2| = 4, not 0
(B) y≥0 y = 0 works, but if y = positive, then same as A which is incorrect
(C) y < 0 This is true, but it doesn't account for y = 0
(D) y≤0 The takes into account all values of y that will make the equation true.
(E) y = 0 This doesn't include all negative numbers, so it is not complete.

I, durgesh, and a few others had a great discussion about the exact same type of question and what does it mean "If [equation], then which of the following MUST be true?" Essentially what we came up with (meaning Durgesh successfully explained to us) is that when you have an equation, treat all values that make that equation true as your "universe". Then pick the answer that includes all possible values of that "universe". Here, D satisfies that.
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Director
Joined: 20 Sep 2006
Posts: 658
Followers: 3

Kudos [?]: 126 [0], given: 7

Re: Mod DS - confused with OA [#permalink]

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18 Aug 2008, 07:07
jallenmorris wrote:
Answer must be D. The absolute value of anything is going to be positive. If y were positive, adding another positive number to it would make the value greater than 1, so y must be negative. But, if y = 0, the 0 + |0| = 0 also. There actually seems to be multiple answers below that MUST be true.

rao_1857 wrote:
If y + | y | = 0, which of the following must be true?
(A) y > 0 y = 2...2 + |2| = 4, not 0
(B) y≥0 y = 0 works, but if y = positive, then same as A which is incorrect
(C) y < 0 This is true, but it doesn't account for y = 0
(D) y≤0 The takes into account all values of y that will make the equation true.
(E) y = 0 This doesn't include all negative numbers, so it is not complete.

I, durgesh, and a few others had a great discussion about the exact same type of question and what does it mean "If [equation], then which of the following MUST be true?" Essentially what we came up with (meaning Durgesh successfully explained to us) is that when you have an equation, treat all values that make that equation true as your "universe". Then pick the answer that includes all possible values of that "universe". Here, D satisfies that.

I see, yeah I was confused between D and E. The reason is because E satisfies the equation as well! But I see your point... and this makes sense why D is the right answer.

Thanks Allen (+1)
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Joined: 19 Mar 2008
Posts: 352
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Kudos [?]: 62 [0], given: 0

Re: Mod DS - confused with OA [#permalink]

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18 Aug 2008, 08:29
If y + | y | = 0, which of the following must be true?
(A) y > 0
if y > 0, l y l >0, then y + | y | will not be 0
So (A) can never be true

(B) y≥0
if y = -1
y + | y | = -1 + 1 = 0
So y ≥ 0 is not always true

(C) y < 0
if y = 0
y + | y | = 0
So y < 0 is not always true

(D) y≤0
See (A), since y cannot be > 0
y≤0 must always be true

(E) y = 0
y can be any negative number. So y = 0 is not always true

Ans is (D)
Director
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Posts: 658
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Kudos [?]: 126 [0], given: 7

Re: Mod DS - confused with OA [#permalink]

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18 Aug 2008, 13:01
thanks for clarifying !!!
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Re: Mod DS - confused with OA [#permalink]

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18 Aug 2008, 13:12
rao_1857 wrote:
If y + | y | = 0, which of the following must be true?
(A) y > 0
(B) y≥0
(C) y < 0
(D) y≤0
(E) y = 0

D. y + | y | = 0 is possible only if y ≤ 0
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Re: Mod DS - confused with OA   [#permalink] 18 Aug 2008, 13:12
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