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# If y=−m^2, which of the following must be true?

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If y=−m^2, which of the following must be true? [#permalink]

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01 Jun 2012, 00:55
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If y=−m^2, which of the following must be true?

I. y is negative.
II. m is non-negative.
III. If m is negative then y is negative.

A. I only
B. II only
C. III only
D. I and II only
E. II and III only
[Reveal] Spoiler: OA
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Re: If y=−m^2, which of the following must be true? [#permalink]

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01 Jun 2012, 01:20
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Joy111 wrote:
If y=−m^2, which of the following must be true?

I. y is negative.
II. m is non-negative.
III. If m is negative then y is negative.

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

Tricky question. +1.

If y=−m^2, which of the following must be true?

First of all notice m^2 is always non-negative, so -m^2 is non-positive (zero or negative), which means that y is zero when m=0 and y is negative for ANY other value of m.

I. y is negative --> not necessarily true, if m=0 then y=-m^2=0;

II. m is non-negative. m can take ANY value: positive, negative, zero. We don't have any restrictions on its value;

III. If m is negative then y is negative. m is negative means that m is not zero. As discussed above if m is other than zero (positive or negative) then y is negative: y=-(negative^2)=-positive=negative (y=-(positive^2)=-positive=negative). So, this option is always true.

Hope it's clear.
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Re: If y=−m^2, which of the following must be true? [#permalink]

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01 Jun 2012, 02:14
sorry bunuel for the question.

I pick the right answer in less than minute (practice helps). As such, the second choice when I read m is NON negative I think to 0 or positive, but you say "ANY value" even negative. I'm the first time that encounter this nuance. Can you give me some thoughts ???

Thanks
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Re: If y=−m^2, which of the following must be true? [#permalink]

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01 Jun 2012, 02:24
carcass wrote:
sorry bunuel for the question.

I pick the right answer in less than minute (practice helps). As such, the second choice when I read m is NON negative I think to 0 or positive, but you say "ANY value" even negative. I'm the first time that encounter this nuance. Can you give me some thoughts ???

Thanks

I say that from y=−m^2 we don't have ANY restriction on the value of m, so it can take ANY value: positive, negative or zero. So, option II which says that "m is non-negative" (read zero or positive) is not always true since m can also be negative.
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Re: If y=−m^2, which of the following must be true? [#permalink]

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01 Jun 2012, 02:28
Joy111 wrote:
If y=−m^2, which of the following must be true?

I. y is negative.
II. m is non-negative.
III. If m is negative then y is negative.

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

Condition I
If m=0 then y=0, hence not always true

COndition II
m can be anything, +ve, 0 or -ve. m^2 will be either 0 (for m=0) or +ve

Condition III
if m is -ve (or to say m is less than 0) than m^2 is +ve.
Hence -m^2 is always -ve.
if m is -ve than y IS -ve
Always True
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Re: If y=−m^2, which of the following must be true? [#permalink]

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01 Jun 2012, 03:03
Bunuel wrote:
Joy111 wrote:
If y=−m^2, which of the following must be true?

I. y is negative.
II. m is non-negative.
III. If m is negative then y is negative.

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

Tricky question. +1.

If y=−m^2, which of the following must be true?

First of all notice m^2 is always non-negative, so -m^2 is non-positive (zero or negative), which means that y is zero when m=0 and y is negative for ANY other value of m.

I. y is negative --> not necessarily true, if m=0 then y=-m^2=0;

II. m is non-negative. m can take ANY value: positive, negative, zero. We don't have any restrictions on its value;

III. If m is negative then y is negative. m is negative means that m is not zero. As discussed above if m is other than zero (positive or negative) then y is negative: y=-(negative^2)=-positive=negative (y=-(positive^2)=-positive=negative). So, this option is always true.

Hope it's clear.

If m is positive then too y is negative so statement iii is contradicted ?
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Re: If y=−m^2, which of the following must be true? [#permalink]

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01 Jun 2012, 03:09
Joy111 wrote:
If m is positive then too y is negative so statement iii is contradicted ?

I think you don't understand the question.

Option III says: If m is negative then y is negative --> m=negative --> y=-(negative^2)=-positive=negative. So, you can see that this option is true.

Why do you even bother to consider positive m for this statement? Anyway, even if m=positive then we would have: y=-(positive^2)=-positive=negative.
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Re: If y=−m^2, which of the following must be true? [#permalink]

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01 Jun 2012, 03:42
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Joy111 wrote:
If m is positive then too y is negative so statement iii is contradicted ?

In response to the doubt (also on PM)

Joy the question is asking which must always be true

I will go thru the conditions 1 and 2 once again to help you understand the condition 3

Condition 1 says "y is -ve"
That means it is saying that "y=-m^2" is always -ve
But if m=0 then y becomes 0.
So condition 1 is not true

We rule out choices A and D

Condition 2 says "m is non-negative"
That means it is saying that in "y=-m^2" m is either 0 or +ve
But it is not true, m can be -ve also
From the question stem, there is no restriction on value of m, and hence m can be any number

We rule out choices B and E

solved

Pursuing further
Codition 3: "If m is negative then y is negative."
This condition limits the values of m
It is saying that IF m<0 then y is always -ve
The only time when y is not -ve is when m=0
as the condition says that m is less than 0 (that is to say that m is not 0)

Hence when m is -ve (less than 0) y is -ve
Always True
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Re: If y=−m^2, which of the following must be true? [#permalink]

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01 Jun 2012, 13:33
manulath wrote:
Joy111 wrote:
If m is positive then too y is negative so statement iii is contradicted ?

In response to the doubt (also on PM)

Joy the question is asking which must always be true

I will go thru the conditions 1 and 2 once again to help you understand the condition 3

Condition 1 says "y is -ve"
That means it is saying that "y=-m^2" is always -ve
But if m=0 then y becomes 0.
So condition 1 is not true

We rule out choices A and D

Condition 2 says "m is non-negative"
That means it is saying that in "y=-m^2" m is either 0 or +ve
But it is not true, m can be -ve also
From the question stem, there is no restriction on value of m, and hence m can be any number

We rule out choices B and E

solved

Pursuing further
Codition 3: "If m is negative then y is negative."
This condition limits the values of m
It is saying that IF m<0 then y is always -ve
The only time when y is not -ve is when m=0
as the condition says that m is less than 0 (that is to say that m is not 0)

Hence when m is -ve (less than 0) y is -ve
Always True

I think both of you are correct, I was thinking the question to be " Which of the following is ALWAYS true "

Please correct me if I am wrong .

I) which of the following MUST be true

II) which of the following is ALWAYS true ,

I think for both of these the answer to this question will be different ?
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Re: If y=−m^2, which of the following must be true? [#permalink]

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02 Jun 2012, 06:26
Joy111 wrote:
manulath wrote:
Joy111 wrote:
If m is positive then too y is negative so statement iii is contradicted ?

In response to the doubt (also on PM)

Joy the question is asking which must always be true

I will go thru the conditions 1 and 2 once again to help you understand the condition 3

Condition 1 says "y is -ve"
That means it is saying that "y=-m^2" is always -ve
But if m=0 then y becomes 0.
So condition 1 is not true

We rule out choices A and D

Condition 2 says "m is non-negative"
That means it is saying that in "y=-m^2" m is either 0 or +ve
But it is not true, m can be -ve also
From the question stem, there is no restriction on value of m, and hence m can be any number

We rule out choices B and E

solved

Pursuing further
Codition 3: "If m is negative then y is negative."
This condition limits the values of m
It is saying that IF m<0 then y is always -ve
The only time when y is not -ve is when m=0
as the condition says that m is less than 0 (that is to say that m is not 0)

Hence when m is -ve (less than 0) y is -ve
Always True

I think both of you are correct, I was thinking the question to be " Which of the following is ALWAYS true "

Please correct me if I am wrong .

I) which of the following MUST be true

II) which of the following is ALWAYS true ,

I think for both of these the answer to this question will be different ?

No, they are the same. Option III must be true because it's always true.
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Re: If y=−m^2, which of the following must be true? [#permalink]

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02 Jun 2012, 06:55
hm,

I ignored m=0, since 0 cant have a sign. is it ok to write y=-0!?
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Re: If y=−m^2, which of the following must be true? [#permalink]

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02 Jun 2012, 07:04
LalaB wrote:
hm,

I ignored m=0, since 0 cant have a sign. is it ok to write y=-0!?

y=-0 simply means that y=0, so there is nothing wrong with that.
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Re: If y=−m^2, which of the following must be true? [#permalink]

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02 Jun 2012, 07:13
Bunuel wrote:
LalaB wrote:
hm,

I ignored m=0, since 0 cant have a sign. is it ok to write y=-0!?

y=-0 simply means that y=0, so there is nothing wrong with that.

aha, I found in wiki - http://en.wikipedia.org/wiki/Sign_%28mathematics%29

The number zero is neither positive nor negative, and therefore has no sign. In arithmetic, +0 and −0 both denote the same number 0, and the negation of zero is zero itself.

I thought it is not allowed to write -0 ,since 0 is neither negative, nor positive. but wiki says -0 is ok and it means just 0.
ok, Bunuel, now I agree with u
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Re: If y=−m^2, which of the following must be true? [#permalink]

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19 Jun 2013, 03:53
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: If y=−m^2, which of the following must be true? [#permalink]

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19 Jun 2013, 07:00
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Joy111 wrote:
If y=−m^2, which of the following must be true?

I. y is negative.
II. m is non-negative.
III. If m is negative then y is negative.

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

Given that $$y = -m^2$$

If m=0, then y =0 --> This eliminates option I. Again, m can be a non-negative value as there is no restriction on that, thus statement II gets eliminated.

Multiply both sides by m assuming $$m\neq{0}$$. Thus, $$my = -m^3$$. Now, if m<0,then $$m^3<0$$and $$-m^3>0$$. Hence, as my>0, m and y must have the same sign.

C.
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Re: If y=−m^2, which of the following must be true? [#permalink]

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30 May 2014, 12:26
The biggest issue here is obviously noticing that m could be 0, thus making y=0 as well. The first option is a tricky one, but normally the other options will at least offer a hint and/or insight into the trick. In this case, option II mentions "non-negative," which suggests that the reader considers that m could be 0.

Summary: Read all of the option choices! They're trying to give you hints
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If y=−m2, which of the following must be true? I) y is negative. [#permalink]

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14 Jun 2015, 11:07
If y=−m^2, which of the following must be true?

I) y is negative.

II) m is non-negative.

III) If m is negative then y is negative.

I only

II only

III only

I and II only

II and III only

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Re: If y=−m^2, which of the following must be true? [#permalink]

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14 Jun 2015, 11:14
Saurav Arora wrote:
If y=−m^2, which of the following must be true?

I) y is negative.

II) m is non-negative.

III) If m is negative then y is negative.

I only

II only

III only

I and II only

II and III only

Please refer to the discussion above. Also, please search before posting. Thank you.
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Re: If y=−m^2, which of the following must be true? [#permalink]

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09 Jul 2016, 12:34
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Re: If y=−m^2, which of the following must be true? [#permalink]

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25 Nov 2016, 08:34
yep, that m=0 does the trick. tricky one!
Re: If y=−m^2, which of the following must be true?   [#permalink] 25 Nov 2016, 08:34
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