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Re: If y=−m^2, which of the following must be true? [#permalink]
01 Jun 2012, 01:20
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Expert's post
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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.
Re: If y=−m^2, which of the following must be true? [#permalink]
01 Jun 2012, 02:14
Expert's post
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 ???
Re: If y=−m^2, which of the following must be true? [#permalink]
01 Jun 2012, 02:24
Expert's post
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. _________________
Re: If y=−m^2, which of the following must be true? [#permalink]
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.
Answer: C (III only).
Hope it's clear.
If m is positive then too y is negative so statement iii is contradicted ?
Re: If y=−m^2, which of the following must be true? [#permalink]
01 Jun 2012, 03:09
Expert's post
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. _________________
Re: If y=−m^2, which of the following must be true? [#permalink]
01 Jun 2012, 03:42
1
This post received KUDOS
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 Answer is C
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
Re: If y=−m^2, which of the following must be true? [#permalink]
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 Answer is C
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 ?
Re: If y=−m^2, which of the following must be true? [#permalink]
02 Jun 2012, 06:26
Expert's post
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 Answer is C
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. _________________
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]
19 Jun 2013, 07:00
1
This post received KUDOS
Expert's post
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.
Re: If y=−m^2, which of the following must be true? [#permalink]
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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