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Given that a and b are positive integers, if a≠1, does a = b?

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Given that a and b are positive integers, if a≠1, does a = b?  [#permalink]

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New post Updated on: 30 Jan 2016, 11:51
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E

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Given that a and b are positive integers, if a≠1, does a = b?

Statement #1: a is a factor of b
Statement #2: a is a multiple of b

Considering Mike suggestion, the question has been edited.
This is a question framed by myself. Please feel free to improvise the question!
Good luck!

Originally posted by MK1480 on 29 Jan 2016, 10:03.
Last edited by MK1480 on 30 Jan 2016, 11:51, edited 1 time in total.
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Re: Given that a and b are positive integers, if a≠1, does a = b?  [#permalink]

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New post 29 Jan 2016, 16:49
1
MK1480 wrote:
Is a = b?

1. 'a' is a factor of 'b'

2. 'b' is a factor of 'a'

This is a question framed by myself. Please feel free to improvise the question!
Good luck!

Dear MK1480,
Very interesting, my friend. :-) When you say "feel free to improvise the question," I assume you mean "feel free to improve the question."

First of all, I think it would be more natural sounding to say "Does a = b?" rather than "Is a = b?"

I think a slightly more interesting set-up would be:
Given that a and b are positive integers, if \(a \neq 1\), does a = b?
Statement #1: a is a factor of b
Statement #2: a is a multiple of b


This version plays on the subtle reciprocal relationship between the idea of a factor and the idea of a multiple. It also explicitly disabuses people of the misconception that if both statements are true, the values must equal 1. One important part of writing a high quality question is anticipating the incorrect assumptions that some students might bring to a question.

What do you think?
Mike
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Re: Given that a and b are positive integers, if a≠1, does a = b?  [#permalink]

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New post 30 Jan 2016, 11:49
Completely agree with you Mike!
Thanks for your suggestions! I will edit the question as you advised!



mikemcgarry wrote:
MK1480 wrote:
Is a = b?

1. 'a' is a factor of 'b'

2. 'b' is a factor of 'a'

This is a question framed by myself. Please feel free to improvise the question!
Good luck!

Dear MK1480,
Very interesting, my friend. :-) When you say "feel free to improvise the question," I assume you mean "feel free to improve the question."

First of all, I think it would be more natural sounding to say "Does a = b?" rather than "Is a = b?"

I think a slightly more interesting set-up would be:
Given that a and b are positive integers, if \(a \neq 1\), does a = b?
Statement #1: a is a factor of b
Statement #2: a is a multiple of b


This version plays on the subtle reciprocal relationship between the idea of a factor and the idea of a multiple. It also explicitly disabuses people of the misconception that if both statements are true, the values must equal 1. One important part of writing a high quality question is anticipating the incorrect assumptions that some students might bring to a question.

What do you think?
Mike
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Re: Given that a and b are positive integers, if a≠1, does a = b?  [#permalink]

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New post 16 Mar 2016, 04:37
HERE is my answer
Obviously statements 1 and two are not sufficient by themselves
Now taking them together we can say that a=b or a=-b
hence E is my call

and one more thing
its been a long time => WILL SOMEONE ADD THE OFFICIAL SOLUTION PLEASE

cc- chetan2u Bunuel

thanks
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Re: Given that a and b are positive integers, if a≠1, does a = b?  [#permalink]

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New post 16 Mar 2016, 05:54
Chiragjordan wrote:
HERE is my answer
Obviously statements 1 and two are not sufficient by themselves
Now taking them together we can say that a=b or a=-b
hence E is my call

and one more thing
its been a long time => WILL SOMEONE ADD THE OFFICIAL SOLUTION PLEASE

cc- chetan2u Bunuel

thanks


Hi,

we should be very careful in reading the Q..

the Q says
Quote:
Given that a and b are positive integers, if a≠1, does a = b?
Statement #1: a is a factor of b
Statement #2: a is a multiple of b


it gives a and b are positive integers, so a cannot be -b, as any one will be negative in that case..

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Given that a and b are positive integers, if a≠1, does a = b?  [#permalink]

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New post 31 Dec 2018, 08:41
MK1480 wrote:
Given that a and b are positive integers, if a≠1, does a = b?

Statement #1: a is a factor of b
Statement #2: a is a multiple of b

Considering Mike suggestion, the question has been edited.
This is a question framed by myself. Please feel free to improvise the question!
Good luck!


Dear Moderator,
Can we have the OA for this one, Thank you.
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Re: Given that a and b are positive integers, if a≠1, does a = b? &nbs [#permalink] 31 Dec 2018, 08:41
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Given that a and b are positive integers, if a≠1, does a = b?

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