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If a, b and c are positive integers, is a = b?

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Bunuel
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If a, b and c are positive integers, is a = b? [#permalink] New post   16 Apr 2021, 01:30
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If a, b and c are positive integers, is a = b?


(1) (a + b)/(ab) is even.

(2) ac = c/b
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D
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aniruddhawarang29
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Re: If a, b and c are positive integers, is a = b? [#permalink] New post   16 Apr 2021, 01:43
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We are given a,b,c > 0 and integers.

i. Gives us that a+b = ab * Even = Even
==> a+b can be resultant of two different odd# or two different even# or two equal even numbers or two equal odd numbers.
Insuff

ii. On rearranging the algebraic expression Gives us that either c = 0 or ab = 1
Since, a,b>0 and integers.. the only case in which this happens is when we a=b=1. Yes, a=b.
Sufficient.
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Re: If a, b and c are positive integers, is a = b? [#permalink] New post   16 Apr 2021, 03:22
aniruddhawarang29 wrote:
We are given a,b,c > 0 and integers.

i. Gives us that a+b = ab * Even = Even
==> a+b can be resultant of two different odd# or two different even# or two equal even numbers or two equal odd numbers.
Insuff

ii. On rearranging the algebraic expression Gives us that either c = 0 or ab = 1
Since, a,b>0 and integers.. the only case in which this happens is when we a=b=1. Yes, a=b.
Sufficient.


Hi aniruddhawarang29

Your answer is correct, B is sufficient.

It is sufficient because we can get result from B that \(a=\frac{1}{b}\) and not equal to b

\(ac=\frac{c}{b}\)
i.e. \(a=\frac{1}{b}\)
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Re: If a, b and c are positive integers, is a = b? [#permalink] New post   16 Apr 2021, 09:32
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Statement 1:
a + b / ab = even
a + b = even * ab
a + b = even
Now a and b can take any values be it two different odd values, two different even values , same odd and same even. So we cant tell for sure if a= b
Not sufficient.

Statement 2 :ac = c/b
ac - c/b =0
c (ab -1) / b =0
c =0 and ab =1
Now a and b are two positive integers as given in the question.
Hence a= b = 1
Sufficient.

IMO B
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Re: If a, b and c are positive integers, is a = b? [#permalink] New post   16 Apr 2021, 12:16
asishron29181 wrote:
Statement 1:
a + b / ab = even
a + b = even * ab
a + b = even
Now a and b can take any values be it two different odd values, two different even values , same odd and same even. So we cant tell for sure if a= b
Not sufficient.

Statement 2 :ac = c/b
ac - c/b =0
c (ab -1) / b =0
c =0 and ab =1
Now a and b are two positive integers as given in the question.
Hence a= b = 1
Sufficient.

IMO B


Hi, the question stem states that a, b and c are positive integers(which means zero is not included), we can directly cancel out c from both sides. a*b = 1. This is only possible when a = b = 1
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Re: If a, b and c are positive integers, is a = b? [#permalink] New post   17 Apr 2021, 00:51
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If a, b and c are positive integers, is a = b?

Stat1: (a + b)/(ab) is even.
So, 1/a +1/b = even, which is possible either, a= b=positive nos. = 1 or 2. Sufficient.

Stat2: ac = c/b
or, c(a-1/b) = 0, as c= positive no. so, a = 1/b, which means a = b= 1. Sufficient.

So, I think D. :)
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Re: If a, b and c are positive integers, is a = b? [#permalink] New post   17 Apr 2021, 02:33
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If a, b and c are positive integers, is a = b?

(1) (a + b)/(ab) is even.
1/a + 1/b is even
Either a = b = 1 or a = b = 2
Sufficient

(2) ac = c/b
ab = 1
a = b = 1
Sufficient

Option D

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If a, b and c are positive integers, is a = b? [#permalink] New post   19 Apr 2021, 01:15
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If a, b and c are positive integers, is a = b?

(1) (a + b)/(ab) is even --> \(\frac{a + b}{ab}=\frac{1}{a}+\frac{1}{b}\). Notice that since a and b are positive integers, then the greatest value of both 1/a and 1/b is 1, when both a and b are 1. In all other cases 1/a and 1/b are less than 1 and their sum is less than or equal to 1. Therefore only case for \(\frac{1}{a}+\frac{1}{b}\) to be even is when \(a=b=1\). Sufficient.

(2) ac = c/b --> reduce by c and multiply both sides by b: \(ab=1\). Again since both of them are integers, then \(a=b=1\). Sufficient.

Answer: D.

Hope it's clear.
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Re: If a, b and c are positive integers, is a = b? [#permalink] New post   30 Apr 2021, 15:35
Bunuel you mentioned since a & b are positive integers then the greatest value for 1/a and 1/b is 1, i don't understand this part. if 1 & be are integers, each of them can be any number (2,3,etc..) then 1/a and 1/b will be fractions in this case
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Re: If a, b and c are positive integers, is a = b? [#permalink] New post   01 May 2021, 01:18
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alisbadr wrote:
Bunuel you mentioned since a & b are positive integers then the greatest value for 1/a and 1/b is 1, i don't understand this part. if 1 & be are integers, each of them can be any number (2,3,etc..) then 1/a and 1/b will be fractions in this case


If a = 1, then 1/a = 1;
If a = 2, then 1/a = 1/2;
If a = 3, then 1/a = 1/3;
If a = 4, then 1/a = 1/4;
...

As a increases the value of 1/a decreases and the greatest value of 1/a is 1, when a = 1.
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Re: If a, b and c are positive integers, is a = b? [#permalink] New post   27 Nov 2022, 22:29
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Re: If a, b and c are positive integers, is a = b? [#permalink]
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