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

Question

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

(2) ac = c/b

aniruddhawarang29 · Answer

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.

ramlala · Answer

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}

asishron29181 · Answer

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

Showmeyaa · Answer

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

TarunKumar1234 · Answer

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

Posted from my mobile device

GCMEMBER · Answer

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

Posted from my mobile device

Bunuel · Answer

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.

alisbadr · Answer

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

Bunuel · Answer

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.

bumpbot · Answer

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

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

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