GATE Civil 2018 Set 2 | GA | Question: 5

Question

For non-negative integers, $a, b, c$, what would be the value of $a+b+c$ if $\log a + \log b + \log c = 0$?

• A. $3$
• B. $1$
• C. $0$
• D. $-1$

Comments

It should be 3

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Answer here!   

Answer 1

Given that $a, b$ and $c$ are non-negative integers, i.e., $a,b,c\geq0$
and $\log a + \log b + \log c = 0$

$\implies\log abc=0$
$\implies abc={10}^{0}$
$\implies abc=1$

Since $a,b,c$ are non-negative integers, $a=b=c=1$
$\implies a+b+c=1+1+1=3$

So, (A) is the correct answer.

Comments

$\log_{10}abc = 0$

$\implies\log_{10}abc = \log_{10}1$

$\implies abc = 1$

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abc=1

from this line we are concluding a=b=c=1 but in the question it is not mentioned that these are equal.

So, why it can’t be a=1/12  b=4  c=3

because It is also abc=1 and non-negative integer too.

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Can you define integers, non-negative integers, and non-positive integers? Rest of the things you will understand.

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this is non-negative but not an integer. I misunderstood it with non-negative real numbers.

Answer 2

Please Try to understand solution it's In very Detailed