What is the value of p? (1) p is an integer (2) 20

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What is the value of p?

(1) p is an integer

(2) √20 < p < 16/3

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$!vakumar.m · Answer

What is the value of p?

(1) p is an integer. Not sufficient to determine unique value of P.

(2) √20 < p < 16/3. P lies in a range (4.47 to 5.33)and can be any number in that range. Hence, not sufficient.

1 & 2 Combined. P is an integer and lies in above range. Since 5 is the only integer therefore both statements together are sufficient to find the value of P.

Answer C

parthAgarwal3033 · Answer

The answer should be E as root(20) can be -4.47 as well. We cannot neglect that value.

Bunuel · Answer

First of all, (1) says that p is an integer, so it cannot be -4.47. p also cannot be negative since (2) says that √20 < p < 16/3. Remember that the square root sign for an even root, such as a square root, fourth root, ... cannot given negative result , hence √20 is positive only (approximately 4.47).

parthAgarwal3033 · Answer

I still don't get why Root(20) can't be negative. (-4.47)^2 is also equal to 20. Also if we solve x^2 = 20 we get 2 real values of x (4.47 and -4.47) Now if we consider integers between -4.47 and 5.33 , there can be many values right??

Bunuel · Answer

Mathematically,  \sqrt{...}  is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign ( \sqrt{...} ) always means non-negative square root.

https://gmatclub.com/forum/download/file.php?id=39502 
 The graph of the function f(x) = √x

Notice that it's defined for non-negative numbers and is producing non-negative results.

TO SUMMARIZE:
 When the GMAT (and generally in math) provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative root.  That is:

\sqrt{9} = 3 , NOT +3 or -3;
 \sqrt {16} = 2 , NOT +2 or -2;

Notice that in contrast, the equation  x^2 = 9  has TWO solutions, +3 and -3. Because  x^2 = 9  means that  x =-\sqrt{9}=-3  or  x=\sqrt{9}=3 .

Hope it helps.

$!vakumar.m · Answer

For GMAT just remember that even number square root is ALWAYS POSITIVE
=> sqrt 9 = 3 only 
Or in general 
Sqrtx^2 = |x| = x if x>=0
 = -x if x<=0

Another way to think about why square root is always positive is ... 
when we do prime factorization do we get negative factors? NO. 
Prime factors are always positive. So, in similar lines, square root is always positive.

Similarly if it is odd root 
(-27)^(1/3) =-3 only, or
(8)^(1/3) = 2 only
i.e., odd root returns the base number.

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What is the value of p? (1) p is an integer (2) 20 < p < 16/3

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