What is the value of p?

What is the value of p?

(1) -|p| = -2 --> |p| = 2 --> p = -2 or p = 2. Not sufficient.

(2) p^2 - 4 = 0 --> p^2 = 4 --> p = -2 or p = 2. Not sufficient.
Basically this statement is the same as the first one: p^2 = 4 <--> |p| = 2 (by taking the square root).

(1)+(2) p still can take the same two values. Not sufficient.

Answer: E.
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-|p| = -p ?
-p=-2
p=2

i know that this is wrong, but please tell me where im wrong

How did you get -p = -2 from -|p| = -2 ?
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as |p| = p
i assume -|p|=-p

Where it is given that |p| = p ??? We are only given that -|p| = -2.
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Hi ikishan,

Please note that for a variable p, |p| = p only in cases where p >= 0. For cases where p =< 0, |p| = -p. To clear your confusion, let me give you a few examples.

Assume the value of p = 3. So, we can write |p| =|3|. Since 3 > 0, we can write |3| = 3. This expression is equivalent to |p| =p when p > 0

Similarly assume p = -3. So, |p| = |-3|. Since - 3 < 0, we need to write |-3| = -(-3) = 3. This expression is equivalent to |p| = -p when p < 0.

As a general understanding |p| denotes the distance of p from point zero on the number line. Since , 3 and -3 both are at the same distance from 0, hence |3| = |-3| = 3.

Hope its clear! Let me know if you have trouble at any point of this explanation.

Regards
Harsh
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Hi ikishan,

Many Test Takers make minor mistakes when dealing with "overlapping" Quant concepts. As such, you should take a more practical approach to these types of situations and not try to do more-complex math than is really necessary.

In Fact 1, we're given that -|P| = -2

Focus on the |P| for a moment. You can see the negative "signs" on both sides of the equation, so you KNOW:

negative |P| = negative 2

So what could P equal?

P = 2 is fairly obvious because -|2| = -2

Since this is a DS question, we have to be on the lookout for any OTHER solutions IF they exist....

So could P equal ANYTHING ELSE?

P = -2 is also an option because -|-2| = -2

No fancy math is required to get to this solution, just a willingness to think and do the practical work.

GMAT assassins aren't born, they're made,
Rich
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i have got a doubt here.
i did exactly same what u did. but i picked option D as we can get solution from both the statements.

does this question ask for a single value instead of multiple values that an expression can have ?

In GMAT DS questions, whenever you get a question, what is the value of p, what is the value of x , what is value of a+b, etc.... for an option to be "sufficient", you must have a UNIQUE value.

As soon as you get >1 possible values for a variable in such questions, the statement is NOT sufficient. You did not get "a" solution, rather you ended up getting 2 solutions.

For the question at hand, you get 2 values instead of 1, making both statements individually and even combined not sufficient.
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), \(-|p| = -2\) is equivalent to \(|p| = 2\). Thus \(p = \pm 2\).
For 2), \(p^2 - 4 = 0\) has \(2\) roots \(p = \pm 2\).
For 1) & 2), both conditions are same and not sufficient.

Therefore, the answer is E.
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Value of P = ?

St 1: -|P| = -2
In this case P can be either 2 or -2

For example, if P = 2
=> -|-2| = -2
=> -2 = -2

On the other hand if P = 2
=>-|2| = -2
=>-2 = -2

Hence we can say that P can take 2 values from the above statement.

St 2: P^2 - 4 = 0

Here also P can take 2 values. Either 2 or -2 because -ve integer will become +ve after squaring it.

Clearly Insufficient

St 1 + St 2: No additional information. P can be either 2 or -2

Therefore our answer is E

Initially i choosed answer E only but this below statement confused me weather sqrt of P^2 is 4 or -4

"By conversion, the symbol \sqrt{} (square root sign - called radical) means the positive square root only. (Example) Even though there are two different numbers whose square is 9 (both 3 and -3), when you see \sqrt{9} (square root symbol on number 9) on the GMAT, it refers to the positive number 3 only." - from Kaplan Premier 2014.


Can u please calrify?

When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive root. That is:

\(\sqrt{9} = 3\), NOT +3 or -3;
\(\sqrt[4]{16} = 2\), 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 \(x=\sqrt{9}=3\).
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