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Prime Number

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Source: — Data Sufficiency |

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by Rahul@gurome » Fri Nov 19, 2010 12:56 pm
Viper83 wrote:Is Root of x a prime number?

(i) Abs (3x-7)= 2x+2

(ii) x to the power 2= 9x
Statement 1: |3x - 7| = (2x + 2)
Absolute value gives rise to two situations,
  • (1) For 3x > 7, (3x - 7) = (2x + 2) => x = 9 => √x = 3 -> Prime
    or
    (2) For 3x < 7, (7 - 3x) = (2x + 2) => x = 1 => √x = 1 -> Not Prime
Not sufficient.

Statement 2: x² = 9x
=> x² - 9x = 0 => x(x - 9) = 0 => x = 0 or 9

Not sufficient.

1 & 2 Together: x = 9 => √x = 3 -> Prime

Sufficient.

The correct answer is C.
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by Viper83 » Fri Nov 19, 2010 1:06 pm
Hi Rahul
thanks very much for your reply and explanation. In fact I solved the questions exactly like that.

My concern with this question is the following: why is the square root of 9 equal to ONLY 3. The square root of 9 should be 3 and -3. Furthermore, -3 is not a prime number.

What am I missing here?

Thanks very much!
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by Rahul@gurome » Fri Nov 19, 2010 1:32 pm
Viper83 wrote:My concern with this question is the following: why is the square root of 9 equal to ONLY 3. The square root of 9 should be 3 and -3. Furthermore, -3 is not a prime number.

What am I missing here?
When we are dealing with square root(s), it is always the positive one.
By definition √(x²) = |x|.

This means, if x² = 9, and we are asked to find the value of x, the answer is -3 and 3. But if are asked to find the value of √(x²), the answer is only 3.
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by gdk800 » Fri Nov 19, 2010 3:11 pm
Viper83 wrote:

Is Root of x a prime number?

(i) Abs (3x-7)= 2x+2

(ii) x to the power 2= 9x
Statement 1: |3x - 7| = (2x + 2)
Absolute value gives rise to two situations,

(1) For 3x > 7, (3x - 7) = (2x + 2) => x = 9 => √x = 3 -> Prime
or
(2) For 3x < 7, (7 - 3x) = (2x + 2) => x = 1 => √x = 1 -> Not Prime



Not sufficient.

Statement 2: x² = 9x
=> x² - 9x = 0 => x(x - 9) = 0 => x = 0 or 9

Not sufficient.

1 & 2 Together: x = 9 => √x = 3 -> Prime

Sufficient.



I have a question for Rahul, can't we ignore x = 0 in the second case because root(0) is not considered? By this, the ans. would be B.

Actually this brings me to another question as to how is root(0) treated?
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by Rahul@gurome » Fri Nov 19, 2010 3:22 pm
gdk800 wrote:I have a question for Rahul, can't we ignore x = 0 in the second case because root(0) is not considered? By this, the ans. would be B.

Actually this brings me to another question as to how is root(0) treated?
Our target is to identify the correct option, not to force an option to be the correct one. If there is a logic to ignore x = 0, we can certainly do that. But as there is none, we can't ignore it. And root of zero is zero only, which is not a prime number.
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