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Is x^2 > 5^2 ?

This topic has 2 expert replies and 0 member replies

Is x^2 > 5^2 ?

Post Tue Dec 05, 2017 9:44 am
Is x^2 > 5^2 ?

(1) |x+5| = 3|x - 5|

(2) |x| > 3

The OA is C.

I don't have this question clear. Experts, may you clarify this to me? Please.

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Post Wed Dec 06, 2017 12:58 am
Vincen wrote:
Is x^2 > 5^2 ?

(1) |x+5| = 3|x - 5|

(2) |x| > 3

The OA is C.

I don't have this question clear. Experts, may you clarify this to me? Please.
We have to find out whether Is x^2 > 5^2?

The inequality x^2 > 5^2 is true if |x| > 5.

(1) |x+5| = 3|x - 5|

Case1: x+5 = 3(x - 5) => x+5 = 3x - 15 => x = 10. The anwer is Yes.
Case2: x+5 = -3(x - 5) => x+5 = -3x + 15 => x = 5/2. The anwer is No. No unique answer. Insufficient.

(2) |x| > 3

Case 1: If x = 6, the answer is Yes.
Case 2: If x = 4, the answer is No. No unique answer. Insufficient.

(1) and (2) together

With (1) and (2) combined, x = 5/2 is not applicable, thus x = 10. So, x^2 > 5^2. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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Thanked by: Vincen
Post Tue Dec 05, 2017 3:29 pm
Taken one step further, this question is asking if x^2 > 25.

You can simplify this by solving the inequality x>5 or x<-5. This is the same as |x|>5.

Now look at the two statements. You would definitely want to focus on Statement (2) since it is much easier to deal with.

We already found that for x^2 > 25 to be true, x has to be bigger than 5 or less than -5. Statement 2 allows for numbers between 3 and 5 and between -3 and -5, which would make x^2 < 25. It also allows for numbers greater than 5 or less than -5, which would make x^2 > 25. So this Statement, alone, is not sufficient. Therefore, Answer B and D are incorrect and should be eliminated.

Next, take a look at Statement (1). An equality with absolute values on both sides is not as common as an equation with an absolute value on one side, so this seems difficult. Here, you can set up two equations: one that is equivalent to simply dropping both absolute value equations, and the other that multiplies the contents of one of the absolute value expressions by -1.

First equation:
x+5 = 3(x-5)
x+5 = 3x-15
x+5-x=3x-15-x
5=2x-15
5+15=2x-15+15
20=2x
x=10

2nd equation:
-(x+5)=3(x-5)
-x-5=3x-15
-x-5+x=3x-15+x
-5=4x-15
-5+15=4x-15+15
10=4x
x=2.5

Here, we have two values for x: x=10 and x=2.5.
If x=10, then x^2 > 25.
If x=2.5, then x^2< 25.

Thus, Statement 1 alone is not sufficient. Answer A is incorrect and should be eliminated.

However, if we take Statement 1 together with Statement 2, x=2.5 is removed as a possible value for x. With these two rules combined, x= 10 and x^2 > 25, and Answer C is correct.

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