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# If S^2 > T^2 , which of the following must be true?

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If S^2 > T^2 , which of the following must be true? [#permalink]  18 Jul 2018, 17:11
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If $$S^2 > T^2$$ , which of the following must be true?

(A) $$S > T$$

(B) $$S^2 > T$$

(C) $$ST > 0$$

(D) $$|S| > |T|$$

(E) $$ST < 0$$

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[Reveal] Spoiler: OA

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Re: If S^2 > T^2 , which of the following must be true? [#permalink]  18 Jul 2018, 19:41
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Carcass wrote:
If $$S^2 > T^2$$ , which of the following must be true?

(A) $$S > T$$

(B) $$S^2 > T$$

(C) $$ST > 0$$

(D) $$|S| > |T|$$

(E) $$ST < 0$$

Kudos for R.A.E

Here,
It will be option D, since The square root of a number squared is equal to the absolute value of that number

i.e. $$\sqrt{S^2} = |S|$$

option (A) does not have to be true, if S could be negative while T is positive.

option (B) does not have to be true. because if we consider fraction

Option (C) does not have to be true because S and T could have opposite signs.

OPtion (E) does not have to be true because S and T could have the same sign.
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Re: If S^2 > T^2 , which of the following must be true? [#permalink]  19 Jul 2018, 12:30
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Carcass wrote:
If $$S^2 > T^2$$ , which of the following must be true?

(A) $$S > T$$

(B) $$S^2 > T$$

(C) $$ST > 0$$

(D) $$|S| > |T|$$

(E) $$ST < 0$$

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Note: squared value is equivalent to absolute value.

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Re: If S^2 > T^2 , which of the following must be true? [#permalink]  22 Jul 2018, 17:30
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Expert's post
Carcass wrote:
If $$S^2 > T^2$$ , which of the following must be true?

(A) $$S > T$$

(B) $$S^2 > T$$

(C) $$ST > 0$$

(D) $$|S| > |T|$$

(E) $$ST < 0$$

Taking the square root of both sides, we have:

|S| > |T|

Note: If you are wondering why B is not true, take S = 2/5 and T = 1/5.

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Re: If S^2 > T^2 , which of the following must be true?   [#permalink] 22 Jul 2018, 17:30
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