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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]

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19 Jul 2018, 00:43
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Difficulty:

15% (low)

Question Stats:

79% (00:47) correct 21% (00:51) wrong based on 61 sessions

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

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Updated on: 19 Jul 2018, 03:05
1
Bunuel 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

As all we're given are equations, we'll work with them.
This is a Precise approach.

Simplifying our given data gives S^2 - T^2 > 0 --> (S - T)(S + T) > 0

So both S - T and S + T are positive in which case both S and T must be positive and S > T.
Or both S - T and S + T are negative in which case both S and T must be negative and S < T.

Looking at our answer choices, (A), (C), (E) are all directly contradicted by one of the above options.
(D) works because if both S and T are positive then S > T --> |S| > |T| and if both are negative then S < T means that S has a larger absolute value.
(B) can fail for some fractional values (such as T = 0.5 and S = 0.6 so S > T but S^2 < T)

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Originally posted by DavidTutorexamPAL on 19 Jul 2018, 00:49.
Last edited by DavidTutorexamPAL on 19 Jul 2018, 03:05, edited 1 time in total.
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Re: If S^2 > T^2 , which of the following must be true?  [#permalink]

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19 Jul 2018, 01:41
Bunuel wrote:
If S^2 > T^2 , which of the following must be true?

(A) S > T --> Incorrect, fails if S is -ve and T is +ve
(B) S^2 > T --> Incorrect, fails in case of fractions
(C) ST > 0 --> Incorrect, fails in case of opposite sign
(D) |S| > |T| --> Correct, means exactly the same, absolute value of a number = squared value of the number
(E) ST < 0 --> Incorrect, fails in case both S and T have same sign

Hence, D.
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Re: If S^2 > T^2 , which of the following must be true?  [#permalink]

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19 Jul 2018, 04:05

Solution

Given:
• S^2 > T^2

To find:
• Among the given option, which one is correct.

Approach and Working:

• $$S^2 > T^2$$
o It only means that Absolute value of S is greater than T.
 For example: $$3^2>2^2$$ and if you see|3|>|2| and |-3| >|-2|
o Thus, |s|> |T|

Hence, the correct answer is option D.

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

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19 Jul 2018, 12:52
Bunuel 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

Note: Squared value and absolute value are alike.

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

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22 Jul 2018, 17:30
Bunuel 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? &nbs [#permalink] 22 Jul 2018, 17:30
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