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If 3^x>10, which of the following must be true?

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If 3^x>10, which of the following must be true?  [#permalink]

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New post 28 Aug 2017, 22:57
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A
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E

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If 3^x>10, which of the following must be true?

I. x>2
II. x>3
III. x>4

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

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Re: If 3^x>10, which of the following must be true?  [#permalink]

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New post 07 Sep 2017, 06:04
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MathRevolution wrote:
If 3^x>10, which of the following must be true?

I. x>2
II. x>3
III. x>4

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


Since 3^2 = 9 and 3^3 = 27, if 3^x = 10, then x must be some number between 2 and 3. So if 3^x > 10, then x must be greater than 2. However, x may not need to be greater than 3 (or 4) to hold the inequality 3^x > 10. For example, if x = 2.5, 3^2.5 = 3^2 x 3^0.5 = 9√3 > 10.

Answer: A
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If 3^x>10, which of the following must be true?  [#permalink]

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New post 28 Aug 2017, 23:14
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MathRevolution wrote:
If 3^x>10, which of the following must be true?

I. x>2
II. x>3
III. x>4

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

\(3^x>10\)

\(3^2 = 9\)

\(3^3 = 27 >10\)

Therefore \(x\) must be \(3\) and greater. ie; \(x\) must be greater than \(2\).

\(x>2\) ------- I Only

Answer (A)...

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Re: If 3^x>10, which of the following must be true?  [#permalink]

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New post 28 Aug 2017, 23:35
Same concept, why not II and III


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If 3^x>10, which of the following must be true?  [#permalink]

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New post 29 Aug 2017, 17:00
MathRevolution wrote:
If 3^x>10, which of the following must be true?

I. x>2
II. x>3
III. x>4

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

habdo wrote:
Same concept [as correct Option I], why not II and III


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habdo , I agree with you. I toggled between answers A and E. I picked A on a gamble. Nothing more.

MathRevolution , thank you for posting the question. It seems to me that by definition, if x > 2, it must also be greater than 3 and 4 unless there is an upper limit restriction, and here there is not.

I understand that Option I is the minimum condition which satisfies the inequality.

That is, x must be greater than 2 for \(3^{x}\) to be greater than 10.

But as I understand the word "must," in logic and in math, "must" includes the transitive cases:

If 3 > 2, and 2 > x, then 3 > x

I am not sure how one could argue that the third statement "must not" be true. Am I missing something?
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Re: If 3^x>10, which of the following must be true?  [#permalink]

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New post 30 Aug 2017, 00:27
=> 3^x > 10 > 3^2
Thus x > 2

Ans: A
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Re: If 3^x>10, which of the following must be true?  [#permalink]

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New post 09 Oct 2017, 23:54
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I'm mixed up with this one.
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Re: If 3^x>10, which of the following must be true?  [#permalink]

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New post 13 Oct 2017, 08:24
MathRevolution wrote:
If 3^x>10, which of the following must be true?

I. x>2
II. x>3
III. x>4

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


As the question does not mention that x is an integer, x=2.01 then 3^2.01 = 9.09, which is not greater than 10. Hence x>10 cannot be the right answer.

Also, the question states that "which ones of these must be true". Any number with x>3 and x>4 will always be true, so why not select these options, as they supply the right numbers
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Re: If 3^x>10, which of the following must be true?  [#permalink]

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New post 21 Jan 2019, 01:01
ScottTargetTestPrep wrote:
MathRevolution wrote:
If 3^x>10, which of the following must be true?

I. x>2
II. x>3
III. x>4

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


Since 3^2 = 9 and 3^3 = 27, if 3^x = 10, then x must be some number between 2 and 3. So if 3^x > 10, then x must be greater than 2. However, x may not need to be greater than 3 (or 4) to hold the inequality 3^x > 10. For example, if x = 2.5, 3^2.5 = 3^2 x 3^0.5 = 9√3 > 10.

Answer: A


ScottTargetTestPrep by the same logic then, \(x=2.01\) would be greater than 2, however \(3^x\) would not (as not given that \(x=integer\))
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Re: If 3^x>10, which of the following must be true?  [#permalink]

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New post 22 Jan 2019, 06:06
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The problem says given the premise that 3^x > 10, then x is... So x can't be 2.01 since 3^2.01 is not greater than 10. However, we know x is 2 point something. Now let's say that 2.1 is the smallest value such that 3^2.1 > 10. Thus, we cannot say that x must be greater than 3 (or 4), since 2.1, 2.2, 2.3, etc. are not greater than 3 (or 4), but it's true to say x must be greater than 2.

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Re: If 3^x>10, which of the following must be true?   [#permalink] 22 Jan 2019, 06:06
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