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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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If 3^x>10, which of the following must be true?  [#permalink]

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Question Stats: 52% (00:47) correct 48% (01:00) wrong based on 221 sessions

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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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2
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.

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

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3
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

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

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Same concept, why not II and III

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

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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

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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8013
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If 3^x>10, which of the following must be true?  [#permalink]

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=> 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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I'm mixed up with this one.
Kudos if you agree!
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Re: If 3^x>10, which of the following must be true?  [#permalink]

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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

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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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.

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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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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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If 3^x>10, which of the following must be true?   [#permalink] 22 Jan 2019, 07:06
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