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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 800 Q59 V59
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If 3^x>10, which of the following must be true? [#permalink]

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28 Aug 2017, 23:57
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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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 04 Dec 2015 Posts: 700 Location: India Concentration: Technology, Strategy Schools: ISB '19, IIMA , IIMB, XLRI WE: Information Technology (Consulting) If 3^x>10, which of the following must be true? [#permalink] ### Show Tags 29 Aug 2017, 00:14 2 This post received KUDOS 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)... _________________ Please Press "+1 Kudos" to appreciate. Intern Joined: 27 May 2017 Posts: 11 Re: If 3^x>10, which of the following must be true? [#permalink] ### Show Tags 29 Aug 2017, 00:35 Same concept, why not II and III Sent from my iPhone using GMAT Club Forum SC Moderator Joined: 22 May 2016 Posts: 1667 If 3^x>10, which of the following must be true? [#permalink] ### Show Tags 29 Aug 2017, 18:00 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 Sent from my iPhone using GMAT Club Forum 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? _________________ In the depths of winter, I finally learned that within me there lay an invincible summer. -- Albert Camus, "Return to Tipasa" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5423 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: If 3^x>10, which of the following must be true? [#permalink] ### Show Tags 30 Aug 2017, 01:27 => 3^x > 10 > 3^2 Thus x > 2 Ans: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 3 month Online Course"
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Re: If 3^x>10, which of the following must be true? [#permalink]

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07 Sep 2017, 07:04
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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.

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Intern
Joined: 12 Mar 2017
Posts: 15
Re: If 3^x>10, which of the following must be true? [#permalink]

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10 Oct 2017, 00:54
1
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I'm mixed up with this one.
Kudos if you agree!
Intern
Joined: 03 Dec 2016
Posts: 33
Re: If 3^x>10, which of the following must be true? [#permalink]

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13 Oct 2017, 09:24
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
Re: If 3^x>10, which of the following must be true?   [#permalink] 13 Oct 2017, 09:24
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