GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Feb 2019, 08:29

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

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

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6985
GMAT 1: 760 Q51 V42
GPA: 3.82
If 3^x>10, which of the following must be true?  [#permalink]

### Show Tags

28 Aug 2017, 22:57
00:00

Difficulty:

35% (medium)

Question Stats:

51% (00:48) correct 49% (01:00) wrong based on 207 sessions

### HideShow timer Statistics

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

_________________

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 $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" ##### Most Helpful Expert Reply Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 4955 Location: United States (CA) Re: If 3^x>10, which of the following must be true? [#permalink] ### Show Tags 07 Sep 2017, 06:04 3 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. Answer: A _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions ##### General Discussion Director Joined: 04 Dec 2015 Posts: 740 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 28 Aug 2017, 23:14 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 Answer (A)... _________________ Please Press "+1 Kudos" to appreciate. Intern Joined: 27 May 2017 Posts: 10 Re: If 3^x>10, which of the following must be true? [#permalink] ### Show Tags 28 Aug 2017, 23:35 Same concept, why not II and III Sent from my iPhone using GMAT Club Forum Senior SC Moderator Joined: 22 May 2016 Posts: 2491 If 3^x>10, which of the following must be true? [#permalink] ### Show Tags 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 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? _________________ To live is the rarest thing in the world. Most people just exist. Oscar Wilde Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6985 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If 3^x>10, which of the following must be true? [#permalink] ### Show Tags 30 Aug 2017, 00:27 => 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$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

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

### Show Tags

09 Oct 2017, 23:54
1
I'm mixed up with this one.
Kudos if you agree!
Intern
Joined: 03 Dec 2016
Posts: 31
Re: If 3^x>10, which of the following must be true?  [#permalink]

### Show Tags

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
Intern
Joined: 03 Sep 2018
Posts: 49
Re: If 3^x>10, which of the following must be true?  [#permalink]

### Show Tags

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.

ScottTargetTestPrep by the same logic then, $$x=2.01$$ would be greater than 2, however $$3^x$$ would not (as not given that $$x=integer$$)
_________________

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4955
Location: United States (CA)
Re: If 3^x>10, which of the following must be true?  [#permalink]

### Show Tags

22 Jan 2019, 06:06
1
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.

Posted from my mobile device
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

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