It is currently 18 Oct 2017, 06:42

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Revolution GMAT Instructor
User avatar
P
Joined: 16 Aug 2015
Posts: 4127

Kudos [?]: 2886 [0], given: 0

GPA: 3.82
Premium Member CAT Tests
If 3^x>10, which of the following must be true? [#permalink]

Show Tags

New post 28 Aug 2017, 23:57
Expert's post
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

49% (00:33) correct 51% (00:40) wrong based on 90 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
[Reveal] Spoiler: OA

_________________

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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Kudos [?]: 2886 [0], given: 0

2 KUDOS received
Director
Director
User avatar
P
Joined: 04 Dec 2015
Posts: 696

Kudos [?]: 299 [2], given: 261

Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
GMAT ToolKit User
If 3^x>10, which of the following must be true? [#permalink]

Show Tags

New post 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. :-)

Kudos [?]: 299 [2], given: 261

Intern
Intern
avatar
B
Joined: 27 May 2017
Posts: 12

Kudos [?]: 3 [0], given: 0

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

Show Tags

New post 29 Aug 2017, 00:35
Same concept, why not II and III


Sent from my iPhone using GMAT Club Forum

Kudos [?]: 3 [0], given: 0

Director
Director
avatar
P
Joined: 22 May 2016
Posts: 806

Kudos [?]: 258 [0], given: 546

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

Show Tags

New post 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?

Kudos [?]: 258 [0], given: 546

Expert Post
Math Revolution GMAT Instructor
User avatar
P
Joined: 16 Aug 2015
Posts: 4127

Kudos [?]: 2886 [0], given: 0

GPA: 3.82
Premium Member CAT Tests
Re: If 3^x>10, which of the following must be true? [#permalink]

Show Tags

New post 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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Kudos [?]: 2886 [0], given: 0

Expert Post
2 KUDOS received
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1634

Kudos [?]: 837 [2], given: 2

Location: United States (CA)
Re: If 3^x>10, which of the following must be true? [#permalink]

Show Tags

New post 07 Sep 2017, 07:04
2
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
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

Kudos [?]: 837 [2], given: 2

Intern
Intern
avatar
B
Joined: 12 Mar 2017
Posts: 6

Kudos [?]: 2 [0], given: 17

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

Show Tags

New post 10 Oct 2017, 00:54
I'm mixed up with this one.
Kudos if you agree!

Kudos [?]: 2 [0], given: 17

Intern
Intern
avatar
B
Joined: 03 Dec 2016
Posts: 17

Kudos [?]: 3 [0], given: 133

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

Show Tags

New post 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

Kudos [?]: 3 [0], given: 133

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

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.