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If 3^x>100, which of the following must be true?

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Math Revolution GMAT Instructor
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If 3^x>100, which of the following must be true?  [#permalink]

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14 Dec 2017, 02:16
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[GMAT math practice question]

If $$3^x>100$$, which of the following must be true?

I. $$x>3$$
II. $$x>4$$
III. $$x>5$$

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

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Sep 2009 Posts: 55804 Re: If 3^x>100, which of the following must be true? [#permalink] Show Tags 14 Dec 2017, 03:50 MathRevolution wrote: [GMAT math practice question] If $$3^x>100$$, which of the following must be true? I. $$x>3$$ II. $$x>4$$ III. $$x>5$$ A. I only B. II only C. III only D. I and II only E. I, II, and III Similar question: https://gmatclub.com/forum/if-3-x-10-wh ... 48146.html _________________ Manager Joined: 15 Aug 2016 Posts: 208 Location: India Concentration: Technology, Operations GMAT 1: 690 Q49 V35 GPA: 3.84 WE: Operations (Consulting) Re: If 3^x>100, which of the following must be true? [#permalink] Show Tags 14 Dec 2017, 04:05 Can someone explain this please.According to me x can be 5 or greater. as 3^4 is 81 and that is less than hundred. How can answer be d? Math Expert Joined: 02 Aug 2009 Posts: 7765 If 3^x>100, which of the following must be true? [#permalink] Show Tags 14 Dec 2017, 08:24 MathRevolution wrote: [GMAT math practice question] If $$3^x>100$$, which of the following must be true? I. $$x>3$$ II. $$x>4$$ III. $$x>5$$ A. I only B. II only C. III only D. I and II only E. I, II, and III since 83% have gone wrong, this may help you... $$3^x>100....3^4=81$$ and $$3^5=243$$.. so minimum value of x is between 4 and 5, remember it need not be INTEGER.. say in actual $$x>4.ab$$ x>3 and x>4 will include all these values above 4.ab BUT if x=4.5, it will NOT come in x>5, hence x>5 is wrong ans D _________________ Manager Joined: 15 Aug 2016 Posts: 208 Location: India Concentration: Technology, Operations GMAT 1: 690 Q49 V35 GPA: 3.84 WE: Operations (Consulting) Re: If 3^x>100, which of the following must be true? [#permalink] Show Tags 14 Dec 2017, 09:54 chetan2u wrote: MathRevolution wrote: [GMAT math practice question] If $$3^x>100$$, which of the following must be true? I. $$x>3$$ II. $$x>4$$ III. $$x>5$$ A. I only B. II only C. III only D. I and II only E. I, II, and III since 83% have gone wrong, this may help you... $$3^x>100....3^4=81$$ and $$3^5=243$$.. so minimum value of x is between 4 and 5, remember it need not be INTEGER.. say in actual $$x>4.ab$$ x>3 and x>4 will include all these values above 4.ab BUT if x=4.5, it will NOT come in x>5, hence x>5 is wrong ans D Hi chetan. Thanks for the prompt reply. I find this question's construction a bit odd. If x>3 then x can be 3.0111 which will yield a value less than 100>.Same for x> 4. X may be 4.0000001 and that would render the conclusion incorrect. but when x>=5 ,in every case 3^x is going to exceed 100. Thats why I marked C. Its not for every value greater than 3 and 4 that would satisfy this equation. Can you please clarify this?Apologies if I missed something Retired Moderator Joined: 25 Feb 2013 Posts: 1196 Location: India GPA: 3.82 Re: If 3^x>100, which of the following must be true? [#permalink] Show Tags 14 Dec 2017, 10:57 MathRevolution wrote: [GMAT math practice question] If $$3^x>100$$, which of the following must be true? I. $$x>3$$ II. $$x>4$$ III. $$x>5$$ A. I only B. II only C. III only D. I and II only E. I, II, and III we know $$3^3 = 27<100$$ ; $$3^4=81<100$$ & $$3^5=243>100$$ As this is a must be true question so whatever will be the value of $$x$$ in $$3^x$$ it has to be greater than $$3$$ & $$4$$ Hence I & II must be true. $$x$$ may or may not be greater than $$5$$, hence III is not always true Option D Manhattan Prep Instructor Joined: 04 Dec 2015 Posts: 756 GMAT 1: 790 Q51 V49 GRE 1: Q170 V170 Re: If 3^x>100, which of the following must be true? [#permalink] Show Tags 14 Dec 2017, 16:59 Utkarsh KOhli wrote: chetan2u wrote: MathRevolution wrote: [GMAT math practice question] If $$3^x>100$$, which of the following must be true? I. $$x>3$$ II. $$x>4$$ III. $$x>5$$ A. I only B. II only C. III only D. I and II only E. I, II, and III since 83% have gone wrong, this may help you... $$3^x>100....3^4=81$$ and $$3^5=243$$.. so minimum value of x is between 4 and 5, remember it need not be INTEGER.. say in actual $$x>4.ab$$ x>3 and x>4 will include all these values above 4.ab BUT if x=4.5, it will NOT come in x>5, hence x>5 is wrong ans D Hi chetan. Thanks for the prompt reply. I find this question's construction a bit odd. If x>3 then x can be 3.0111 which will yield a value less than 100>.Same for x> 4. X may be 4.0000001 and that would render the conclusion incorrect. but when x>=5 ,in every case 3^x is going to exceed 100. Thats why I marked C. Its not for every value greater than 3 and 4 that would satisfy this equation. Can you please clarify this?Apologies if I missed something You're looking for the options that must be true. If $$3^x>100$$, then x is definitely bigger than 4, right? It can't be smaller than 4, or equal to 4, so it's bigger than 4. So, the statement 'x > 4' must be true. That's why you want to pick that one. Same with the statement 'x > 3'. However, when it comes to 'x > 5', you don't know whether that's true or not, given the information you have. x could be 4.9, or x could be 5.1. In other words, maybe x is bigger than 5, and maybe it isn't. So, it's incorrect to say that 'x>5' must be true. _________________ Chelsey Cooley | Manhattan Prep | Seattle and Online My latest GMAT blog posts | Suggestions for blog articles are always welcome! Math Expert Joined: 02 Aug 2009 Posts: 7765 Re: If 3^x>100, which of the following must be true? [#permalink] Show Tags 14 Dec 2017, 18:05 Utkarsh KOhli wrote: chetan2u wrote: MathRevolution wrote: [GMAT math practice question] If $$3^x>100$$, which of the following must be true? I. $$x>3$$ II. $$x>4$$ III. $$x>5$$ A. I only B. II only C. III only D. I and II only E. I, II, and III since 83% have gone wrong, this may help you... $$3^x>100....3^4=81$$ and $$3^5=243$$.. so minimum value of x is between 4 and 5, remember it need not be INTEGER.. say in actual $$x>4.ab$$ x>3 and x>4 will include all these values above 4.ab BUT if x=4.5, it will NOT come in x>5, hence x>5 is wrong ans D Hi chetan. Thanks for the prompt reply. I find this question's construction a bit odd. If x>3 then x can be 3.0111 which will yield a value less than 100>.Same for x> 4. X may be 4.0000001 and that would render the conclusion incorrect. but when x>=5 ,in every case 3^x is going to exceed 100. Thats why I marked C. Its not for every value greater than 3 and 4 that would satisfy this equation. Can you please clarify this?Apologies if I missed something Hi.. There are two type of Questions .. Questions where your reasoning would stand.. 1) if 3^x>100, for which values of x will the equation be true.. Here x>3 will not be true because statement means 3^4 should be >100 And then ans can be x>5.. Questions where it will not be true.. 2) if 3^x>100, what must be true? Here x>5 may not be true because 4.7 or 4.8 can also be the values.. x>3 will contain all values. So answer would depend on WHAT has been asked. Hope it clarifies your doubt. _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7508 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If 3^x>100, which of the following must be true? [#permalink] Show Tags 18 Dec 2017, 00:26 => Since $$3^x>100$$ and $$100>81=3^4$$, $$x > 4$$. This implies that $$x > 3$$, too. $$3^5 = 243 > 100$$, so statement III may not be true. As only statements I and II are true, the answer is D. Answer: D _________________ 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 1 month Online Course"
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If 3^x>100, which of the following must be true?  [#permalink]

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18 Dec 2017, 06:22
Hi Chetan,
Thank you
Yes it's cleared.
Intern
Joined: 19 Aug 2017
Posts: 21
Re: If 3^x>100, which of the following must be true?  [#permalink]

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20 Dec 2017, 23:00
Such an Irrelevant question and an irrelevant logic!!

The question asks which of the folloeing MUST be true... so for all values of x> 5 the statement 3^x > 100 holds true !
So the answer must be C !
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Joined: 25 Feb 2013
Posts: 1196
Location: India
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Re: If 3^x>100, which of the following must be true?  [#permalink]

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20 Dec 2017, 23:04
MSarmah wrote:
Such an Irrelevant question and an irrelevant logic!!

The question asks which of the folloeing MUST be true... so for all values of x> 5 the statement 3^x > 100 holds true !
So the answer must be C !

Hi MSarmah

Good that you found the question easy. What happens if x=4.9 or 4.2?

will you still say x>5???
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Posts: 21
Re: If 3^x>100, which of the following must be true?  [#permalink]

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20 Dec 2017, 23:08
niks18 wrote:
MSarmah wrote:
Such an Irrelevant question and an irrelevant logic!!

The question asks which of the folloeing MUST be true... so for all values of x> 5 the statement 3^x > 100 holds true !
So the answer must be C !

Hi MSarmah

Good that you found the question easy. What happens if x=4.9 or 4.2?

will you still say x>5???

Sir,
will u say that x>4????
Retired Moderator
Joined: 25 Feb 2013
Posts: 1196
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Re: If 3^x>100, which of the following must be true?  [#permalink]

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20 Dec 2017, 23:39
MSarmah wrote:
niks18 wrote:
MSarmah wrote:
Such an Irrelevant question and an irrelevant logic!!

The question asks which of the folloeing MUST be true... so for all values of x> 5 the statement 3^x > 100 holds true !
So the answer must be C !

Hi MSarmah

Good that you found the question easy. What happens if x=4.9 or 4.2?

will you still say x>5???

Sir,
will u say that x>4????

Hi MSarmah

4.1>4 what is the issue with that?

This is Must be true question. Read the wording of the question stem. it Says "If" and not "Is". by using "if" the stem confirms that the equation holds true for all values of $$x$$. so we need to identify the ranges which will be always true.

So here whatever will be the value of $$x$$ it will definitely greater than 3 & 4 but may or may not be greater than 5. Hence you cannot with certainty say that x>5

the question is not that easy as it may look like
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Posts: 55804
Re: If 3^x>100, which of the following must be true?  [#permalink]

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21 Dec 2017, 00:56
MSarmah wrote:
Such an Irrelevant question and an irrelevant logic!!

The question asks which of the folloeing MUST be true... so for all values of x> 5 the statement 3^x > 100 holds true !
So the answer must be C !

To understand the underline concept better practice other Trickiest Inequality Questions Type: Confusing Ranges.
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Re: If 3^x>100, which of the following must be true?  [#permalink]

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21 Dec 2017, 02:06
i think the answer is C,

choice A : yes x may be larger than 3, but what if x = 3.1 ? then $$3^{3.1}$$ which would be equal to 30.1 (cor. to 1.d.p) which would be smaller than 100.

choice B : x may be larger than 4, but what if x = 4.1 ? then $$3^{4.1}$$ which would be equal to 90.4 (cor. to 1.d.p) which would still be smaller than 100

choice C : x must be larger than 5, since$$3^{5}$$ = 243, which would be definitely be larger than 100
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If 3^x>100, which of the following must be true?  [#permalink]

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21 Dec 2017, 02:51
MathNoob123 wrote:
i think the answer is C,

choice A : yes x may be larger than 3, but what if x = 3.1 ? then $$3^{3.1}$$ which would be equal to 30.1 (cor. to 1.d.p) which would be smaller than 100.

choice B : x may be larger than 4, but what if x = 4.1 ? then $$3^{4.1}$$ which would be equal to 90.4 (cor. to 1.d.p) which would still be smaller than 100

choice C : x must be larger than 5, since$$3^{5}$$ = 243, which would be definitely be larger than 100

Hi MathNoob123,

The trick here is that we are not trying to find the value of x but the ranges for which the equation will be always true. Kindly follow the discussions above to get more clarity.
If 3^x>100, which of the following must be true?   [#permalink] 21 Dec 2017, 02:51
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