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

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

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14 Dec 2017, 01:16
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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
[Reveal] Spoiler: OA

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Re: If 3^x>100, which of the following must be true? [#permalink]

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14 Dec 2017, 02:50
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
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Re: If 3^x>100, which of the following must be true? [#permalink]

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14 Dec 2017, 03:05
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.

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

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14 Dec 2017, 07:24
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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

$$3^x>100....3^4=81$$ 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
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Re: If 3^x>100, which of the following must be true? [#permalink]

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14 Dec 2017, 08:54
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

$$3^x>100....3^4=81$$ 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

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Re: If 3^x>100, which of the following must be true? [#permalink]

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14 Dec 2017, 09:57
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

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Re: If 3^x>100, which of the following must be true? [#permalink]

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14 Dec 2017, 15:59
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

$$3^x>100....3^4=81$$ 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.
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Re: If 3^x>100, which of the following must be true? [#permalink]

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14 Dec 2017, 17:05
Expert's post
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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

$$3^x>100....3^4=81$$ 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.

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Re: If 3^x>100, which of the following must be true? [#permalink]

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17 Dec 2017, 23:26
=>
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.

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

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18 Dec 2017, 05:22
Hi Chetan,
Thank you
Yes it's cleared.

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Re: If 3^x>100, which of the following must be true? [#permalink]

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20 Dec 2017, 22:00
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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Re: If 3^x>100, which of the following must be true? [#permalink]

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20 Dec 2017, 22:04
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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Re: If 3^x>100, which of the following must be true? [#permalink]

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20 Dec 2017, 22:08
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????

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Re: If 3^x>100, which of the following must be true? [#permalink]

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20 Dec 2017, 22:39
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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Re: If 3^x>100, which of the following must be true? [#permalink]

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20 Dec 2017, 23:56
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, 01:06
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, 01:51
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.

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If 3^x>100, which of the following must be true?   [#permalink] 21 Dec 2017, 01:51
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