Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 : GMAT Data Sufficiency (DS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 07 Dec 2016, 16:58

### 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 June
Open Detailed Calendar

# Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35

Author Message
TAGS:

### Hide Tags

Manager
Joined: 19 Oct 2011
Posts: 132
Location: India
Followers: 3

Kudos [?]: 367 [3] , given: 33

Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

### Show Tags

20 Feb 2012, 17:55
3
KUDOS
19
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:52) correct 40% (00:58) wrong based on 519 sessions

### HideShow timer Statistics

Is x > 10^10 ?

(1) x > 2^34
(2) x = 2^35
[Reveal] Spoiler: OA

_________________

Encourage me by pressing the KUDOS if you find my post to be helpful.

Help me win "The One Thing You Wish You Knew - GMAT Club Contest"
http://gmatclub.com/forum/the-one-thing-you-wish-you-knew-gmat-club-contest-140358.html#p1130989

Math Expert
Joined: 02 Sep 2009
Posts: 35912
Followers: 6851

Kudos [?]: 90026 [26] , given: 10402

Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

### Show Tags

20 Feb 2012, 20:41
26
KUDOS
Expert's post
11
This post was
BOOKMARKED
Is x > 10^10 ?

(1) x > 2^34 --> we should compare $$2^{34}$$ and $$10^{10}$$ --> take the square root from both: we should compare $$2^{17}$$ and $$10^5=100,000$$. Now, $$2^{17}=2^{10}*2^7=1,024*128>100,000$$. Sufficient.

OR: $$2^{34}=(2^{10})^{3.4}=(1,024)^{3.4}>(10^3)^{3.4}=10^{(3*3.4)}=10^{10.2}>10^{10}$$.

(2) x = 2^35. Since we have the exact numerical value of x we should be able compare it to 10^10 and answer the question. It really doesn't matter whether 2^35>10^10, the main point is that we have sufficient information to get the answer. Sufficient.

_________________
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 98

Kudos [?]: 868 [7] , given: 43

Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

### Show Tags

30 Jul 2012, 02:09
7
KUDOS
dvinoth86 wrote:
Is x > 10^10 ?

(1) x > 2^34
(2) x = 2^35

(1) Let's see if $$2^{34}>10^{10}$$.

$$2^{34}>2^{10}*5^{10}$$. Divide through by $$2^{10}$$, and we get $$2^{24}>5^{10}$$. Take the square root of both sides:
$$2^{12}>5^5$$. This we can compute quite easily, and we find that 1024*4=4096 > 625*5= 3125, TRUE.
Sufficient.

(2) We have already seen that (1) is sufficient, obviously (2) is also sufficient.
Just to play with powers, we can check that $$2^{35}>10^{10}$$:
Start again with $$2^{35}>2^{10}*5^{10}$$, divide through by $$2^{10}$$, then $$2^{25}>5^{10}$$. Now we can take the 5th order root of both sides and obtain $$2^5>5^2$$ or 32 > 25, TRUE.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Director
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 584
Followers: 111

Kudos [?]: 425 [2] , given: 14

Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

### Show Tags

30 Jul 2012, 12:22
2
KUDOS
In my personal opinion, I just don't see this question following the style of the GMAT test writers. Unless, whoever wrote this can confirm that they recently saw a similar idea on the exam.

Dabral
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 98

Kudos [?]: 868 [1] , given: 43

Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

### Show Tags

30 Jul 2012, 05:19
1
KUDOS
venmic wrote:
Bunuel rocks this is a very nice solution compared to the other ones I ve seen

Bunuel wrote:
Is x > 10^10 ?

(1) x > 2^34 --> we should compare $$2^{34}$$ and $$10^{10}$$ --> take the square root from both: we should compare $$2^{17}$$ and $$10^5=100,000$$. Now, $$2^{17}=2^{10}*2^7=1,024*128>100,000$$. Sufficient.

OR: $$2^{34}=(2^{10})^{3.4}=(1,024)^{3.4}>(10^3)^{3.4}=10^{(3*3.4)}=10^{10.2}>10^{10}$$.

(2) x = 2^35. Since we have the exact numerical value of x we should be able compare it to 10^10 and answer the question. It really doesn't matter whether 2^35>10^10, the main point is that we have sufficient information to get the answer. Sufficient.

Bunuel's logic for testing assumption (2) is excellent. In the present form of the question, one can use that $$2^{35}>2^{34}$$, so once (1) turns out sufficient and necessarily provides the info that $$2^{34}>10^{10}$$, testing (2) is very easy. Maybe, it would have been somehow more challenging to choose a smaller exponent in statement (2), like 33, with which direct comparison would have been not so straightforward, and a time saving approach would need similar logic to Bunuel's.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Math Expert
Joined: 02 Sep 2009
Posts: 35912
Followers: 6851

Kudos [?]: 90026 [1] , given: 10402

Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

### Show Tags

04 Sep 2012, 02:49
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
reklaw wrote:
Why would you need to compute anything in this problem?

Statement 1 gives us a minimum value of x. It doesn't matter if 10^10 is smaller or larger, it is sufficient to answer the question.
Statement 2 needs no computation either, which Bunuel already pointed out.

We do need to compare 10^10 and 2^34 in (1). Because if 2^34 were less than 10^10, then the statement wouldn't b sufficient. Consider this:

Is x>10?

(1) x>2. If x=5 then the answer is NO but if x=15, then the answer is YES. Not sufficient.

Hope it's clear.
_________________
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 631
Followers: 79

Kudos [?]: 1091 [1] , given: 136

Re: Is x > 10^10 [#permalink]

### Show Tags

17 Feb 2013, 23:35
1
KUDOS
A very coarse method but I would do this problem by log.

F.S.1 gives logx > 34 log2 = 34*0.3 = 10.2(approx). As problem statement is asking about whether x>10^10, it boils down to logx>10. Thus suficient.

F.S.2 anyways gives the value of logx = 35*0.3. Again logx>10.
Sufficient.

D.

Not the best method but a pretty quick one. I don't think it is a 700+ level question.
_________________
Director
Joined: 14 Dec 2012
Posts: 841
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
Followers: 57

Kudos [?]: 1248 [1] , given: 197

Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

### Show Tags

08 Jul 2013, 14:25
1
KUDOS
dvinoth86 wrote:
Is x > 10^10 ?

(1) x > 2^34
(2) x = 2^35

hi,

statement 2 is clear we are able to calculate...HENCE SUFFICIENT
for statement 1
2^34=2^10*8^8===>(1
10^10=2^10*5^10===>(2

actually we have to compare 2^34..and 10^10
both of them have 2^10 common...so we have to compare actually 8^8 and 5^10...

5^10=(8-3)^8*25=25*(8-3)^8
lets divide 5^10..with 8^8..==>25*((8-3)/8)^8==>clearly we can see that 25 is multiplied to a very small no.(as bracket number is less than 1,and it has been raised to power 8)==>end resul will be less than 1...==>this proves 8^8 is greater than 5^10....hence...2^34>10^10==>sufficient.

both statements are sufficient..hence D
_________________

When you want to succeed as bad as you want to breathe ...then you will be successfull....

GIVE VALUE TO OFFICIAL QUESTIONS...

learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment

VP
Joined: 08 Jul 2010
Posts: 1432
Location: India
GMAT: INSIGHT
WE: Education (Education)
Followers: 65

Kudos [?]: 1340 [1] , given: 42

Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

### Show Tags

11 Oct 2016, 08:10
1
KUDOS
Expert's post
dvinoth86 wrote:
Is x > 10^10 ?

(1) x > 2^34
(2) x = 2^35

Statement 1: x > 2^34

Comparing 2^34 with 10^10
Comparing 2^34 with 2^10 * 5^10 [Now we can cancel out common terms 2^10 from both sides]
Comparing 2^24 with 5^10
Comparing (2^2)^12 with 5^10
Comparing (4)^12 with (5)^10
Comparing (4^6)^2 with (5^5)^2 [Now we can cancel out common powers 2 from both sides]
Comparing (4)^6 with (5)^5
Comparing (4096) with (3125)

Since 4096 > 3125
therefore, 2^34 > 10^10
SUFFICIENT

Statement 2: x = 2^35

Since I know the exact value of x so a comparison can be established hence the statement is sufficient
SUFFICIENT

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com
Call us : +91-9999687183 / 9891333772
http://www.GMATinsight.com/testimonials.html

Feel free to give a Kudos if it is a useful post .

Manager
Joined: 19 Oct 2011
Posts: 132
Location: India
Followers: 3

Kudos [?]: 367 [0], given: 33

Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

### Show Tags

21 Feb 2012, 19:36
u r awesome Bunuel
_________________

Encourage me by pressing the KUDOS if you find my post to be helpful.

Help me win "The One Thing You Wish You Knew - GMAT Club Contest"
http://gmatclub.com/forum/the-one-thing-you-wish-you-knew-gmat-club-contest-140358.html#p1130989

Manager
Joined: 02 Nov 2009
Posts: 138
Followers: 3

Kudos [?]: 162 [0], given: 97

Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

### Show Tags

29 Jul 2012, 20:58
Bunuel rocks this is a very nice solution compared to the other ones I ve seen

Bunuel wrote:
Is x > 10^10 ?

(1) x > 2^34 --> we should compare $$2^{34}$$ and $$10^{10}$$ --> take the square root from both: we should compare $$2^{17}$$ and $$10^5=100,000$$. Now, $$2^{17}=2^{10}*2^7=1,024*128>100,000$$. Sufficient.

OR: $$2^{34}=(2^{10})^{3.4}=(1,024)^{3.4}>(10^3)^{3.4}=10^{(3*3.4)}=10^{10.2}>10^{10}$$.

(2) x = 2^35. Since we have the exact numerical value of x we should be able compare it to 10^10 and answer the question. It really doesn't matter whether 2^35>10^10, the main point is that we have sufficient information to get the answer. Sufficient.

Intern
Joined: 28 Nov 2010
Posts: 2
Followers: 0

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

Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

### Show Tags

04 Sep 2012, 02:43
Why would you need to compute anything in this problem?

Statement 1 gives us a minimum value of x. It doesn't matter if 10^10 is smaller or larger, it is sufficient to answer the question.
Statement 2 needs no computation either, which Bunuel already pointed out.
Intern
Joined: 28 Nov 2010
Posts: 2
Followers: 0

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

Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

### Show Tags

04 Sep 2012, 02:54
Crystal.

Classic mistake, which is what is probably REALLY being tested, realised it when re-reading my post.

Thanks for response though.
Intern
Joined: 24 Dec 2012
Posts: 14
Location: United States
Concentration: Finance, Entrepreneurship
GPA: 3
WE: Corporate Finance (Investment Banking)
Followers: 0

Kudos [?]: 21 [0], given: 2

Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

### Show Tags

16 Feb 2013, 13:19
Bunuel wrote:
Is x > 10^10 ?

(1) x > 2^34 --> we should compare $$2^{34}$$ and $$10^{10}$$ --> take the square root from both: we should compare $$2^{17}$$ and $$10^5=100,000$$. Now, $$2^{17}=2^{10}*2^7=1,024*128>100,000$$. Sufficient.

OR: $$2^{34}=(2^{10})^{3.4}=(1,024)^{3.4}>(10^3)^{3.4}=10^{(3*3.4)}=10^{10.2}>10^{10}$$.

(2) x = 2^35. Since we have the exact numerical value of x we should be able compare it to 10^10 and answer the question. It really doesn't matter whether 2^35>10^10, the main point is that we have sufficient information to get the answer. Sufficient.

Bunuel,

I solved it a different way- would you mind checking my approach?

I restructured the qstem to is x =,> 2^11 * 5^11?

(1) x > 2^34

- x has 2^11 therefore 2^35 - 2^11 = 2^24
- estimated 2^2 to be 5 and divided 24 by 2 and got 5^12
- x = 2^11 * 5^12 -------- SUFFICIENT

(2) X = 2^35

- SUFFICIENT

Is this approach correct?
Senior Manager
Joined: 22 Nov 2010
Posts: 289
Location: India
GMAT 1: 670 Q49 V33
WE: Consulting (Telecommunications)
Followers: 5

Kudos [?]: 133 [0], given: 75

Re: Is x > 10^10 [#permalink]

### Show Tags

18 Feb 2013, 01:22
vinaymimani wrote:
A very coarse method but I would do this problem by log.

F.S.1 gives logx > 34 log2 = 34*0.3 = 10.2(approx). As problem statement is asking about whether x>10^10, it boils down to logx>10. Thus suficient.

F.S.2 anyways gives the value of logx = 35*0.3. Again logx>10.
Sufficient.

D.

Not the best method but pretty quick. I don't think it is a 700+ level question.

Good one. Can you please share some source/ tutorial of this method?
_________________

YOU CAN, IF YOU THINK YOU CAN

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 631
Followers: 79

Kudos [?]: 1091 [0], given: 136

Re: Is x > 10^10 [#permalink]

### Show Tags

18 Feb 2013, 01:25
greatps24 wrote:
vinaymimani wrote:
A very coarse method but I would do this problem by log.

F.S.1 gives logx > 34 log2 = 34*0.3 = 10.2(approx). As problem statement is asking about whether x>10^10, it boils down to logx>10. Thus suficient.

F.S.2 anyways gives the value of logx = 35*0.3. Again logx>10.
Sufficient.

D.

Not the best method but pretty quick. I don't think it is a 700+ level question.

Good one. Can you please share some source/ tutorial of this method?

No tutorial as such. Just that they gave a power of 10 in this question and also 2^something. So it just struck me. Worked in this question, might not work always!
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 35912
Followers: 6851

Kudos [?]: 90026 [0], given: 10402

Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

### Show Tags

07 Jul 2013, 23:54
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

To find DS questions by Kudos, sort by Kudos here: gmat-data-sufficiency-ds-141/
To find PS questions by Kudos, sort by Kudos here: gmat-problem-solving-ps-140/

_________________
Manager
Joined: 22 Feb 2009
Posts: 229
Followers: 5

Kudos [?]: 126 [0], given: 148

Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

### Show Tags

31 Jul 2014, 13:15
dvinoth86 wrote:
Is x > 10^10 ?

(1) x > 2^34
(2) x = 2^35

(2) is 1 number, so it is sufficient
(1) compare 2^34 > 10^10 ?
-> 2^10 * 2^24 > 2^10 * 5^10
-> 2^24 > 5^10
-> 2^12 > 5^5 ( square root)
-> 2^10 * 2^2 > 5^3 * 5^2
-> 1028*4 > 125*25
-> 4112 > 3125 ( correct)

_________________

.........................................................................
+1 Kudos please, if you like my post

Intern
Joined: 09 May 2013
Posts: 39
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT 1: Q V
GPA: 3.28
Followers: 0

Kudos [?]: 5 [0], given: 64

Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

### Show Tags

08 Dec 2014, 00:34
Bunuel wrote:
Is x > 10^10 ?

(1) x > 2^34 --> we should compare $$2^{34}$$ and $$10^{10}$$ --> take the square root from both: we should compare $$2^{17}$$ and $$10^5=100,000$$. Now, $$2^{17}=2^{10}*2^7=1,024*128>100,000$$. Sufficient.

OR: $$2^{34}=(2^{10})^{3.4}=(1,024)^{3.4}>(10^3)^{3.4}=10^{(3*3.4)}=10^{10.2}>10^{10}$$.

(2) x = 2^35. Since we have the exact numerical value of x we should be able compare it to 10^10 and answer the question. It really doesn't matter whether 2^35>10^10, the main point is that we have sufficient information to get the answer. Sufficient.

Oh Bunuel, you are always awesome. For me, your approach is always faster than Manhanttan's.
Highly recommend GMAT club for all GMAT learner!!!
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12890
Followers: 561

Kudos [?]: 158 [0], given: 0

Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 [#permalink]

### Show Tags

27 Dec 2015, 06:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35   [#permalink] 27 Dec 2015, 06:10

Go to page    1   2    Next  [ 25 posts ]

Similar topics Replies Last post
Similar
Topics:
1 Is y > -8? (1) y = 2013^2 - 155^3 - 23^4 (2) y > (2w - 3x - 1)^2 I 5 23 Sep 2015, 01:51
10 Is x^3 > x^2? (1) x > 0 (2) x^2 > x 13 22 Sep 2011, 00:18
2 Is x>3 ? 1. (x-1)(x-2)(x-3)>0 2. x>1 12 16 Oct 2011, 16:14
8 Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35 10 21 Jun 2011, 23:22
Is x^2 > x? (1) x^2 > 1 (2) x > -1 10 17 Mar 2007, 01:40
Display posts from previous: Sort by