It is currently 19 Oct 2017, 06:02

### 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

# Which of the following best approximates the value of q if

Author Message
TAGS:

### Hide Tags

Moderator
Status: battlecruiser, operational...
Joined: 25 Apr 2010
Posts: 981

Kudos [?]: 170 [3], given: 71

Schools: Carey '16
Which of the following best approximates the value of q if [#permalink]

### Show Tags

23 Aug 2010, 09:32
3
KUDOS
22
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

42% (01:07) correct 58% (01:32) wrong based on 510 sessions

### HideShow timer Statistics

Which of the following best approximates the value of q if 5^28+3^11=5^q ?

A. 39
B. 30
C. 28
D. 27
E. 17
[Reveal] Spoiler: OA

_________________

Last edited by Bunuel on 02 Apr 2012, 00:18, edited 2 times in total.
Edited the question.

Kudos [?]: 170 [3], given: 71

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128837 [2], given: 12183

### Show Tags

23 Aug 2010, 10:12
2
KUDOS
Expert's post
10
This post was
BOOKMARKED

Which of the following best approximates the value of q if $$5^{28}+3^{11}=5^q$$?

A. 39
B. 30
C. 28
D. 27
E. 17

Note that we need approximate value of $$q$$. Now, $$5^{28}$$ is much, much, much bigger than $$3^{11}$$. So adding $$3^{11}$$ to $$5^{28}$$ will be closer to $$5^{28}$$ then to $$5^{29}$$, basically $$3^{11}$$ is negligible in this case. So $$q\approx{28}$$.

_________________

Kudos [?]: 128837 [2], given: 12183

Moderator
Status: battlecruiser, operational...
Joined: 25 Apr 2010
Posts: 981

Kudos [?]: 170 [0], given: 71

Schools: Carey '16

### Show Tags

24 Aug 2010, 06:47
thx i guess i need to go review my exponents haha. i was trying to actually do the problem until it started to get out of hand....sigh...
_________________

Kudos [?]: 170 [0], given: 71

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7674

Kudos [?]: 17358 [11], given: 232

Location: Pune, India

### Show Tags

01 Apr 2012, 23:51
11
KUDOS
Expert's post
5
This post was
BOOKMARKED
Smita04 wrote:
Which of the following best approximates the value of q if 5^28 + 3^11 = 5^q ?
(A) 39
(B) 30
(C) 28
(D) 27
(E) 17

The answer has to be at least 28 since you are adding something to 5^28.

Note that 3^11 is much much smaller than 5^28 so adding it will not change the value of 5^28 much. If it is hard to visualize, think of it this way:

The next possible answer is 5^30 which is greater than 5^28
5^30 = 25*5^28

But
5^28 + 5^28 = 2*5^28
Even if we add 5^28 to 5^28, all we get is 2*5^28 which is much much smaller than 25*5^28
In fact, what we are actually adding is only 3^11 so 5^28 + 3^11 must be much closer to 5^28. Hence its value must be approximately 5^28.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17358 [11], given: 232

Senior Manager
Joined: 13 Mar 2012
Posts: 351

Kudos [?]: 196 [1], given: 31

Concentration: Operations, Strategy

### Show Tags

01 Apr 2012, 23:56
1
KUDOS
Smita04 wrote:
Which of the following best approximates the value of q if 5^28 + 3^11 = 5^q ?
(A) 39
(B) 30
(C) 28
(D) 27
(E) 17

Pay attention to the funda here that 3^11 is much less than 5^28 (obviously its superlarge number)

hence q can be approximated to 28.

ANALOGY: suppose you need to add 10...... trillion to 100 then obviously the result after addition can be approximated to 10......trillion.

Hence C
_________________

Practice Practice and practice...!!

If there's a loophole in my analysis--> suggest measures to make it airtight.

Kudos [?]: 196 [1], given: 31

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128837 [0], given: 12183

Re: Which of the following best approximates the value of q if [#permalink]

### Show Tags

02 Apr 2012, 00:25
Smita04 wrote:
Which of the following best approximates the value of q if 5^28 + 3^11 = 5^q ?

(A) 39
(B) 30
(C) 28
(D) 27
(E) 17

Similar questions to practice:
gmat-number-properties-exponents-84309.html
tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029229

Hope it helps.
_________________

Kudos [?]: 128837 [0], given: 12183

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128837 [0], given: 12183

Re: Which of the following best approximates the value of q if [#permalink]

### Show Tags

25 Jun 2013, 05:55
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

_________________

Kudos [?]: 128837 [0], given: 12183

Manager
Joined: 12 Jan 2013
Posts: 218

Kudos [?]: 79 [0], given: 47

### Show Tags

28 Dec 2013, 06:13
Bunuel wrote:

Which of the following best approximates the value of q if $$5^{28}+3^{11}=5^q$$?

A. 39
B. 30
C. 28
D. 27
E. 17

Note that we need approximate value of $$q$$. Now, $$5^{28}$$ is much, much, much bigger than $$3^{11}$$. So adding $$3^{11}$$ to $$5^{28}$$ will be closer to $$5^{28}$$ then to $$5^{29}$$, basically $$3^{11}$$ is negligible in this case. So $$q\approx{28}$$.

Bunuel, my approach for this question was:

I approximated $$3^{11}$$ to $$30^{10}$$ and thus $$3^{11}$$ = $$5*6^{10}$$ ----> factor ---> $$5^{10}$$ ($$5^{18}$$ + 6) .. Since the addition in the parenthesis is minescule, we can ignore it. And thus we have $$5^{10}$$ * $$5^{18}$$ = $$5^{28}$$ .... so q = 28

But obviously 30^10 is about a third of the size of 3^11 so I do not know if these operations work in general. Do they?

Kudos [?]: 79 [0], given: 47

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128837 [0], given: 12183

### Show Tags

28 Dec 2013, 06:17
aeglorre wrote:
Bunuel wrote:

Which of the following best approximates the value of q if $$5^{28}+3^{11}=5^q$$?

A. 39
B. 30
C. 28
D. 27
E. 17

Note that we need approximate value of $$q$$. Now, $$5^{28}$$ is much, much, much bigger than $$3^{11}$$. So adding $$3^{11}$$ to $$5^{28}$$ will be closer to $$5^{28}$$ then to $$5^{29}$$, basically $$3^{11}$$ is negligible in this case. So $$q\approx{28}$$.

Bunuel, my approach for this question was:

I approximated $$3^{11}$$ to $$30^{10}$$ and thus $$3^{11}$$ = $$5*6^{10}$$ ----> factor ---> $$5^{10}$$ ($$5^{18}$$ + 6) .. Since the addition in the parenthesis is minescule, we can ignore it. And thus we have $$5^{10}$$ * $$5^{18}$$ = $$5^{28}$$ .... so q = 28

But obviously 30^10 is about a third of the size of 3^11 so I do not know if these operations work in general. Do they?

It seems that you need to brush up fundamentals on this topic, because unfortunately very little above is correct.

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

Hope this helps.
_________________

Kudos [?]: 128837 [0], given: 12183

Manager
Joined: 04 Oct 2013
Posts: 176

Kudos [?]: 157 [1], given: 29

GMAT 1: 590 Q40 V30
GMAT 2: 730 Q49 V40
WE: Project Management (Entertainment and Sports)

### Show Tags

28 Dec 2013, 11:02
1
KUDOS
I solved it this way:

$$5^2^8+3^1^1=5^q$$

$$3^3=27$$ which is pretty close to $$5^2$$
$$3^1^1$$ is 3 times $$3^3$$ and one time $$3^2$$ thus we can approximate to 3 times $$5^2$$ and one 5

$$5^2^8+5^7=5^7(5^2^1+1)$$.

we can conclude that the best approximation is $$5^2^8$$ since $$5^2^1+1$$ is a little bit more than $$5^2^1$$. and $$5^7$$ times (a little bit more than $$5^2^1$$) = around $$5^2^8$$

hope it helps.
_________________

learn the rules of the game, then play better than anyone else.

Last edited by gmat6nplus1 on 29 Dec 2013, 04:18, edited 1 time in total.

Kudos [?]: 157 [1], given: 29

Manager
Joined: 04 Oct 2013
Posts: 162

Kudos [?]: 119 [0], given: 55

Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Which of the following best approximates the value of q if [#permalink]

### Show Tags

29 Dec 2013, 03:34
Which of the following best approximates the value of q if $$5^{28} + 3^{11} = 5^q$$ ?
(A) 39
(B) 30
(C) 28
(D) 27
(E) 17

$$5^{28} + 3^{11} = 5^q$$

Or, $$5^{28}( 1 + \frac{3^{11}}{5^{28}}) = 5^q$$

Since, $$\frac{3^{11}}{5^{28}} << 1$$, the term $$(1 + \frac{3^{11}}{5^{28}})$$can be approximated to 1.

Thus, $$5 ^ {28} = 5 ^q$$

Or, $$q = 28$$.

Last edited by arunspanda on 29 Sep 2014, 05:48, edited 1 time in total.

Kudos [?]: 119 [0], given: 55

Verbal Forum Moderator
Joined: 16 Jun 2012
Posts: 1127

Kudos [?]: 3478 [0], given: 123

Location: United States
Re: Which of the following best approximates the value of q if [#permalink]

### Show Tags

29 Dec 2013, 03:35
vwjetty wrote:
Which of the following best approximates the value of q if 5^28+3^11=5^q ?

A. 39
B. 30
C. 28
D. 27
E. 17

We have: 5^28+3^11=5^q
==> because 3^11 > 0 --> 5^q MUST be equal or greater than 5^28 ==> q MUST be equal or greater than 28
==> Option D and E are out immediately.

Divide both sides by 5^q and q >= 28
We have:
5^(28-q) + 3^11/5^q = 1

Because q >= 28 ==> 3^11/5^q = 0.0000xyz that is very small, we can ignore it.
Thus, 5^(28-q) must be approximate 1
==> 28-q = 0 ==> q is approximate 28

Hope it helps.
_________________

Please +1 KUDO if my post helps. Thank you.

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

Chris Bangle - Former BMW Chief of Design.

Kudos [?]: 3478 [0], given: 123

Senior Manager
Joined: 20 Dec 2013
Posts: 267

Kudos [?]: 106 [0], given: 29

Location: India

### Show Tags

11 Apr 2014, 21:29
Bunuel wrote:

Which of the following best approximates the value of q if $$5^{28}+3^{11}=5^q$$?

A. 39
B. 30
C. 28
D. 27
E. 17

Note that we need approximate value of $$q$$. Now, $$5^{28}$$ is much, much, much bigger than $$3^{11}$$. So adding $$3^{11}$$ to $$5^{28}$$ will be closer to $$5^{28}$$ then to $$5^{29}$$, basically $$3^{11}$$ is negligible in this case. So $$q\approx{28}$$.

I thought it this way:$$3^11=5^q-5^28$$.Now if we take$$q>28$$,we'll be able to take out $$5^28$$ common from RHS;that cannot equal $$3^11$$.And if we take $$q<28$$,We'll get -ve RHS;that again cannot equal $$3^11$$.
So the closest value can be $$q=28$$ only.But can this question be there in the GMAT?Even the closest/aprox. value in this case is quite far away!

Kudos [?]: 106 [0], given: 29

Manager
Joined: 20 Dec 2013
Posts: 130

Kudos [?]: 106 [0], given: 1

Re: Which of the following best approximates the value of q if [#permalink]

### Show Tags

11 Apr 2014, 23:04
vwjetty wrote:
Which of the following best approximates the value of q if 5^28+3^11=5^q ?

A. 39
B. 30
C. 28
D. 27
E. 17

Raise to the power (1/10) to both the sides we will get:

5^2.8 + 3^1.1 = 5^q/10

3^1.1 is negligible as compared to 5^2.8 hence q = 28
_________________

76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org

Kudos [?]: 106 [0], given: 1

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1853

Kudos [?]: 2618 [0], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Which of the following best approximates the value of q if [#permalink]

### Show Tags

14 Apr 2014, 01:13
Option D & E can be neglected as the power would either be SAME or increase

Try to close in the powers of both the expressions

Consider $$5^{28}$$

$$= 5^{4*7}$$

$$= (5^4)^7$$

$$= 625^7$$

$$625^7$$ is a huge number as compared to $$3^{11}$$; so addition of the later will not have any significant effect to the exponent

_________________

Kindly press "+1 Kudos" to appreciate

Kudos [?]: 2618 [0], given: 193

Current Student
Joined: 20 Jan 2014
Posts: 175

Kudos [?]: 69 [0], given: 120

Location: India
Concentration: Technology, Marketing
Re: Which of the following best approximates the value of q if [#permalink]

### Show Tags

29 Sep 2014, 04:43
I solved it in this way:

5^28+3^11=5^q ?

3^2 = 27~ 5^2

So we can write 3^11 = 5^7

Now

5^28+5^7=5^q

5^7 (5^21 + 1) = 5^q => We can ignore 1 as it is much smaller than 5^21
5^28 = 5^q => q= 28 Hence C
_________________

Kudos [?]: 69 [0], given: 120

Chat Moderator
Joined: 19 Apr 2013
Posts: 690

Kudos [?]: 170 [0], given: 537

Concentration: Strategy, Healthcare
Schools: Sloan '18 (A)
GMAT 1: 730 Q48 V41
GPA: 4
Re: Which of the following best approximates the value of q if [#permalink]

### Show Tags

23 Feb 2015, 08:00
Karishma's explanation is great. Thanks Karishma. It helps to better visualize.
_________________

If my post was helpful, press Kudos. If not, then just press Kudos !!!

Kudos [?]: 170 [0], given: 537

CEO
Joined: 17 Jul 2014
Posts: 2604

Kudos [?]: 394 [0], given: 184

Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: Which of the following best approximates the value of q if [#permalink]

### Show Tags

20 Feb 2016, 11:13
VeritasPrepKarishma wrote:
Smita04 wrote:
Which of the following best approximates the value of q if 5^28 + 3^11 = 5^q ?
(A) 39
(B) 30
(C) 28
(D) 27
(E) 17

The answer has to be at least 28 since you are adding something to 5^28.

Note that 3^11 is much much smaller than 5^28 so adding it will not change the value of 5^28 much. If it is hard to visualize, think of it this way:

The next possible answer is 5^30 which is greater than 5^28
5^30 = 25*5^28

But
5^28 + 5^28 = 2*5^28
Even if we add 5^28 to 5^28, all we get is 2*5^28 which is much much smaller than 25*5^28
In fact, what we are actually adding is only 3^11 so 5^28 + 3^11 must be much closer to 5^28. Hence its value must be approximately 5^28.

great explanation...I tried to solve it by logic..and eliminated right away D and E. A is way too much. Between B and C, went with B..now I see why I did the mistake..

Kudos [?]: 394 [0], given: 184

Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2676

Kudos [?]: 1723 [0], given: 792

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Which of the following best approximates the value of q if [#permalink]

### Show Tags

20 Feb 2016, 11:32
mvictor wrote:
VeritasPrepKarishma wrote:
Smita04 wrote:
Which of the following best approximates the value of q if 5^28 + 3^11 = 5^q ?
(A) 39
(B) 30
(C) 28
(D) 27
(E) 17

The answer has to be at least 28 since you are adding something to 5^28.

Note that 3^11 is much much smaller than 5^28 so adding it will not change the value of 5^28 much. If it is hard to visualize, think of it this way:

The next possible answer is 5^30 which is greater than 5^28
5^30 = 25*5^28

But
5^28 + 5^28 = 2*5^28
Even if we add 5^28 to 5^28, all we get is 2*5^28 which is much much smaller than 25*5^28
In fact, what we are actually adding is only 3^11 so 5^28 + 3^11 must be much closer to 5^28. Hence its value must be approximately 5^28.

great explanation...I tried to solve it by logic..and eliminated right away D and E. A is way too much. Between B and C, went with B..now I see why I did the mistake..

B could've been easily eliminated as for increasing another power of 5, you will need to atleast multiply that number by 5 atleast. 3^11 can be approximated to (3^6)^2 and 3^6 will give you 5^4 so you will end up getting almost 5^8 and this when added to 5^28 will still not do anything.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Kudos [?]: 1723 [0], given: 792

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2212

Kudos [?]: 836 [0], given: 595

Which of the following best approximates the value of q if [#permalink]

### Show Tags

29 Nov 2016, 14:07
Here is how i solved it up=>
5^q=5^28+3^11
I didn't realise that 3^11 was negligible when saw this statement.
So i followed as -->
3^3=5^2(approx)
hence 5^q=(5)^28+5^7(approx)=> 5^75^21+1
Here i neglected 1 and wrote 5^q=5^28
hence q=28(approx)

_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 836 [0], given: 595

Which of the following best approximates the value of q if   [#permalink] 29 Nov 2016, 14:07
Display posts from previous: Sort by