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If N = 2^0.15 and N^b = 16, b must equal

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If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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New post 13 Mar 2015, 07:53
2
6
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A
B
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D
E

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82% (01:47) correct 18% (01:40) wrong based on 122 sessions

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Re: If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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New post 13 Mar 2015, 08:19
1
Bunuel wrote:
If N = 2^0.15 and N^b = 16, b must equal

A. 3/80
B. 3/5
C. 4
D. 5/3
E. 80/3

Kudos for a correct solution.



N = 2^0.15 and N^b = 16
so
\(2^(^(^1^5^/^1^0^0^)^*^b^)= 2^4\)
\((15/100) * b = 4\)
\(b = 80/3\)


on a different note , is there an easy way to write the exponents , square roots , less than , subscripts (X1,X2 etc.)?
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Re: If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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New post 13 Mar 2015, 09:21
15/100 = 3/20
N = 2 ^ 3/20

N^b = 2^4

(2^3/20)^b = 2^4
b = 80/3

Answer: E
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Re: If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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New post 13 Mar 2015, 09:26
1
If N = 2^0.15 and N^b = 16, b must equal

we can rewrite this as

(2^0.15)^b = 16
2^0.15b = 2^4
and 0.15b = 4
we can rewrite this as:
b= 4/0.15 = 400/15
this is definitely more than answer choices A,B,C,D.

hence, the only possible answer is E.
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Re: If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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New post 15 Mar 2015, 22:56
Bunuel wrote:
If N = 2^0.15 and N^b = 16, b must equal

A. 3/80
B. 3/5
C. 4
D. 5/3
E. 80/3

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

First, we have to express 0.15 as a fraction: 0.15 = 3/20.

Also, 16 is 2 to the power of 4, so the equation with b tells us: \((2^{\frac{3}{20}})^b=2^4\)

Bases are the same, so we can equate the exponents.

3/20*b = 4 --> b = 80/3.

Answer = (E).
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Re: If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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New post 17 Mar 2015, 03:23
\(N = 2^{0.15}\)

\(n^b = 2^{0.15b}\)

Given that \(n^b = 16 = 2^4\)

Bases are same, equating powers

0.15b = 4

\(b = \frac{400}{15} = \frac{80}{3}\)

Answer = E
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Re: If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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New post 12 Apr 2015, 09:26
Bunuel wrote:
Bunuel wrote:
If N = 2^0.15 and N^b = 16, b must equal

A. 3/80
B. 3/5
C. 4
D. 5/3
E. 80/3

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

First, we have to express 0.15 as a fraction: 0.15 = 3/20.

Also, 16 is 2 to the power of 4, so the equation with b tells us: \((2^{\frac{3}{20}})^b=2^4\)



Bases are the same, so we can equate the exponents.

3/20*b = 4 --> b = 80/3.

Answer = (E).



should the equation not be (2^3/20)^b = 2^4

giving us 3/20^b = 4

why are we saying 3/20 * b = 4 ?
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Re: If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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New post 12 Apr 2015, 11:04
2^0.15b = 2^4, by substituting N - 2^0.15in the second Equation. Therefore, 0.15 b = 4, b = 80/3
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Re: If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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New post 14 Apr 2015, 05:43
LaxAvenger wrote:
Bunuel wrote:
Bunuel wrote:
If N = 2^0.15 and N^b = 16, b must equal

A. 3/80
B. 3/5
C. 4
D. 5/3
E. 80/3

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

First, we have to express 0.15 as a fraction: 0.15 = 3/20.

Also, 16 is 2 to the power of 4, so the equation with b tells us: \((2^{\frac{3}{20}})^b=2^4\)



Bases are the same, so we can equate the exponents.

3/20*b = 4 --> b = 80/3.

Answer = (E).



should the equation not be (2^3/20)^b = 2^4

giving us 3/20^b = 4

why are we saying 3/20 * b = 4 ?


(2^3/20)^b = 2^(3/20*b), so we have that 2^(3/20*b) = 2^4 --> 3/20*b = 4.

Theory on Exponents: math-number-theory-88376.html
Tips on Exponents: exponents-and-roots-on-the-gmat-tips-and-hints-174993.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

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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If N = 2^0.15 and N^b = 16, b must equal  [#permalink]

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