8^a*(1/4)^b = ? (1) b = 1.5a (2) a = 2

Question

Tough and Tricky questions: Exponents.

8^a*(\frac{1}{4})^b = ?

(1) b = 1.5a 
(2) a = 2

Kudos for a correct  solution .

pqhai · Accepted Answer

We have: 8^a*(1/4)^b = 2^3a*2^(-2b) = 2^(3a - 2b)

S1:b = 1.5a --> 2b = 3a --> 3a - 2b = 0
--> 2^0 = 1
SUFF

S2: a = 2
NOT SUFF because we don't know b.

Ans:A

WoundedTiger · Answer

Question can written as 2^3a*(1/2^2)^b or 2^3a*2-2b...We need to find the value of 2^(3a-2b)

St 1 b=1.5a or 2b=3a so we have 2^0=1..Sufficient

St2 says a=2...but we don't know anything about b...in sufficient

Ans A

kinghyts · Answer

8^a*(1/4)^b = 2^(3a-2b)

Statement 1 : b = 1.5a => b = 3/2*a => 2b = 3a

Therefore 3a -2b = 0. Hence 2^(3a-2b) = 2^0 =1. Sufficient

Statement 2 : a = 2. It is clearly insufficient

Nunuboy1994 · Answer

I personally think this is a 700 level question...classic "C" trap anyways

St 1

b =3/2 a

Just plug in a number

8^2 (1/4)^3 = 1 some reciprocal property

St 2

No info about B

Insuff

A

BrentGMATPrepNow · Answer

Target question :    What is the value of (8^a)(1/4)^b?  
This is a good candidate for  rephrasing the target question.

Let's take (8^a)(1/4)^b and rewrite both parts with the same base of 2.
Notice that 8 =  2^3  and 1/4 =  2^(-2) 
So, we can rewrite the original expression as:  2^3 )^ a] 2^(-2) ]^b
Simplify to get: (2^3a)(2^-2b)    
Combine terms to get: 2^(3a - 2b)
To determine the value of 2^(3a - 2b), we must determine the value of (3a - 2b)
So, let's rephrase the  target question . 
  REPHRASED target question :    What is the value of 3a - 2b?

Statement 1 : b = 1.5a   
Take: b = 1.5a 
Multiply both sides by 2 to get: 2b = 3a
Subtract 2b from both sides to get:  3a - 2b = 0 
PERFECT!!
Since we can answer the  REPHRASED target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : a = 2 
Not enough info to determine the value of  3a - 2b  
Since we cannot answer the  REPHRASED target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

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KanishkM · Answer

Always manipulate the given equation

2^{3a}* 2^{-2b} = 2^0

3a - 2b = 0
3a=2b
b =1.5 a

Statement 1) True

Statement 2) b can be any value.

Answer A

Basshead · Answer

8^a*(\frac{1}{4})^b = ?

Before we even look at the statements lets rewrite the question prompt:  2^{3a} * \frac{1^{b}}{2^{2b}}

(1) b = 1.5a

2^{3a} * \frac{1^{b}}{2^{2b}} 
=  2^{2b} * \frac{1}{2^{2b}} 
=  \frac{2^{2b}}{2^{2b}} 
=  1

Sufficient.

(2) a = 2

Don't know what b is; insufficient.

Answer is A.

Sof22 · Answer

8^a*(1/4)^b = ? ,

1) if b = 1.5,

{8^a}*{(1/4)^b} = {8^a}*(1/4)^{1.5a} =2^{3a}*2^{-3a} = 2^{3a-3a} = 1 
Sufficient

2) If a = 2
 {8^a}*{(1/4)^b} = {4^3}*4^{-b}= 4^{3-b} 
Insufficient

Answer: A

8^a*(1/4)^b = ? (1) b = 1.5a (2) a = 2

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GMAT Data Sufficiency (DS) Questions

8^a*(1/4)^b = ? (1) b = 1.5a (2) a = 2

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