48(1/2^4 + 1/3^2 + 1/2^2)/3^2

Question

\frac{48(\frac{1}{2^4} + \frac{1}{3^2} + \frac{1}{2^2})}{3^2}

A. 16/27

B. 61/27

C. 61/3

D. 129

E. 183

Archit3110 · Answer

solve the expression 
 \frac{48(\frac{1}{2^4} + \frac{1}{3^2} + \frac{1}{2^2})}{3^2}

we get
 61/27
IMO B

Asariol · Answer

Can you explain your work please? Not following this solution at all! Thanks for the help.

Archit3110 · Answer

Asariol 
 \frac{48(\frac{1}{2^4} + \frac{1}{3^2} + \frac{1}{2^2})}{3^2} 
can be written as
48* ( 1/16+1/9+1/4) *1/9
solve we get
48/144*( 9+16+36) *1/9
1/3*1/9* ( 61) 
option A ; 61/27

Asariol · Answer

Thanks so much! Where is the 144 coming from?

daniformic · Answer

48*(1/16+1/9+1/4) = (48)  or (48/144)(9+16+36) are the same = 61/3

CrackverbalGMAT · Answer

Simplifying the expression, we have  \frac{48(\frac{1}{16} + \frac{1}{9} + \frac{1}{4})}{9}

The LCM of 16, 9 and 4 is 144

Reducing the expression, we get  \frac{48 * (\frac{9 + 16 + 36}{144})}{9} = \frac{48 * \frac{61}{144}}{9} = \frac{48 * 61}{144 * 9} = \frac{61}{3 * 9} = \frac{61}{27}

Option B

Arun Kumar

MathRevolution · Answer

48 =  2^4  * 3

=>  \frac{48}{2^4}  =  \frac{(2^4 * 3) }{ 2^4}  = 3

=>  \frac{48}{3^2}  =  \frac{(2^4 * 3) }{ 3^2}  =  \frac{16}{3}

=>  \frac{48}{2^4}  =  \frac{(2^4 * 3) }{ 2^2}  = 12

=> 3 +  \frac{16}{3}  + 12 =  \frac{(9 + 16 + 36) }{ 3} = \frac{61 }{ 3}

=>  \frac{61 }{ ( 3 * 3^2)} = \frac{61 }{27}

Answer B

jcerdae · Answer

Hi everyone!
Fist what I did was turning the 48 into the smallest terms as possible, which is 48=(2^4)(3). I did this hoping that the fractions might cancel later.
Secondly, multiplied the (2^4)(3) for (1/2^4 + 1/3^2 + 1/2^2) which gave me (3) + (2^4)/3 + (1/2^2)
Finally did the division of the 3^2 which turned into 1/3 + 16/27 + 4/3. (Here the LCM is 27) getting the result of 61/27

Hope it helps!!

dagrawal · Answer

I used approximation:
48/16=3
48/9 approx 5.3
48/4=12

3+5.3+12=20 (In numerator)

9(In denominator)

so, 20/9 which is approx 61/27

ScottTargetTestPrep · Answer

Solution:
 
Distributing the expression in the numerator, we have:

48(1/16 + 1/9 + 1/4) = 3 + 16/3 + 12

So we have:

(3 + 16/3 + 12) / 3^2 = (9/3 + 16/3 + 36/3)/9 = (61/3)/9 = 61/27

Answer: B

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48(1/2^4 + 1/3^2 + 1/2^2)/3^2

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48(1/2^4 + 1/3^2 + 1/2^2)/3^2

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