What is the median of the four numbers above ?

Question

16^3 
 (\sqrt{32})^4 
 2^8 + 2^8 
 \frac{2^{16}}{2^4}

A.  2^8 
B.  2^9 
C.  2^{10} 
D.  1.25(2^{11}) 
E.  2^{12}

kevincan · Answer

To find the median of these four numbers, we need to compare them. It’s a good idea to write each as a power of two.

We get 2^12 , 2^10, 2^9 and 2^12.

Thus the median is the average of 2^10 and 2^12. Some would mistakenly conclude that the median is 2^11, which mercifully is not one of the answer choices.

The average of 2^10 and 2^12 is :

(2^10 + 2^12)/2 =2^9 + 2^ 11 = 2^11/2^2 + 2^11 = 0.25(2^11) + 2^11

ReetArora · Answer

Please explain this

kevincan · Answer

I added a couple of details !

Shaunak3004 · Answer

Rearrange, all numbers as exponents of 2:
16^3 = 2^12
(root 32)^4 = 2^10
2^8 + 2^8 = 2^9
2^16 / 2^4 = 2^12

now order according to exponent, which gives:
2^9, 2^10, 2^12, 2^12

Median is the term at half-way point (odd set) or average of middle two numbers (even set)
=> (2^10 + 2^12) / 2
= 2^10 (5) / 2

If you check the answer choices, none have a 2.5 or a 5/2 option.
The only relatable one is 1.25 (2^11), which you can get if you multiply and divide our answer by 2.

What is the median of the four numbers above ?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

What is the median of the four numbers above ?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards