Problem Solving

Vincen wrote:4+2^2+2^3+2^4+2^5+2^6+2^7=

A) 2^7
B) 2^8
C) 2^16
D) 2^28
E) 2^29

Let's look for a pattern...

We want: 4 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 = ?

4 + 2^2 = 4 + 4 = 8 = 2^3
So, 4 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 = 2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7

2^3 + 2^3 = 2(2^3) = 2^4
So, 2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 = 2^4 + 2^4 + 2^5 + 2^6 + 2^7

2^4 + 2^4 = 2(2^4) = 2^5
So, 2^4 + 2^4 + 2^5 + 2^6 + 2^7 = 2^5 + 2^5 + 2^6 + 2^7

Continuing the pattern, we get: 4 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 = 2^8

Answer: B

Cheers,
Brent

Hi Vincen,

With a little math and a bit of logic, you can get to the correct answer here without too much trouble. To start, you have to recognize what it really means to raise 2 to higher and higher exponents. With each increase of 1 to the exponent, the total DOUBLES.

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
Etc.

Thus, at higher and higher exponents, the numbers are NOT close together. From the sum of terms given to us, we can see that the largest term will be 2^7 and (when we word 'down' the list) we're adding smaller and smaller numbers to it. Clearly the sum will be GREATER than 2^7, but not that much greater (relatively speaking). Looking at the answer choices, there's only one option that makes sense...

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Vincen wrote: ↑

Fri Sep 29, 2017 6:37 pm

4+2^2+2^3+2^4+2^5+2^6+2^7=

A) 2^7
B) 2^8
C) 2^16
D) 2^28
E) 2^29

The OA is B.

Is there any way to make this PS question without using a calculator?

We can use the rule that 2^n + 2^n = 2^(n+1).

Starting with the first two terms, we have:

2^2 + 2^2 = 2^3

Then we have:

2^3 + 2^3 = 2^4

If we continue this pattern, we end with:

2^7 + 2^7 = 2^8.

Answer: B