Problem Solving

Needgmat wrote:The function f is defined by f(x)= 2^x - 3. If f(x) = 31, then the value of x is between

A) 1 and 2

B) 2 and 3

C) 3 and 4

D) 4 and 5

E) 5 and 6

OAE

Please explain

Given: f(x) = 2^x - 3
So, if f(x) = 31, we can write: 2^x - 3 = 31
Add 3 to both sides to get: 2^x = 34 [solve this equation for x]

We know that 2^5 = 32
and 2^6 = 64
Since 34 lies between 32 and 64, we can conclude that x is between 5 and 6

Answer: E

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Hi Needgmat,

To answer this question, we can TEST THE ANSWERS.

From the answer choices, we can see that we're dealing with RANGES and that each of the ranges includes POSITIVE numbers only.

The function f(X) = 2^X - 3 will lead to an increasing result as X increases (since we'll be raising 2 to a higher-and-higer exponent). We're told that f(X) = 31, so we just have to find the 'boundary' numbers for that result.

Let's TEST Answer D: 4 and 5

2^4 - 3 = 13
2^5 - 3 = 29

Since 31 is TOO BIG for this range, we clearly need a higher pair of boundary numbers. There's only one answer left...

Final Answer: E

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

Needgmat wrote:The function f is defined by f(x)= 2^x - 3. If f(x) = 31, then the value of x is between

A) 1 and 2

B) 2 and 3

C) 3 and 4

D) 4 and 5

E) 5 and 6

We can create the following equation:

2^x - 3 = 31

2^x = 34

Since 2^5 = 32 and 2^6 = 64, the value of x must be between 5 and 6.

Answer: E

Needgmat wrote:The function f is defined by f(x)= 2^x - 3. If f(x) = 31, then the value of x is between

A) 1 and 2

B) 2 and 3

C) 3 and 4

D) 4 and 5

E) 5 and 6

OAE

Please explain

Given: f(x) = 2^x - 3
So, if f(x) = 31, we can write: 2^x - 3 = 31
Add 3 to both sides to get: 2^x = 34 [solve this equation for x]

We know that 2^5 = 32
and 2^6 = 64
Since 34 lies between 32 and 64, we can conclude that x is between 5 and 6

Answer: E

Cheers,
Brent