If x is an integer and 4^x < 100, what is x?

[venkygct]

If x is an integer and 4^x < 100, what is x?

(1) 4^(x + 1) - 4^(x - 1) > 100
(2) 4^(x + 1) + 4^x > 100

[venkygct]

please ignore this question. MGMAT explaination is very clear

[Ben Ku]

Please ask if there are additional questions about this problem. Thanks!

[yousuf_azim]

Dears,

What is the ans?

BR

yousuf azim

[mithunsam]

Let us try...

From the question, we have 4^x < 100. That means x could be any -ve value or any of 0, 1, 2, or 3.

Statement 1
4^(x + 1) - 4^(x - 1) > 100
4^(x - 1) [4^2 - 1] > 100
15 * 4^(x-1) > 100
For this statement to be true, (x-1) should be > 2. In other words, x should be > 3. But, from the question, we know that x cannot be > 3. Therefore, x = 3. Sufficient.

Statement 2
4^(x + 1) + 4^x > 100
4^x(4 + 1) > 100
5 * 4^x > 100
For this statement to be true, x should be > 3. But, from the question, we know that x cannot be > 3. Therefore, x = 3. Sufficient.

So, it looks like D is the correct Answer.

[jnelson0612]

mithunsam, as always, you are awesome!

[carlosutrillas]

There is something I do not get here...

You say "From the question, we have 4^x < 100. That means x could be any -ve value or any of 0, 1, 2, or 3"

However, why you do not consider negative numbers?

I mean...if we only have this information: 4^x < 100. And we know x is an integer, x could be 2 (for example) but also -2.

Am I right?

THanks.

[jnelson0612]

There is something I do not get here...

You say "From the question, we have 4^x < 100. That means x could be any -ve value or any of 0, 1, 2, or 3"

However, why you do not consider negative numbers?

I mean...if we only have this information: 4^x < 100. And we know x is an integer, x could be 2 (for example) but also -2.

Am I right?

THanks.

Sure, just looking at the question stem, we could certainly consider that x might be negative.

However, once we move to the statements we can see that a negative value for x would not fit either of those statements and that we have to stick with positive values to find possibilities.

[carlosutrillas]

got it! thanks!

[jnelson0612]

My pleasure! :-)