What is the least integer value of x for which 1 - (1/4)^x is greater

Question

What is the least integer value of x for which  1 - (\frac{1}{4})^x  is greater than zero ?

A. -2

B. -1

C. 0

D. 1

E. 2

gmatmo · Answer

We are aiming to small the number as least as possible therefor the denominator has to be the smallest.

Exponent with a negative sign does exchange the denominator and numerator

so (1/4)^-1 = 1^-1/4^-1 = -4 to big 
same for B

because we are looking for the least possible value for x
x=1
1-(1/4)^1

1-1/4= 3/4
Therefore: D

praveenkuragodi · Answer

The question asks for least integer value, for the equation to be greater than 0, negatives are out as they reverse the fraction even 0 is out, now the least integer is 1 which gives 1-(1/4)=3/4 => Condition is TRUE.
Therefore Ans is D

rahulsehgal · Answer

I would go with answer choice D as that's the LEAST value when our expression will be > 0. The expression will be > 0 for options D and E. The answer choice D (value of 1) is certainly the LEAST value between the two choices available to us and thus, satisfies the condition the question has asked for.

The negative values in options a and b will make the expression's value less than 0. The value of will make the value of expression as zero.

Hope the explanation helps. Thank you!

chetan2u · Answer

1 - (\frac{1}{4})^x>0...........1>\frac{1}{4}^x

now for all negative integer values of x, say y=-x,  \frac{1}{4^x}=4^{-x}=4^y , least value will be 1, when y is 0 but 1>1 is wrong...
so we are looking for a positive integer value..

for positive values
 1>\frac{1}{4}^x........ 
clearly 1 will be the smallest integer value as a fraction<1 will become lesser with each increasing value of x

D

gmatlover12 · Answer

This is a classic question where some skills with graphs will highly improve both your speed and accuracy. You do not need to plot in exactitude. All you need is a rough sketch, with the important points plotted (where the graphs intersect the axes or each other). I've attached a graph for this question. It gets very difficult to get the question wrong after this.

This question asks for the least integer where (1/4)^x becomes less than 1. The attached graph sketches both (1/4)^x and the constant function 1. All you need for your answer is just take a glance at the graph.

https://imgur.com/a/je1H0BM

EgmatQuantExpert · Answer

Solution

Given:  
• The variable x is an integer

To find:  
• The least integer value of x for which 1 –  (\frac{1}{4})^x  > 0

Approach and Working:   
• From the given expression 1 –  (\frac{1}{4})^x  > 0, we can write it as
1 >  (\frac{1}{4})^x 
Or, 1 <  4^x 
Now,  4^x  > 1 can be written as  4^x > 4^0 
Or, x > 0
As x is an integer, the least possible value of x will be 1
Hence, the correct answer is option D.

Answer: D

KSBGC · Answer

Before performing any calculation, pay max afford to understand the inner sense of this question. While solving this one, i note down a couple of thing : 
1. x is the power of a fraction 
2. we have to take least value of x
3. Zero is also a option. Remember that any number having exponent 0 will have 1 as ultimate value. 
4. Negative options are also here

Now, we have to understand that if we take any negative integer as a power of x , fraction will turn into a integer in this question. Ultimately, we will get a negative value but we are looking for a value which is greater that 0.
So, we can eliminate all the negative options. Secondly, o as exponents give us 1. but ultimate value will be 0.

Thus the correct answer is D. this the least and positive integer conforms our condition stated in the question.

D3N0 · Answer

We can put the values one by one starting from the lowest one in the options and check if condition holds true or not. This way least number for which condition holds true.. That is the ans.

ScottTargetTestPrep · Answer

When x < 0, we see that (1/4)^x is greater than 1, so the expression 1 - (¼)^x would be negative. When x = 0, then 1 - (¼)^x would equal 0. Thus, the least integer that makes the expression 1 - (¼)^x greater than zero is x = 1.

Answer: D

gracie · Answer

if x=0, then 1-(1/4)^x=0
so x must be least positive integer=1
D

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

What is the least integer value of x for which 1 - (1/4)^x is greater

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 least integer value of x for which 1 - (1/4)^x is greater

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