Is 4^x less than 5,000?

Question

(1)  4^{x+1} > 16,000

(2)  4^{x+1} = 4^x + 12,288

exc4libur · Accepted Answer

Is 4^x < 5,000 = 4^x < 5*10^3 ? (1) 4^{x+1} > 16,000 = 4^x*4 > 16,000 = 4^x > 4 * 10^3 ; So, 4^x could be smaller or greater than 5,000, not sufficient. (2) 4^{x+1} = 4^x + 12,288; 4^{x+1}-4^x = 12,288; 4^x*(4-1) = 12,288; 4^x = \frac{12,288}{3} ; sufficient. (B) is the answer.

Bunuel · Answer

Similar question from GMAT Prep: https://gmatclub.com/forum/is-5-k-less- ... fl=similar

ImAnkitKaushik · Answer

B is the answer.

Using  Statement 1:

4^7 > 16,000 and 4^6 = 4096. x=6 can be a solution.
But 4^8, 4^9....and so on are also greater than 16,000. So we cannot find the value of x for sure.

Using  Statement 2:  4^{x+1} = 4^x + 12,288

4^{x+1} - 4^x = 12,288

4^{x+1} can be written as 4^x.4^1 i.e. 4.4^x

so our statement can be written as: 4^x{4-1}=12,288
4^x= {12,288/3} = 4096

so we can be sure from here that 4,096 is less than 5,000.

So, Statement 2 alone is sufficient to answer the question.

Thanks,
 Ankit Kaushik 
 Hit Kudos if it helped.

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Is 4^x less than 5,000?

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Is 4^x less than 5,000?

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