bySayantani Barman Experta en el extranjero
Question: If x is an integer and, what is x?
- \(4^{x+1}-4^{x-1}>100\)
- \(4^{x+1} +4^{x-1}>100\)
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
“If x is an integer and, what is x?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.
Answer:
Approach Solution (1):
Given: x is an integer and \(4^x<100\)
So x could be 3/2/1/0/-1/-2/-3… For each of these values, 4x < 100
Question: What is x?
Statement 1: \(4^{x+1}-4^{x-1}>100\)
From the above statement, factor out \(4^{x-1}\). Try and factor out the smallest index to avoid dealing with fractions.
\(4^{x-1}*4^{2-1}>100\)
\(4^{x-1}*15>100\)
For this product to be greater than 100, \(4^{x-1}\) should be atleast \(4^2\) or x must be 3 or greater than 3
Since x is one of 3/2/1/0/-1/…, x must be 3.
Hence sufficient
Statement 2: \(4^{x+1} +4^{x-1}>100\)
From above, factor out \(4^x\)
\(4^x*(4+1)>100\)
\(4^x*5>100\)
For this product to be greater than 100, \(4^x\) should be atleast \(4^3\) or x must be 3 or greater
Since x is one of 3/2/1/0/-1/…, x must be 3.
Hence sufficient
Correct option: D
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