If y=\({2^{(x+1)}}\), What is the Value of y

bySayantani Barman Experta en el extranjero

If y=\(2^{(x+1)}\), what is the value of y – x? is the topic from GMAT Quantitative problem set. GMAT quantitative reasoning section tests the candidate's ability to solve mathematical and quantitative problems, interpret graph data, and mathematical reasoning. The quantitative section of the GMAT exam consists of 31 questions. If y=\(2^{(x+1)}\), what is the value of y – x? has two options to answer from. The candidate has to check whether the two options are sufficient to answer the problem or not. The candidate is given five options, and only one of them is correct. GMAT quantitative section has mainly two sections:

Problem-solving: This section has the type of questions that tests the candidate’s logical and analytical skills. In this section candidates get MCQs having five options out of which only one is true.
Data sufficiency: This section has types of questions that tests candidates’ ability to analyze quantitative problems and to identify relevant data in the given question.

Topic: If y = \(2^{(x+1)}\), what is the value of y – x?

(1)\(2^{(2x+2)}\)= 64
(2) y= \(2^{(2x-1)}\)

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.

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Answer: D

Model Answer:

This question has only one approach.

Explanation:

It is given to us that y = \(2^{(x+1)}\) . It is asked to find out the value of y-x
We are given two statements. We have to check whether these two statements are sufficient to find the answer or not.
Firstly coming to statement 1,
\(2^{(2x+2)}\) = 64
Also given in the question,
y = \(2^{(x+1)}\)
We have to find the values of x and y in order to get the answer.
From given statement 1 we get
\(2^{(2x+2)}\) = 64
Here LHS is in power of two
We have to convert 64 to the power of two so that base could be same and the exponents can be compared.
64 can be written as
64 = 2*2*2*2*2*2
64 =\(2^6\)
Putting this in equation we get,
\(2^{(2x+2)}\) = \(2^6\)
2x+2 = 6
2x = 6-2
2x = 4
x = 2
Putting the value of x in the equation we get,
y =\(2^{(x+1)}\)
y = \(2^{(2+1)}\) = 8
The value of y and x is 8 and 2 respectively.
Y-x will be 8-2 = 6.
Therefore this statement is sufficient to get the answer.
Coming to the statement 2,
y= \(2^{(2x-1)}\)
Here it is a equation of two variable. Another equation given to us is
y =\(2^{(x+1)}\)

Equating them and eliminating y we get,
\(2^{(x+1)}\) = \(2^{(2x-1)}\)
Here already the base of two numbers is same.

Equating the exponents,
X +1 = 2x - 1
2x - x = 1 + 1
X = 2
Putting this value in the equation,
Y = \(2^{(x+1)}\)Y = \(2^{(2+1)}\) = 8
The value of y - x will be 8-2 = 6.
Therefore this statement is also sufficient to get the answer.
The correct option will be option D.

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If y=\({2^{(x+1)}}\), What is the Value of y – x?

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