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555-605 (Medium)|   Algebra|   Exponents|         
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Lolaergasheva
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If y = 2^(x+1), what is the value of y – x? Updated on: 21 Sep 2019, 17:27
Originally posted by Lolaergasheva on 05 Mar 2011, 08:12.
Last edited by Bunuel on 21 Sep 2019, 17:27, edited 3 times in total.
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D
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77% (01:33) correct 23% (01:39) wrong based on 2079 sessions

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


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

(2) \(y = 2^{(2x –1)}\)


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D
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If y = 2^(x+1), what is the value of y – x? Updated on: 05 Mar 2011, 09:40
Originally posted by beyondgmatscore on 05 Mar 2011, 08:24.
Last edited by beyondgmatscore on 05 Mar 2011, 09:40, edited 2 times in total.
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Lolaergasheva
If y = 2^x+1, what is the value of y – x?
(1) 2^2x+2 = 64
(2) y = 2^2x –1

1) 2^2x+2=2^6
2x+2=6
x=2
2^x+1-2^1 => x+1-1=0 ==> x=0

2) I don't know how to solve
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I assume that the questions reads as follows:

If y = \(2^{x+1}\), what is the value of y – x?
(1) \(2^{2x+2}\) = 64
(2) \(y = 2^{2x-1}\)


Then, 1st statement gives us 2x+2 = 6 and hence x =2 and therefore y = \(2^{2+1}\) = \(2^3\) = 8 hence y-x = 8-2 = 6, So sufficient

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

or 2x-1 = x+1 and hence x =2 and hence like in 1, y =8 and hence y-x = 8-2 = 6, So sufficient

Answer is D
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If y = 2^(x+1), what is the value of y – x? 05 Mar 2011, 08:45
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Lolaergasheva
If y = 2^x+1, what is the value of y – x?
(1) 2^2x+2 = 64
(2) y = 2^2x –1

1) 2^2x+2=2^6
2x+2=6
x=2
2^x+1-2^1 => x+1-1=0 ==> x=0

2) I don't know how to solve
Show more

Please, format the questions properly.

Original question is:
If y = 2^(x+1), what is the value of y – x?

(1) 2^(2x+2) = 64 --> \(2^{2x+2}=2^6\) --> as bases are equal we can equate the powers: \(2x+2=6\) --> \(x=2\). From the stem: \(y=2^{x+1}=2^3=8\), so \(y-x=8-2=6\). Sufficient.

(2) y = 2^(2x –1) --> as also given that \(y=2^{x+1}\) then \(2^{x+1}=2^{2x-1}\) --> \(x+1=2x-1\) --> \(x=2\), then the same way as above \(y=8\) --> \(y-x=8-2=6\). Sufficient.

Answer: D.
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If y = 2^(x+1), what is the value of y – x? 10 Nov 2015, 11:11
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If y = 2^(x+1), what is the value of y – x?

(1) 2^(2x+2) = 64

(2) y = 2^(2x –1)

There are 2 variables (x,y) one equation (y = 2^(x+1)), and 2 more equations from the 2 conditions, so there is high chance (D) will be our answer.
From condition 1, 2^(2x+2)=64=2^6, or 2x+2=6, x=2, y=2^3=8. This is sufficient
From condition 2, 2^(2x-1)=2^(x+1), or 2x-1=x+1, x=2, y=8 . This is sufficient as well.
Therefore, the answer becomes (D).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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If y = 2^(x+1), what is the value of y – x? 21 Dec 2016, 00:09
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(1) 2^2x+2=64
2^2x+2=2^6
2x+2=6
x=2, y=2^x+1=2^2+1=8 Sufficient
(2) y=2^2x-1
2^2x-1=2^x+1
2x-1=x+1
x=2, y=8 Sufficient

Answer D
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If y = 2^(x+1), what is the value of y – x? 16 Jul 2017, 15:04
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If \(y = 2^{x+1}\), what is the value of y – x?

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

\(2^{2x+2} = 2^6\)

\(2x+2 = 6\)

\(2x = 4\)

\(x = 2\)

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

\(y = 2^{2+1} = 2^3 = 8\)

\(y - x = 8 - 2 = 6\)

Hence, (1) ===== is SUFFICIENT

(2) \(y = 2^{2x –1}\)

\(y = 2^{2x –1}\)

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

\(2^{2x –1} = = 2^{x+1}\)

\(2x - 1 = x + 1\)

\(x = 2\)

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

\(y = 2^{2+1} = 2^3 = 8\)

\(y - x = 8 - 2 = 6\)

Hence, (2) ===== is SUFFICIENT

Hence, Answer is D

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If y = 2^(x+1), what is the value of y – x? 29 Jan 2021, 06:14
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Given: y = \(2^{x+1} \)

Question: y – x = ?

(1) \(2^{2x+2} = 64 = 2^{6}\)
=> 2x + 2 = 6
=> x = 2
Sufficient

(2) We know that \(y = 2^{x+1}\) from the information given on the question. So, \(y = 2^{x+1} = 2^{2x–1}\)
=> x + 1 = 2x - 1
=> x = 2
Sufficient

Answer is D.

Hope this helps. :)
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If y = 2^(x+1), what is the value of y – x? 13 Aug 2025, 05:52
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