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If 2^(x + y) = 4^8, what is the value of y?
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26 Oct 2015, 08:51
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If 2^(x + y) = 4^8, what is the value of y? (1) x^2 = 81 (2) x − y = 2 Kudos for a correct solution.
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Re: If 2^(x + y) = 4^8, what is the value of y?
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26 Oct 2015, 08:59
Bunuel wrote: If 2^(x + y) = 4^8, what is the value of y?
(1) x^2 = 81 (2) x − y = 2
Kudos for a correct solution. Target question: What is the value of y? Given: 2^(x + y) = 4^8 Notice that 4^8 = (2^2)^8 = 2^16 In other words, 2^ (x + y) = 2^ 16, which means x + y = 16 Statement 1: x^2 = 81 This tells us that x = 9 OR x = 9 Let's examine each possible case Case a: x = 9. If x + y = 16, then we can conclude that y = 7Case b: x = 9. If x + y = 16, then we can conclude that y = 25Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: x − y = 2 When we combine this information with x + y = 16, we see that we have TWO different equations and TWO variables. So, we COULD solve this system to find one unique value of y (incidentally, we get y = 7) Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer = B Cheers, Brent
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Re: If 2^(x + y) = 4^8, what is the value of y?
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30 Nov 2016, 11:57
Bunuel wrote: If 2^(x + y) = 4^8, what is the value of y?
(1) x^2 = 81 (2) x − y = 2
Kudos for a correct solution. \(2^{(x + y)} = 4^8\) Or, \(2^{(x + y)} = 2^{16}\) So, \(x + y = 16\) FROM STATEMENT  I ( INSUFFICIENT )\(x^2 = 81\) So, x = + 9If x = +9 ; y = 7 & If x =  9 ; y = 25 We do not have a unique value of yFROM STATEMENT  II ( SUFFICIENT )Given, \(x − y = 2\) and we know \(x + y = 16\) thus \(x = 9\) & \(y = 7\) Thus, Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked, answer will be (B)
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Re: If 2^(x + y) = 4^8, what is the value of y?
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26 Oct 2015, 09:06
Bunuel wrote: If 2^(x + y) = 4^8, what is the value of y?
(1) x^2 = 81 (2) x − y = 2
Kudos for a correct solution. \(2^(x+y)=2^16\), x+y=16 (1) x=+/ 9 different values of y possible NOT SUFFICIENT (2) x=2+y > 2+2y=16 > y=7 Sufficient Answer (B)



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Re: If 2^(x + y) = 4^8, what is the value of y?
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10 Sep 2017, 11:00
Quote: Statement 1: x^2 = 81 This tells us that x = 9 OR x = 9 Let's examine each possible case Case a: x = 9. If x + y = 16, then we can conclude that y = 7 Case b: x = 9. If x + y = 16, then we can conclude that y = 25 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT To my understanding, a sqrt of a number can never be negative. How come the sqyt of 81 is 9 or 9?



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Re: If 2^(x + y) = 4^8, what is the value of y?
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10 Sep 2017, 20:31
Zoser wrote: Quote: Statement 1: x^2 = 81 This tells us that x = 9 OR x = 9 Let's examine each possible case Case a: x = 9. If x + y = 16, then we can conclude that y = 7 Case b: x = 9. If x + y = 16, then we can conclude that y = 25 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT To my understanding, a sqrt of a number can never be negative. How come the sqyt of 81 is 9 or 9? Yes, when the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root. That is, \(\sqrt{81}=9\), NOT +9 or 9. Even roots have only a positive value on the GMAT.In contrast, the equation \(x^2=81\) has TWO solutions, +9 and 9.
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Re: If 2^(x + y) = 4^8, what is the value of y?
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10 Sep 2017, 23:04
Bunuel wrote: If 2^(x + y) = 4^8, what is the value of y?
(1) x^2 = 81 (2) x − y = 2
Kudos for a correct solution. Given 2^(x+y)= 2^16; so we have x+y=16 from q. With x^2=81 we have 2 values for x +9 or 9. So y would also have 2 values. So S1 is not sufficient. From S2 given xy=2; Solving for 2y=14; so y=2; Sufficient. Ans:B



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Re: If 2^(x + y) = 4^8, what is the value of y?
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31 Mar 2018, 13:51
Bunuel wrote: If 2^(x + y) = 4^8, what is the value of y?
(1) x^2 = 81 (2) x − y = 2
Kudos for a correct solution. On the OG2018, 6.3 Practice Questions, Prob. 350. It appears as follows: 2^x +y = 4^8 But in the 6.5 Answer explanations, Prob 350. It appears as follows: 2^(x+y) = 4^8 The correct statement is the second one! I hope this helps someone! Kudos +1 if it helps you!



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Re: If 2^(x + y) = 4^8, what is the value of y?
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10 Jul 2019, 21:11
Bunuel wrote: If 2^(x + y) = 4^8, what is the value of y?
(1) x^2 = 81 (2) x − y = 2
Kudos for a correct solution. 2^(x+y) = 4^8 = (2^2)^8 = 2^16 => x+y = 16 Q y = ? S1: x^2 = 81 x = +/ 9 If x = 9, y = 7 If x = 9 y = 25 NOT SUFFICIENT. S2: xy=2 x = y+2 2y +2 = 16 y = 7 SUFFICIENT. IMO B
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Re: If 2^(x + y) = 4^8, what is the value of y?
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03 Mar 2020, 10:55
If 2^(x + y) = 4^8, what is the value of y?
(1) x^2 = 81 (2) x − y = 2
The question asks if we can find Y or not. Immediately, before we start testing each statement, let's see if we can simplify this problem to make it easier on ourselves. 2^(x+y) = 4^8. Wouldn't it be easier if we could compare the two sides of the equation if they had the same base? Adjust accordingly. The given information turns into 2(x+y) = 2(^2^8) = 2^16. So we have this information: 2(x+y) = 2^16. But wait, we can go even further with the simplification. We know we are looking for Y. Each side has the same base (2), so we can simplify this into x+y=16. Now this is much more manageable.
Statement 1) x^2 = 81 We know that x can be either 9 or 9. Let's plug each into our equation x+y=16, or y=16x
X=9: y=16(9)=7 X=9: y=16(9)=25.
We get two different answers for y: 7 and 25, so this is an insufficient statement to determine what the value of y is.
Statement 2) xy=2 We know that x+y=16 and xy=2. We have two different 2variable equations that aren't the same, so we can use whatever method we want (combination, substitution, case testing) to solve. I think combinations is the easiest, so let's solve:
x+y=16 +(xy=2) :2x=18, so we know that x=9. Plug this back into any of the two equations to find y. 9+y=16. y=7 This is sufficient, there is only one answer for y.



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Re: If 2^(x + y) = 4^8, what is the value of y?
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25 Jun 2020, 11:14
FYI  the 2020 GMAT official prep book has a typo in this problem, #406. The problem is shown as 2^(x)+y=4^8. I was so annoyed when I looked at the solution and the equation was supposed to be written 2^(x+y)=4^8.




Re: If 2^(x + y) = 4^8, what is the value of y?
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25 Jun 2020, 11:14




