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Re: If x is a positive integer, what is the value of (x + 24)^(1/2) - x
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08 Dec 2016, 09:59

5

2

Bunuel wrote:

If x is a positive integer, what is the value of \(\sqrt{x+24}-\sqrt{x}\)?

(1) \(\sqrt{x}\) is an integer (2) \(\sqrt{x+24}\) is an integer

We are given that x is a positive integer and must determine the value of √(x+24) - √x.

Statement One Alone:

√x is an integer.

Using the information in statement one, we could obtain multiple values for √(x+24) - √x. If x = 1, then √(x+24) - √x = √25 - √1 = 5 - 1 = 4; however, if x = 4, then √(x+24) - √x = √28 - √4 = √28 - 2. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

√(x+24) is an integer.

Using the information in statement two, we could obtain multiple values for √(x+24) - √x. If x = 1, then √(x+24) - √x = √25 - √1 = 5 - 1 = 4; however, if x = 12, then √(x+24) - √x = √36 - √12 = 6 - √12. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the information in statements one and two, we still could obtain multiple values for √(x+24) - √x. If x = 1, then √(x+24) - √x = √25 - √1 = 5 - 1 = 4; however, if x = 25, then √(x+24) - √x = √49 - √25 = 7 - 5 = 2.

Re: If x is a positive integer, what is the value of (x + 24)^(1/2) - x
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09 Aug 2017, 07:19

1

Top Contributor

1

Bunuel wrote:

If x is a positive integer, what is the value of \(\sqrt{x+24}-\sqrt{x}\)?

(1) \(\sqrt{x}\) is an integer (2) \(\sqrt{x+24}\) is an integer

Target question:What is the value of √(x + 24) - √x?

Given: x is a positive integer

Statement 1: √x is an integer There are several values of x that satisfy statement 1. Here are two: Case a: x = 1 (notice that √1 is an integer). In this case, √(x + 24) - √x = √(1 + 24) - √1 = 5 - 1 = 4 Case b: x = 4 (notice that √4 is an integer). In this case, √(x + 24) - √x = √(4 + 24) - √4 = √28 - 2 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: √(x + 24) is an integer There are several values of x that satisfy statement 2. Here are two: Case a: x = 1 (notice that √(1 + 24) = √25 = 5, which is an integer). In this case, √(x + 24) - √x = √(1 + 24) - √1 = 5 - 1 = 4 Case b: x = 25 (notice that √(25 + 24) = √49 = 7, which is an integer). In this case, √(x + 24) - √x = √(25 + 24) - √25 = 7 - 5 = 2 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined Case a: x = 1. In this case, √(x + 24) - √x = √(1 + 24) - √1 = 5 - 1 = 4 Case b: x = 25. In this case, √(x + 24) - √x = √(25 + 24) - √25 = 7 - 5 = 2 Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Re: If x is a positive integer, what is the value of (x + 24)^(1/2) - x
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26 May 2019, 20:04

thinkpad18 wrote:

Would this be considered a classic "C-Trap?"

How often are C-traps not actually C traps?

thinkpad18 1 - No, we need a finite value. Both the statements just say that the values are integers. 2 - Seldom. If are doing well on exam and then sense a c-trap then it is possibly a c-trap.

If you can correctly sense a c-trap when you are running out of time or if you have faced a difficult question, make sure not to mark C (as it's a C-trap), D (as each statement alone isn't sufficient), or E (Because it is impossible! Combining both the statements would definitely get you an answer). So you have cut down 3 choices (C, D, and E) and now there is a 50-50 chance to guess the right answer. Either A or B.

Also, if any of A or B alone seems impossible, you can pick the other answer choice and it would be correct every single time. Make sure all of this only happens only if you correctly sense a c-trap, but I hope such situation never occur to you. All the best!

Re: If x is a positive integer, what is the value of (x + 24)^(1/2) - x
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28 May 2019, 20:46

Statement 1 - Clearly insufficient, x can be any number that is perfect square. Statement 2- Same explanation as statement 1 Combining both statement-

Let \(\sqrt{x+24}\)=a and \(\sqrt{x}\)=b x+24=a^2 and x=b^2 a^2-b^2=24 (a+b)(a-b)=24 Possible Solutions 1. a+b=12 and a-b=2 a=7,b=5 2. a+b=6 and a-b=4 a=5 and b=1

Insufficient.

Bunuel wrote:

If x is a positive integer, what is the value of \(\sqrt{x+24}-\sqrt{x}\)?

(1) \(\sqrt{x}\) is an integer (2) \(\sqrt{x+24}\) is an integer

gmatclubot

Re: If x is a positive integer, what is the value of (x + 24)^(1/2) - x
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28 May 2019, 20:46