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# If x is a positive integer, what is the value of (x + 24)^(1/2) - x

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If x is a positive integer, what is the value of (x + 24)^(1/2) - x  [#permalink]

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16 Jun 2016, 05:48
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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

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Re: If x is a positive integer, what is the value of (x + 24)^(1/2) - x  [#permalink]

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08 Dec 2016, 09:59
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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.

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Re: If x is a positive integer, what is the value of (x + 24)^(1/2) - x  [#permalink]

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16 Jun 2016, 05:56
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If x is a positive integer, what is the value of x+24−−−−−√−x√x+24−x?

(1) √x is an integer
(2)√x+24 is an integer

Answer is E. We get different values when you test x = 1 we get 5 - 1 =4
x = 25 we get 7-5 = 2
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Re: If x is a positive integer, what is the value of (x + 24)^(1/2) - x  [#permalink]

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16 Jun 2016, 09:20
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2
(1) x could be 1, 4,9,25,36,49..any number ,which is a perfect square. Hence , insufficient.

(2) x could be 1, 12,25... Hence, insufficient

(1) + (2)..x could be 1 giving result 5-1=4 or x could be 25, giving result 7-5=2. Hence, Insufficient.

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Re: If x is a positive integer, what is the value of (x + 24)^(1/2) - x  [#permalink]

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16 Jun 2016, 09:31
E
getting possibilities more than 1

4 and 2.
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Re: If x is a positive integer, what is the value of (x + 24)^(1/2) - x  [#permalink]

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16 Jun 2016, 09:32
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

Bunuel, are these questions from OG 2017?
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Posts: 55721
Re: If x is a positive integer, what is the value of (x + 24)^(1/2) - x  [#permalink]

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16 Jun 2016, 09:35
1
hsbinfy wrote:
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

Bunuel, are these questions from OG 2017?

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Yes.
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Re: If x is a positive integer, what is the value of (x + 24)^(1/2) - x  [#permalink]

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16 Jun 2016, 09:37
Bunuel wrote:
hsbinfy wrote:
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

Bunuel, are these questions from OG 2017?

________________________
Yes.

appreciate ur effort in putting these up.Tnks
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Re: If x is a positive integer, what is the value of (x + 24)^(1/2) - x  [#permalink]

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16 Jun 2016, 12:32
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

Statement 1- x is a square of an integer.
There are many numbers that can fulfill this condition. Not sufficient

Statement 2- x+24 is a square

x can be 1 to make the expression 25 (square of 5)

x can be 24 to make the expression 49 (square of 7)
Not sufficient

Combining two statements does not give us a unique result. Hence, E is the answer
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Re: If x is a positive integer, what is the value of (x + 24)^(1/2) - x  [#permalink]

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09 Aug 2017, 07:19
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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

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Re: If x is a positive integer, what is the value of (x + 24)^(1/2) - x  [#permalink]

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24 Apr 2018, 12:23
1
Would this be considered a classic "C-Trap?"

How often are C-traps not actually C traps?
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Re: If x is a positive integer, what is the value of (x + 24)^(1/2) - x  [#permalink]

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26 May 2019, 20:04
Would this be considered a classic "C-Trap?"

How often are C-traps not actually C traps?

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!
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Re: If x is a positive integer, what is the value of (x + 24)^(1/2) - x  [#permalink]

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