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If x is a positive integer, what is the value of ? + ?? – ?? 1) ?

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If x is a positive integer, what is the value of ? + ?? – ?? 1) ? [#permalink]

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Re: If x is a positive integer, what is the value of ? + ?? – ?? 1) ? [#permalink]

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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 ? + ?? – ?? 1) ? [#permalink]

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(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.

Answer is E.
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Re: If x is a positive integer, what is the value of ? + ?? – ?? 1) ? [#permalink]

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New post 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 ? + ?? – ?? 1) ? [#permalink]

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New post 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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Re: If x is a positive integer, what is the value of ? + ?? – ?? 1) ? [#permalink]

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Re: If x is a positive integer, what is the value of ? + ?? – ?? 1) ? [#permalink]

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New post 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?

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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 ? + ?? – ?? 1) ? [#permalink]

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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


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 ? + ?? – ?? 1) ? [#permalink]

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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.

Answer: E
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Re: If x is a positive integer, what is the value of ? + ?? – ?? 1) ? [#permalink]

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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


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

Answer:
[Reveal] Spoiler:
E


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Re: If x is a positive integer, what is the value of ? + ?? – ?? 1) ?   [#permalink] 09 Aug 2017, 07:19
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