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# If x and k are both integers, x > k, and x−k = 625, what is x? (1) |k|

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If x and k are both integers, x > k, and x−k = 625, what is x? (1) |k| [#permalink]

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20 May 2017, 09:25
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Question Stats:

39% (01:26) correct 61% (01:31) wrong based on 137 sessions

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If x and k are both integers, x > k, and $$x^{−k} = 625$$, what is x?

(1) |k| is a prime number
(2) x + k > 20
[Reveal] Spoiler: OA

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Re: If x and k are both integers, x > k, and x−k = 625, what is x? (1) |k| [#permalink]

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20 May 2017, 09:33
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hazelnut wrote:
If x and k are both integers, x > k, and $$x^{−k} = 625$$, what is x?

(1) |k| is a prime number
(2) x + k > 20

Interesting problem!

The first thing I noticed is that the question itself really limits the possibilities. There can't be that many integers where $$x^{−k} = 625$$, right? Also, I know 625 as a 'special number' - you should memorize the perfect squares up to about 25^2, so that you notice things like this quickly on test day. 625 = 25^2, so I immediately know one of the possibilities. x could be 25, and k could be -2. (Note the 'double negative' there).

However, you should never be able to solve a DS question without either statement. That's something that never happens on DS. So, there must be at least one possibility. The GMAT likes to trick you into forgetting about the simplest exponent of all: 1. x could be 625, and k could be -1.

Also, notice that 25 can be factored down more. 25^2 = 5^4. So, finally, x could be 5, and k could be -4.

List the three possibilities on your paper:
x = 25, k = -2
x = 625, k = -1
x = 5, k = -4

Then, start working with the statements. Your question to ask yourself: do the statements let me 'narrow it down' to just one of these possibilities?

(1) does exactly that. 2 is the only prime value for k in our list. So, if we know that |k| is prime, then the first possibility is the only one that works. (1) is sufficient.

(2) is insufficient, because the first two possibilities could both work. (They're really hoping that you don't think of x = 625, k=-1. If you didn't think of that, you'd think this was sufficient as well.)
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Re: If x and k are both integers, x > k, and x−k = 625, what is x? (1) |k| [#permalink]

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22 Aug 2017, 03:20
ccooley wrote:
hazelnut wrote:
If x and k are both integers, x > k, and $$x^{−k} = 625$$, what is x?

(1) |k| is a prime number
(2) x + k > 20

Interesting problem!

The first thing I noticed is that the question itself really limits the possibilities. There can't be that many integers where $$x^{−k} = 625$$, right? Also, I know 625 as a 'special number' - you should memorize the perfect squares up to about 25^2, so that you notice things like this quickly on test day. 625 = 25^2, so I immediately know one of the possibilities. x could be 25, and k could be -2. (Note the 'double negative' there).

However, you should never be able to solve a DS question without either statement. That's something that never happens on DS. So, there must be at least one possibility. The GMAT likes to trick you into forgetting about the simplest exponent of all: 1. x could be 625, and k could be -1.

Also, notice that 25 can be factored down more. 25^2 = 5^4. So, finally, x could be 5, and k could be -4.

List the three possibilities on your paper:
x = 25, k = -2
x = 625, k = -1
x = 5, k = -4

Then, start working with the statements. Your question to ask yourself: do the statements let me 'narrow it down' to just one of these possibilities?

(1) does exactly that. 2 is the only prime value for k in our list. So, if we know that |k| is prime, then the first possibility is the only one that works. (1) is sufficient.

(2) is insufficient, because the first two possibilities could both work. (They're really hoping that you don't think of x = 625, k=-1. If you didn't think of that, you'd think this was sufficient as well.)

x can be a negative number.. so it can be equal to -5 no? which means that there are two options for the first statement.

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Re: If x and k are both integers, x > k, and x−k = 625, what is x? (1) |k| [#permalink]

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22 Aug 2017, 03:23
tinayni552 wrote:
ccooley wrote:
hazelnut wrote:
If x and k are both integers, x > k, and $$x^{−k} = 625$$, what is x?

(1) |k| is a prime number
(2) x + k > 20

Interesting problem!

The first thing I noticed is that the question itself really limits the possibilities. There can't be that many integers where $$x^{−k} = 625$$, right? Also, I know 625 as a 'special number' - you should memorize the perfect squares up to about 25^2, so that you notice things like this quickly on test day. 625 = 25^2, so I immediately know one of the possibilities. x could be 25, and k could be -2. (Note the 'double negative' there).

However, you should never be able to solve a DS question without either statement. That's something that never happens on DS. So, there must be at least one possibility. The GMAT likes to trick you into forgetting about the simplest exponent of all: 1. x could be 625, and k could be -1.

Also, notice that 25 can be factored down more. 25^2 = 5^4. So, finally, x could be 5, and k could be -4.

List the three possibilities on your paper:
x = 25, k = -2
x = 625, k = -1
x = 5, k = -4

Then, start working with the statements. Your question to ask yourself: do the statements let me 'narrow it down' to just one of these possibilities?

(1) does exactly that. 2 is the only prime value for k in our list. So, if we know that |k| is prime, then the first possibility is the only one that works. (1) is sufficient.

(2) is insufficient, because the first two possibilities could both work. (They're really hoping that you don't think of x = 625, k=-1. If you didn't think of that, you'd think this was sufficient as well.)

x can be a negative number.. so it can be equal to -5 no? which means that there are two options for the first statement.

Notice that we are given that x > k, so x cannot be -5 if k = -2.
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Kudos [?]: 129056 [0], given: 12187

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Re: If x and k are both integers, x > k, and x−k = 625, what is x? (1) |k| [#permalink]

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22 Aug 2017, 03:35
tinayni552 wrote:
ccooley wrote:
hazelnut wrote:
If x and k are both integers, x > k, and $$x^{−k} = 625$$, what is x?

(1) |k| is a prime number
(2) x + k > 20

Interesting problem!

The first thing I noticed is that the question itself really limits the possibilities. There can't be that many integers where $$x^{−k} = 625$$, right? Also, I know 625 as a 'special number' - you should memorize the perfect squares up to about 25^2, so that you notice things like this quickly on test day. 625 = 25^2, so I immediately know one of the possibilities. x could be 25, and k could be -2. (Note the 'double negative' there).

However, you should never be able to solve a DS question without either statement. That's something that never happens on DS. So, there must be at least one possibility. The GMAT likes to trick you into forgetting about the simplest exponent of all: 1. x could be 625, and k could be -1.

Also, notice that 25 can be factored down more. 25^2 = 5^4. So, finally, x could be 5, and k could be -4.

List the three possibilities on your paper:
x = 25, k = -2
x = 625, k = -1
x = 5, k = -4

Then, start working with the statements. Your question to ask yourself: do the statements let me 'narrow it down' to just one of these possibilities?

(1) does exactly that. 2 is the only prime value for k in our list. So, if we know that |k| is prime, then the first possibility is the only one that works. (1) is sufficient.

(2) is insufficient, because the first two possibilities could both work. (They're really hoping that you don't think of x = 625, k=-1. If you didn't think of that, you'd think this was sufficient as well.)

x can be a negative number.. so it can be equal to -5 no? which means that there are two options for the first statement.

Thanks! I should be more careful when reading the stem

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If x and k are both integers, x > k, and x−k = 625, what is x? (1) |k| [#permalink]

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22 Aug 2017, 06:02
Bunuel wrote:
If x and k are both integers, x > k, and $$x^{−k} = 625$$, what is x?

(1) |k| is a prime number
(2) x + k > 20

Hi Bunuel here how i saw statement (1) |k| is a prime number

But k can be -2 or 2. So when k = -2 and when k = 2 the equation $$x^{−k} = 625$$ should give different results !
What am I missing here ?

Regards

Sandy da Silva
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Re: If x and k are both integers, x > k, and x−k = 625, what is x? (1) |k| [#permalink]

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22 Aug 2017, 07:05
sandysilva wrote:
Bunuel wrote:
If x and k are both integers, x > k, and $$x^{−k} = 625$$, what is x?

(1) |k| is a prime number
(2) x + k > 20

Hi Bunuel here how i saw statement (1) |k| is a prime number

But k can be -2 or 2. So when k = -2 and when k = 2 the equation $$x^{−k} = 625$$ should give different results !
What am I missing here ?

Regards

Sandy da Silva

Not sure I understand what you mean. We have the following possible cases for $$x^{−k} = 625$$:

x = 25, k = -2
x = 625, k = -1
x = 5, k = -4

(1) says: |k| is a prime number, thus k = -2 and x = 25.
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Re: If x and k are both integers, x > k, and x−k = 625, what is x? (1) |k|   [#permalink] 22 Aug 2017, 07:05
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# If x and k are both integers, x > k, and x−k = 625, what is x? (1) |k|

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