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# If x, y, and z are three integers, are they consecutive integers?

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Re: If x, y, and z are three integers, are they consecutive integers? [#permalink]
Statement (1) does not give any information about y. So, insufficient.
Statement (2) tells that x<y<z; it could be 8<9<10 or 5<10<15; So, insufficient.

Both combined gives us the clue that x and z differ by 2 and that y is between x and z.

Hence, (C) is sufficient.
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Re: If x, y, and z are three integers, are they consecutive integers? [#permalink]
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If x, y, and z are three integers, are they consecutive integers?

(1) z - x= 2
(2) x < y < z

Statement 1) z is greater than x by 2 , we don't know about y. Not sufficient.
Statement 2) the integers need not be consecutive. Not sufficient.

Combining the two statements, z-x = 2 so y can to be between x and z as all are integers. Hence option C)
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Re: If x, y, and z are three integers, are they consecutive integers? [#permalink]
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Bunuel wrote:
If x, y, and z are three integers, are they consecutive integers?

(1) z - x= 2
(2) x < y < z

Solution:

Question Stem Analysis:

We need to determine whether x, y, and z are consecutive integers.

Statement One Alone:

Since we don’t know anything about y, statement one alone is sufficient.

Statement Two Alone:

Even though we know the order of the three integers, we can’t determine whether x, y, and z are consecutive integers. Statement two alone is not sufficient.

Statements One and Two Together:

Since z - x = 2 and x < y < z, y = x +1 and z = x + 2. This makes the three integers consecutive integers. Both statements together are sufficient.

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Re: If x, y, and z are three integers, are they consecutive integers? [#permalink]
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x, y and z are three integers. We need to find if they are consecutive integers.

From statement I alone, z – x = 2. There is no information about y.

If z = 3 and x = 1 along with y = 2, x, y and z are three consecutive integers.
If z = 4 and x = 2 along with y = 1, x, y and z are NOT consecutive integers.
Statement I alone is insufficient. Answer options A and D can be eliminated.

From statement II alone, x<y<z. This is insufficient to find out if x, y and x are consecutive integers.
Statement II alone is insufficient. Answer option B can be eliminated.

Combining statements I and II, we have the following:

From statement II, x<y<z; from statement II alone, z – x = 2.
This is possible only if all the three integers are consecutive integers.
The combination of statements is sufficient. Answer option E can be eliminated.

The correct answer option is C

Hope that helps!
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Re: X,Y,Z & Inequalities [#permalink]
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Re: X,Y,Z & Inequalities [#permalink]
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