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Math Expert V
Joined: 02 Sep 2009
Posts: 56277
If x, y, and z are positive integers, what is the value of x?  [#permalink]

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Difficulty:   15% (low)

Question Stats: 77% (01:26) correct 23% (01:09) wrong based on 136 sessions

### HideShow timer Statistics GMAT Club Tests' Fresh Question:

If x, y, and z are positive integers, what is the value of x?

(1) xyz = z!

(2) x! + y! = 3

_________________
examPAL Representative P
Joined: 07 Dec 2017
Posts: 1074
If x, y, and z are positive integers, what is the value of x?  [#permalink]

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Bunuel wrote:

GMAT Club Tests' Fresh Question:

If x, y, and z are positive integers, what is the value of x?

(1) xyz = z!

(2) x! + y! = 3

As all we're given are equations, we'll work with them.
This is a Precise approach.

(1) xyz = z! can be rewritten as xyz = z(z -1)(z - 2)….. which simplifies to xy = (z - 1)(z - 2)…. we cannot solve for x so this is insufficient.
Insufficient.

(2) Let's look at a few examples. if x = 1 then x! = 1 so y! = 3 - 1 = 2 and y = 2. If x = 2 then x! = 2 so y! = 1 and y = 1. If x = 3 then x! = 6 and y! = 3 - 6 which is negative and therefore impossible. That is, we have two solutions: x = 1 and y = 2 or x = 2 and y = 1.
Insufficient.

Combined.
(1) lets us solve for z (as xyz = z! --> 2z = z! --> z = 3) but does not help us separate between x = 1, y =2 and y = 2, x = 1.
That is, we still have two possible values for x.
Insufficient.

_________________
Intern  B
Joined: 16 Aug 2015
Posts: 18
Location: India
Re: If x, y, and z are positive integers, what is the value of x?  [#permalink]

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2
(1) xyz = z!
=> xy = (z-1)!
value of x cannot be determined using this information, therefore not sufficient

(2) x! + y! = 3
only possible solution is 1! + 2!
But x can take any value i.e. 1 or 2
Therefore not sufficient

Both statements together does not solve our problem of statement 2, i.e. x can take 2 values

Manager  B
Joined: 02 Jul 2017
Posts: 67
Re: If x, y, and z are positive integers, what is the value of x?  [#permalink]

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2
1)

XYZ=z! =1.2.3.4.5.......(z-1)Z

Not sufficient..can not infer much ...

2)X!+y!=3

two possibilities either X=1,Y=2 or X=2,Y=1

Not sufficient

1 & 2..

XYZ=1.2.....(Z-1)Z
i.e 1.2.Z=1.2......(z-1)Z
Z=3

we can't tell X is 1 or 2 ..hence answer is E
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7597
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If x, y, and z are positive integers, what is the value of x?  [#permalink]

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1
Bunuel wrote:

GMAT Club Tests' Fresh Question:

If x, y, and z are positive integers, what is the value of x?

(1) xyz = z!

(2) x! + y! = 3

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables (x, y and z) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Since x! + y! = 3, we have x = 1, y = 2 or x = 2, y = 1.
If x = 1, y = 2 or x = 2, y = 1, we have z = 3 from xyz = z! or 2z = z!.
Then we have x = 1, y = 2, z = 3 or x = 2, y = 1, z = 3.
Thus we don't have a unique solution for the variable x.
Both conditions together are not sufficient.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 56277
Re: If x, y, and z are positive integers, what is the value of x?  [#permalink]

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Bunuel wrote:

GMAT Club Tests' Fresh Question:

If x, y, and z are positive integers, what is the value of x?

(1) xyz = z!

(2) x! + y! = 3

_________________ Re: If x, y, and z are positive integers, what is the value of x?   [#permalink] 24 Dec 2018, 02:21
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