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Math Expert V
Joined: 02 Sep 2009
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If x + y + z = 6, then do any two of the three numbers x, y, and z sum  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 68% (01:09) correct 32% (01:11) wrong based on 186 sessions

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If x + y + z = 6, then do any two of the three numbers x, y, and z sum to 3?

(1) x, y, and z are three different positive integers.
(2) x, y, and z are consecutive integers.

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Re: If x + y + z = 6, then do any two of the three numbers x, y, and z sum  [#permalink]

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Bunuel wrote:
If x + y + z = 6, then do any two of the three numbers x, y, and z sum to 3?

(1) x, y, and z are three different positive integers.
(2) x, y, and z are consecutive integers.

Given : x + y + z = 6

Question : Do any two of the three Number sum up to 3?

Statement 1: x, y, and z are three different positive integers.
sum of any three different Integer will be 6 only when numbers are 1, 2 and 3
i.e. Sum of Two of those three will definitely be 1+2 = 3
SUFFICIENT

Statement 2: x, y, and z are consecutive integers.
sum of any three Consecutive Integer will be 6 only when numbers are 1, 2 and 3
i.e. Sum of Two of those three will definitely be 1+2 = 3
SUFFICIENT

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GMAT 1: 710 Q50 V34 Re: If x + y + z = 6, then do any two of the three numbers x, y, and z sum  [#permalink]

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Bunuel wrote:
If x + y + z = 6, then do any two of the three numbers x, y, and z sum to 3?

(1) x, y, and z are three different positive integers.
(2) x, y, and z are consecutive integers.

IMO : D

Statement 1 : x, y, and z are three different positive integers.
Minimum value of sum of 3 different positive integers = 1+2+3 =6
Thus, only one solution set we can have for the given condition.
Hence suff

Statement 2: x, y, and z are consecutive integers.
So Let x = a , y = a+1 , z = a+2 (consecutive integers)
Now x + y + z = 6 is the given condition. Sub values
(a)+(a+1)+(a+2) = 6
a=1
Thus x=1, y=2, z=3
Hence suff
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Re: If x + y + z = 6, then do any two of the three numbers x, y, and z sum  [#permalink]

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Stmt 1: ENOUGH because 1,2,3 are the only three pos integers that sum upto 6 since they are the least 3 pos integers.
Thus, 1+2 = 3
Stmt 2: ENOUGH because among all integers, 1,2,3 are the only 3 consecutive integers that sum up to 6.
Thus, 1+2 = 3

Ans. = D
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Re: If x + y + z = 6, then do any two of the three numbers x, y, and z sum  [#permalink]

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Bunuel wrote:
If x + y + z = 6, then do any two of the three numbers x, y, and z sum to 3?

(1) x, y, and z are three different positive integers.
(2) x, y, and z are consecutive integers.

Statement 1: for x + y + z = 6 and given that x, y, z are distinct integers, x, y, z must be 1, 2, 3 in order to equal to 6. The answer is always yes (x+y=3) > S
Statement 2: for x + y + z = 6 only 1, 2, 3 distinct integers amount to 6. The answer is always yes (x+y=3) > S

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Re: If x + y + z = 6, then do any two of the three numbers x, y, and z sum  [#permalink]

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If x + y + z = 6, then do any two of the three numbers x, y, and z sum to 3?

(1) x, y, and z are three different positive integers.The only three positive integers than can add to 6 are 1, 2, and 3. 1 and 2 sum to 3. Sufficient
(2) x, y, and z are consecutive integers. The only consecutive integers that add to 6 are 1, 2, and 3. 1 and 2 sum to 3. Sufficient

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Re: If x + y + z = 6, then do any two of the three numbers x, y, and z sum  [#permalink]

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If x + y + z = 6, then do any two of the three numbers x, y, and z sum to 3?

(1) x, y, and z are three different positive integers.
(2) x, y, and z are consecutive integers.

Given : x + y + z = 6

Question : Do any two of the three Number sum up to 3?

Statement 1: x, y, and z are three different positive integers.
sum of any three different Integer will be 6 only when numbers are 1, 2 and 3
i.e. Sum of Two of those three will definitely be 1+2 = 3
SUFFICIENT

Statement 2: x, y, and z are consecutive integers.
sum of any three Consecutive Integer will be 6 only when numbers are 1, 2 and 3
i.e. Sum of Two of those three will definitely be 1+2 = 3
SUFFICIENT

Let me know where i am wrong
Question mention that do any two of the three numbers x, y, and z sum to 3?

therefore if i take x=1 , y=2 then x+y = 3 Yes

but if take x=1 , z=3 , then x+z =4 no

Not sufficient

because it is mention ---ANY TWO

The same applicable for the statement 2 also .
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Re: If x + y + z = 6, then do any two of the three numbers x, y, and z sum  [#permalink]

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vijayshree wrote:

Let me know where i am wrong
Question mention that do any two of the three numbers x, y, and z sum to 3?

therefore if i take x=1 , y=2 then x+y = 3 Yes

but if take x=1 , z=3 , then x+z =4 no

Not sufficient

because it is mention ---ANY TWO

The same applicable for the statement 2 also .

You are misinterpreting the question wording. The question is asking whether you will get a combination of 2 numbers that will give you 3 when added and when they satisfy : x+y+z = 6. When you take x=1, z =3, y = 2 and then x+y =3. So you do have 1 combination that will give you 3. Thus this statement is sufficient. The statement will be sufficient as soon as you get 1 combination that satisfies x1+x2 =3 and x1+x2+x3 =6.

Hope this helps.
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Re: If x + y + z = 6, then do any two of the three numbers x, y, and z sum  [#permalink]

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Bunuel wrote:
If x + y + z = 6, then do any two of the three numbers x, y, and z sum to 3?

(1) x, y, and z are three different positive integers.
(2) x, y, and z are consecutive integers.

Ans: D

Solution: given x+y+z=6
1) x,y, and z are different positive integers means x,y, and z belong to the group (1,2,3,4,5,6)
since they are distinct only possible values for them is 1,2,3 and it ans the question
[Sufficient]

2) consecutive integers.. so they can only have 1,2,and 3 as their values.
[Sufficient]

Ans: D each statement alone is sufficient to ans the question.
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Re: If x + y + z = 6, then do any two of the three numbers x, y, and z sum  [#permalink]

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x + y + z = 6

Do any two of the three numbers x, y, and z sum to 3?

(1) x, y, and z are three different positive integers.

If, x, y and Z are three DIFFERENT positive integers and their sum is 6 as per given information, there are only three possible choices of numbers.

3,2 & 1 - And as we can see that the sum of two of these numbers (2 & 1) can definitely be 3.

Hence =====> (1) is SUFFICIENT

(2) x, y, and z are consecutive integers.

If x,y & X are CONSECUTIVE integers, and their sum is 6 as per given information, there are again only three possible choices of numbers.

3,2 & 1 - And as we can see that the sum of two of these numbers (2 & 1) can definitely be 3.

Hence =====> (2) is SUFFICIENT

Hence, Answer is D
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GMAT 1: 640 Q48 V28 Re: If x + y + z = 6, then do any two of the three numbers x, y, and z sum  [#permalink]

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Take in mind that 0 is an even integer but ... neither positive, nor negative.

This will help Re: If x + y + z = 6, then do any two of the three numbers x, y, and z sum   [#permalink] 28 Mar 2018, 01:22
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