If x, y, and z are consecutive integers such that x y z

Question

If x, y, and z are consecutive integers such that x > y > z and the sum of x, y, and z is a multiple of 10, which of the following could be the value of x?

A. 0 
B. 1
C. 9 
D. 10
E. 12

Guys I think 2 answers are correct. What do you come up with?

Bunuel · Accepted Answer

Given that  z + y +x = (y-1) + y + (y+1) = 3y = 10k  -->  y  is a multiple of 10 -->  x = y+1 , so x is a multiple of 10 plus 1. Only answer choices B fits:  z=-1 ,  y=0 , and  z=1  -->  z+y+x=0 .

Answer: B.

Else you could simply plug-in values for x in (x-2) + (x-1) + x and see which one yields a multiple of 10.

vibhav · Answer

Bunuel why can't it be 11,10,9 totals to 30 which is divisible by 10?

Bunuel · Answer

Yes, x could be 11, but 11 is not among the options.

EMPOWERgmatRichC · Answer

Hi All,

This question can be easily beaten by a bit of "brute force" and TESTing THE ANSWERS.

We're given a very specific set of restrictions in this prompt:
1) X, Y and Z are CONSECUTIVE INTEGERS
2) X > Y > Z
3) X+Y+Z = a multiple of 10

We're asked which of the 5 answer COULD be the value of X given these restrictions. Rather than staring at the screen or doing layered math, we can "brute force" the answers until we find one that fits these restrictions..

Answer A: X = 0
In this case, the numbers would be 0, -1, and -2. The sum = -3 which is NOT a multiple of 10. Eliminate A.

Answer B: X = 1
In this case, the numbers would be 1, 0, and -1. The sum = 0 which IS a multiple of 10. B IS the answer.

Final Answer: B

For the sake of argument, if you did not immediately realize that 0 is a multiple of 10, then you could quickly TEST the remaining 3 options and quickly disprove them.

GMAT assassins aren't born, they're made,
Rich

pacifist85 · Answer

I did it this way, which might be a bit similar in a way:

1) Since they are consecutive integers, these could be: x, x-1, x-2 (x>y>z)

2) I added them to give 0 (the 1st multiple of 10, if we say that they add up to 0*Unckown value): 
x+x-1+x-2=0
3x-3=0
3x=3
x=3/3
x=1, Answer is B

EMPOWERgmatRichC · Answer

Hi pacifist85,

Your approach works here, but ONLY because 0 is the multiple of 10 that is involved in the correct answer. If it was any other multiple of 10, then you would have only gotten the solution by "brute forcing" your equation into every possible multiple of 10.

eg.

3x - 3 = 10
3x - 3 = 20
3x - 3 = 30
Etc.

Since these answer choices in this question are all relatively small, even if you did have to brute force multiple possibilities, you would have gotten to the answer relatively quickly, so I think that your approach is fine. In the end, I measure any approach by 2 things:

1) Did it get you the correct answer.
2) Were you able to complete the question relatively quickly (for that prompt).

If the answer to both questions is YES, then you did well.

GMAT assassins aren't born, they're made,
Rich

GmatPoint · Answer

Since x, y, and z are consecutive integers, if x is a + 1, y will be a, and z will be a - 1.
Also, as the some is a multiple of 10, it will be in the form of 10k, where k can be any integer.

Thus, a - 1 + a + a + 1 = 10k
 3a = 10k
 And a = 10/3k.

Since x = a + 1,
x = 10/3k + 1.

The fraction will be in the form of an integer only when k is a multiple of 3.
Thus x will be in the form 10p + 1, where p is an integer.
If p = 0, x = 1. No other option is in the form 10p + 1.

Thus, the correct option is B.

bumpbot · Answer

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If x, y, and z are consecutive integers such that x > y > z

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