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# If x, y, and z represent consecutive integers, and x < y < z, which of

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Math Expert
Joined: 02 Sep 2009
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If x, y, and z represent consecutive integers, and x < y < z, which of  [#permalink]

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18 Jul 2018, 00:43
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15% (low)

Question Stats:

79% (00:47) correct 21% (00:59) wrong based on 56 sessions

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If x, y, and z represent consecutive integers, and x < y < z, which of the following equals y?

I. x + 1
II. (x +z)/2
III. (x + y + z)/3

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III

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Re: If x, y, and z represent consecutive integers, and x < y < z, which of  [#permalink]

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18 Jul 2018, 01:32
Bunuel wrote:
If x, y, and z represent consecutive integers, and x < y < z, which of the following equals y?

Let,
x = 1, y = 2, z = 3 : since x < y < z

Putting respective values in given cases, each one of case is satisfied.
I. x + 1 --> y = x + 1 --> 2 = 1 + 1 = 2
II. (x +z)/2 --> y = (x + z)/2 --> 2 = 4/2 = 2
III. (x + y + z)/3 --> y = (1 + 2 + 3) / 3 = 2

Hence, E.
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Re: If x, y, and z represent consecutive integers, and x < y < z, which of  [#permalink]

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18 Jul 2018, 01:56
Bunuel wrote:
If x, y, and z represent consecutive integers, and x < y < z, which of the following equals y?

I. x + 1
II. (x +z)/2
III. (x + y + z)/3

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III

Assigning different values for consecutive integers x< y< z.

x = 2
y= 3
z = 4.

I. x+1 = y

2+1 = 3

II. (x+z)/2 = y

(2+4)/2 = 3

III. (x+y+z) /3 = y

(2+3+4) / 3 =3

All the options are correct. Note: Consecutive integers can be negative. Same rules.

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Joined: 04 Jan 2015
Posts: 1985
Re: If x, y, and z represent consecutive integers, and x < y < z, which of  [#permalink]

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18 Jul 2018, 03:09

Solution

Given:
• x, y, and z represent consecutive integers
• x < y < z

To find:
• Among the three given options, which equals y.

Approach and Working:

x, y, and z are consecutive integers.
• Hence, y= x+1 and z= x+2

Now, look at every option.
I. x + 1= y
Hence, x+1 is equal to y.

II.$$\frac{(x +z)}{2}= \frac{x+x+2}{2}$$= 2x+2= x+1
Hence,$$\frac{(x+z)}{2}$$ is equal to y.

III. $$\frac{(x + y + z)}{3}= \frac{x+x+1+x+2}{3}= \frac{3x+3}{3}$$= x+1
Hence, $$\frac{(x + y + z)}{3}$$ is equal to y.

Hence, the correct answer is option E.

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Re: If x, y, and z represent consecutive integers, and x < y < z, which of  [#permalink]

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22 Jul 2018, 18:35
Bunuel wrote:
If x, y, and z represent consecutive integers, and x < y < z, which of the following equals y?

I. x + 1
II. (x +z)/2
III. (x + y + z)/3

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III

The easiest way to solve this problem is pick numbers for x, y, z. So let x = 2, y = 3, and z = 4. We see that y = x + 1. So I is true.

Since (x + z)/2 = (2 + 4)/2 = 3, we see that II is also true.

Finally, since (x + y + z)/3 = (2 + 3 + 4)/3 = 3, we see that III is also true.

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Re: If x, y, and z represent consecutive integers, and x < y < z, which of &nbs [#permalink] 22 Jul 2018, 18:35
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