If x, y, and z represent consecutive integers, and x

Question

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

sudarshan22 · Answer

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 .

KSBGC · Answer

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.

The best answer is E.

EgmatQuantExpert · Answer

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.

Answer: E

ScottTargetTestPrep · Answer

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.

Answer: E

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

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