The operation denoted by the symbol # is defined for all real numbers

Question

The operation denoted by the symbol # is defined for all real numbers p and r as p#r equals the larger of p and r. For example, 5#3 = 5. Which one of the distinct numbers x, y and z is the largest?

(1) (x#y)#z = x#z
(2) (x#z)#y = z#y

Archit3110 · Answer

given p#r equals the larger of p and r. For example, 5#3 = 5
so from #1
(x#y)#z = x#z
x>y ; but no relation between x & z
insufficient
#2
(x#z)#y = z#y
z>x ; but relation b/w x & y
insufficient
from 1 &2 
z>x>y
IMO C

aryanrgupta · Answer

Options are:
(1) (x#y)#z = x#z
(2) (x#z)#y = z#y

(1) When X and Y are together: X turns out to be greater than Y, hence we get to see X#Z on the RHS so X>Y but no information on relation of X and Z -  INSUFFICIENT

(2) When X and Z are together: Z turns out to be greater than X, hence we get to see Z#Y on the RHS so Z>X but no information on relation of Z and Y -  INSUFFICIENT

Considering both - So X>Y and Z>X hence the relation is  Z>X>Y

Hence the answer is C

Ertucinar · Answer

Step 1: Evaluate Statement (1) Alone 
(x#y)#z = x#z 
It's mean y is not the largest one.The largest one is x or z.
Statement (1) alone is  insufficient .

Step 2: Evaluate Statement (2) Alone 
(x#z)#y = z#y 
It's mean x is not the largest one.The largest one is y or z.
Statement (2) alone is  insufficient .

Step 3: Evaluate Both Statements Together 
From statement (1), y is not the largest. 
From statement (2), x is not the largest. 
Since x, y, and z are distinct, the only possibility is that z is the largest.

Since we can determine the answer, both statements together are  sufficient .

---

Final Answer: C  (Both statements together are sufficient, but neither alone is sufficient).

Some have found a connection between x and y, but it is not possible to deduce this from the given information. 
Statement (1)
(x#y)#z = z
x#z = z
z = z
x>y or x<y are possible.

The operation denoted by the symbol # is defined for all real numbers

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GMAT Data Sufficiency (DS) Questions

The operation denoted by the symbol # is defined for all real numbers

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