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02 May 2018, 01:55
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
70% (01:42) correct
30%
(01:54)
wrong
based on 225
sessions
History
Date
Time
Result
Not Attempted Yet
The operation ? is defined for all integers x and y as \(x?y = xy - y\). If x and y are positive integers, which of the following CANNOT be zero?
A. \(x?y\)
B. \(y?x\)
C. \((x-1)?y\)
D. \((x+1)?y\)
E. \(x?(y-1)\)
A. \(x?y\)
B. \(y?x\)
C. \((x-1)?y\)
D. \((x+1)?y\)
E. \(x?(y-1)\)
02 May 2018, 05:30
Kudos
Bookmarks
Bunuel
Provide that , \(x?y = xy - y\) = \(x(y-1)\)
A. \(x?y\) ===========>=\(xy-y\)=\(x(y-1)\).............................................. is 0 when y=1
B. \(y?x\) ===========>=\(yx-x\) =\(y(x-1)\)............................................. is 0 when x=1
C. \((x-1)?y\) =====>=\((x-1)y-y\) =\(xy-y-y\) =\((xy-2y)\) =\(y(x-2)\) ...... is 0 when x=2
D. \((x+1)?y\) =====>=\((x+1)y-y\) =\(xy+y-y\) =\(xy\) ............................ can not be 0 as x, y are both positive integer
E. \(x?(y-1)\) =====>=\(x(y-1)-(y-1)\) =\((x-1)(y-1)\) .............................. is 0 when x=1 or y=1 or both
Hence the answer would be D
03 May 2018, 10:42
Kudos
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Bunuel
Let’s analyze each answer choice.
A) x?y
x?y = 0
xy - y = 0
y(x - 1) = 0
y = 0 or x = 1
Since y can’t be 0, then x = 1. However, as long as x = 1, regardless of what y is, we will have x?y = 0. Thus, A is not the answer.
B) y?x
y?x = 0
yx - x = 0
x(y - 1) = 0
x = 0 or y = 1
Since x can’t be 0, then y = 1. However, as long as y = 1, regardless of what x is, we will have y?x = 0. Thus, B is not the answer.
C) (x - 1)?y
(x - 1)?y = 0
(x - 1)y - y = 0
xy - 2y = 0
y(x - 2) = 0
y = 0 or x = 2
Since y can’t be 0, then x = 2. However, as long as x = 2, regardless of what y is, we will have (x - 1)?y = 0. Thus C is not the answer.
D) (x + 1)?y
(x + 1)?y = 0
(x + 1)y - y = 0
xy = 0
y = 0 or x = 0
We see that the only way (x + 1)?y can be 0 is if y = 0 or x = 0. However, we are given that both x and y are positive integers. Therefore, there is no way (x + 1)?y can be 0. Thus, D is the answer.
Answer: D
