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30 Dec 2020, 10:46
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A
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Difficulty:
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71% (01:43) correct
29%
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If x and y are consecutive even integers, is x > y ?
(1) x - 2 and y + 2 are consecutive even integers.
(2) x is greater than 2.
(1) x - 2 and y + 2 are consecutive even integers.
(2) x is greater than 2.
30 Dec 2020, 11:17
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Bunuel
If x and y are consecutive even integers, is x > y ?
(1) x - 2 and y + 2 are consecutive even integers.
(2) x is greater than 2.
Given: x and y are consecutive even integers (1) x - 2 and y + 2 are consecutive even integers.
(2) x is greater than 2.
So, for example it COULD be the case that x = 6 and y = 8 (i.e., x < y)
Alternatively, it could be the case that x = 8 and y = 6 (i.e., x > y)
Target question: Is x > y
Statement 1: x - 2 and y + 2 are consecutive even integers.
This automatically tells us that x > y.
We know this because there are only two possible cases: x < y and y > x (since the given information tells us that x and y are consecutive even integers)
If it were the case that x < y (e.g., x = 6 and y = 8), then subtracting 2 from x (the smaller value) and adding 2 to y (the bigger value) certainly won't yield two numbers that are consecutive even integers.
Since it's impossible for x < y, it must be the case that x > y
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: x is greater than 2
Since we have no information about the value of y, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
30 Dec 2020, 11:33
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Bunuel
If x and y are consecutive even integers, is x > y ?
(1) x - 2 and y + 2 are consecutive even integers.
(2) x is greater than 2.
(1) x - 2 and y + 2 are consecutive even integers.
(2) x is greater than 2.
Either x=y+2 or y=x+2.
(1) x - 2 and y + 2 are consecutive even integers.
If x=y+2, then x-2=y+2-2=y and y and y+2 are consecutive. Possible
If y=x+2, then y+2=x+2+2=x+4 and x-2 and x+4 are not consecutive. Not possible
Thus x=y+2 or x>y
Sufficient
(2) x is greater than 2.
Nothing about y
Insufficient
A
