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Difficulty:
45%
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Question Stats:
65% (01:51) correct
35%
(02:02)
wrong
based on 126
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If x = y + 2, where x, y are positive integers. Is (x + y) a multiple of 4 ?
(1) x is odd
(2) (3x + y) = 58
(1) x is odd
(2) (3x + y) = 58
12 Nov 2018, 23:09
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If x = y + 2, where x, y are positive integers. Is (x + y) a multiple of 4 ?
since x=y+2, both x and y will have same property either both are odd or both are even...
Thus x+y=y+2+y=2y+2
So the question can be eventually rephrased as " Are x and y even or odd?"
(1) x is odd
so y is odd...
answer is yes, x+y is divisible by 4
sufficient
(2) (3x + y) = 58
3x+y=58...... => 3(y+2)+y=58 => 3y+6+y=58 => 4y=52.....y=13
thus x = 13+2=15
x+y=13+15=28 and 28 is divisible by 4
sufficient
D
since x=y+2, both x and y will have same property either both are odd or both are even...
Thus x+y=y+2+y=2y+2
- if y is even, 2y will be a multiple of 4 and, therefore, 2y+2 will not be a multiple of 4.
if y is odd, 2y will NOT be a multiple of 4 and, therefore, 2y+2 will be a multiple of 4.
So the question can be eventually rephrased as " Are x and y even or odd?"
(1) x is odd
so y is odd...
answer is yes, x+y is divisible by 4
sufficient
(2) (3x + y) = 58
3x+y=58...... => 3(y+2)+y=58 => 3y+6+y=58 => 4y=52.....y=13
thus x = 13+2=15
x+y=13+15=28 and 28 is divisible by 4
sufficient
D
13 Nov 2018, 07:07
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v12345
Given: x = y + 2
Target question: Is (x + y) a multiple of 4 ?
This is a good candidate for rephrasing the target question.
Since x = y + 2, we can take the target question Is (x + y) a multiple of 4 ? and replace x with y+2.
When we do this, we get: Is (y+2 + y) a multiple of 4 ?
Simplify: Is (2y + 2) a multiple of 4 ?
Factor to get: Is 2(y + 1) a multiple of 4 ?
We can see that, if y+1 is EVEN, then 2(y + 1) will be a multiple of 4
In order for y+1 to be EVEN, we need y to be ODD
So, we can write: REPHRASED target question: Is y odd?
NOW ONTO THE STATEMENTS!!
Statement 1: x is odd
We already know that x = y + 2
So, we can write: ODD = y + 2
This means: ODD - 2 = y
Since 2 is EVEN, we get: ODD - EVEN = y
This means y must be ODD
So, the answer to the REPHRASED target question is YES, y IS odd
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: (3x + y) = 58
Since x = y + 2, we can replace x with y+2 to get: 3(y + 2) + y = 58
At this point, we can see that we COULD solve this question to find the value of y, in which case, we COULD determine whether y is ODD.
Since we COULD answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer: D
RELATED VIDEO FROM OUR COURSE (rephrasing the target question)
