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06 May 2006, 11:43
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x and y are positive integers, where (x + y)/3 = 36. What is x?
(1) x > y
(2) | xy | > 32
The answer is explained below. My question is simple: How the heck do you manipulate (x + y)/3 = 36, to (x + y) = 12
(x+y)/3 = 36 ---> multiply both sides by 3 and x+y = 108.
*******************************
Principle - Missing the Constraint
In this problem, we are given a value for (x + y) where x and y are positive integers: (x + y)/3 = 36, which we manipulate to:(x+y) = 12
As we know that x and y are positive integers, there are a limited number of value for each of x and y: 1 + 11 where x = 1 and y = 11, 2 + 10 where x = 2 and y = 10 . . . up to 11 + 1 where x = 11 and y = 1.
(1) INSUFFICIENT. Statement 1 indicates that x is greater than y. This means that x could be 7, 8, 9, 10, or 11. Eliminate A and D.
(2) INSUFFICIENT. Statement 2 tells us that | xy | > 32.
This information restricts the values for x substantially, as seen in the following:
1 x 11 = 11
2 x 10 = 20
3 x 9 = 27
4 x 8 = 32
5 x 7 = 35
6 x 6 = 36
7 x 5 = 35
8 x 4 = 32, etc.
In order for statement 2 to be true, x could only be 5, 6, or 7. Eliminate B.
(1) + (2) SUFFICIENT. The only value for x in which x > y and | xy | > 32 is 7. This question utilized a hidden constraint on the number of values for x based on the information that x and y are positive integers and that x + y = 12.
(1) x > y
(2) | xy | > 32
The answer is explained below. My question is simple: How the heck do you manipulate (x + y)/3 = 36, to (x + y) = 12
(x+y)/3 = 36 ---> multiply both sides by 3 and x+y = 108.
*******************************
Principle - Missing the Constraint
In this problem, we are given a value for (x + y) where x and y are positive integers: (x + y)/3 = 36, which we manipulate to:(x+y) = 12
As we know that x and y are positive integers, there are a limited number of value for each of x and y: 1 + 11 where x = 1 and y = 11, 2 + 10 where x = 2 and y = 10 . . . up to 11 + 1 where x = 11 and y = 1.
(1) INSUFFICIENT. Statement 1 indicates that x is greater than y. This means that x could be 7, 8, 9, 10, or 11. Eliminate A and D.
(2) INSUFFICIENT. Statement 2 tells us that | xy | > 32.
This information restricts the values for x substantially, as seen in the following:
1 x 11 = 11
2 x 10 = 20
3 x 9 = 27
4 x 8 = 32
5 x 7 = 35
6 x 6 = 36
7 x 5 = 35
8 x 4 = 32, etc.
In order for statement 2 to be true, x could only be 5, 6, or 7. Eliminate B.
(1) + (2) SUFFICIENT. The only value for x in which x > y and | xy | > 32 is 7. This question utilized a hidden constraint on the number of values for x based on the information that x and y are positive integers and that x + y = 12.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
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06 May 2006, 17:29
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The explanation and the answer are wrong unless there are typos. Both 1 and 2 yield the same set of numbers.
x + y = 108 and not 12.
1. x > y ==> {(x,y) = (107,1) ........(55,53)). So no unique value for x.
2. |xy| > 32 ==> gives the same set of numbers above.
So answer is E.
x + y = 108 and not 12.
1. x > y ==> {(x,y) = (107,1) ........(55,53)). So no unique value for x.
2. |xy| > 32 ==> gives the same set of numbers above.
So answer is E.
19 Jun 2006, 18:36
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basically, X+Y=108
STMT1,
X=100, Y=8
X=58,Y=50 insuff
stmt2,
again
x=100, y=8
x=58,y=50
insuff
combining, insuff
STMT1,
X=100, Y=8
X=58,Y=50 insuff
stmt2,
again
x=100, y=8
x=58,y=50
insuff
combining, insuff
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
