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16 Sep 2014, 00:17
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If \(x\) and \(y\) are positive integers and \(x \gt y\), what is the value of \(xy^2 + yx^2\)?
(1) \(xy = 6\)
(2) \(x\) is a prime number
(1) \(xy = 6\)
(2) \(x\) is a prime number
16 Sep 2014, 00:17
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Official Solution:
If \(x\) and \(y\) are positive integers and \(x \gt y\), then what is the value of \(xy^2 + yx^2\)?
The question asks to find the value of \(xy^2 + yx^2=xy(y+x)\).
(1) \(xy = 6\).
By plugging \(xy = 6\) into the equation, it becomes: what is the value of \(xy(y+x) = 6(y+x)\)? Now, since \(x\) and \(y\) are positive integers and \(x > y\), then from \(xy = 6\) it follows that \(x=6\) and \(y=1\) OR \(x=3\) and \(y=2\), thus \(6(y+x)=42\) or \(6(y+x)=30\). Two different values, thus this statement is NOT sufficient.
(2) \(x\) is a prime number.
This statement alone is clearly insufficient.
(1)+(2) Since from (2) we know that \(x\) is a prime number, then from (1) we get that \(x=3=prime\) and \(y=2\), thus \(6(y+x)=42\). Sufficient.
Answer: C
If \(x\) and \(y\) are positive integers and \(x \gt y\), then what is the value of \(xy^2 + yx^2\)?
The question asks to find the value of \(xy^2 + yx^2=xy(y+x)\).
(1) \(xy = 6\).
By plugging \(xy = 6\) into the equation, it becomes: what is the value of \(xy(y+x) = 6(y+x)\)? Now, since \(x\) and \(y\) are positive integers and \(x > y\), then from \(xy = 6\) it follows that \(x=6\) and \(y=1\) OR \(x=3\) and \(y=2\), thus \(6(y+x)=42\) or \(6(y+x)=30\). Two different values, thus this statement is NOT sufficient.
(2) \(x\) is a prime number.
This statement alone is clearly insufficient.
(1)+(2) Since from (2) we know that \(x\) is a prime number, then from (1) we get that \(x=3=prime\) and \(y=2\), thus \(6(y+x)=42\). Sufficient.
Answer: C
General Discussion
29 Apr 2019, 09:54
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Here's my detailed solution since I don't think anyone broke this down step by step.
Statement (1):
xy=6
We know from the prompt that x>y , therefore:
xy=6
(6)(1)=6 OR
(3)(2)=6
In the first instance, x=6 and y=1, the result of [x(y^2)]+[y(x^2)]=42
In the second instance, x=3 and y=2, the result of [x(y^2)]+[y(x^2)]=30
Statement (1) is not sufficient.
Statement (2):
x is a prime number
There are an infinite number of values for x that would be prime and an infinite number of values for y that would be less than x.
Statement (2) is not sufficient.
Statements (1)&(2):
The only values that satisfy both statement (1) and statement (2) are: x=3 and y=2
Statements (1)&(2) together are sufficient.
I hope this is clear. Please give kudos if this helped you understand the solution in any way!
Statement (1):
xy=6
We know from the prompt that x>y , therefore:
xy=6
(6)(1)=6 OR
(3)(2)=6
In the first instance, x=6 and y=1, the result of [x(y^2)]+[y(x^2)]=42
In the second instance, x=3 and y=2, the result of [x(y^2)]+[y(x^2)]=30
Statement (1) is not sufficient.
Statement (2):
x is a prime number
There are an infinite number of values for x that would be prime and an infinite number of values for y that would be less than x.
Statement (2) is not sufficient.
Statements (1)&(2):
The only values that satisfy both statement (1) and statement (2) are: x=3 and y=2
Statements (1)&(2) together are sufficient.
I hope this is clear. Please give kudos if this helped you understand the solution in any way!
