Hi vinay1983,
This DS question combines a variety of algebra steps (and Classic Quadratics) and TESTing values.
The question: Is x = y? This is a YES/NO question.
Fact 1: (x + y){1/x + 1/y] = 4
Lots of algebra steps to simplify this:
(x + y)[y/xy + x/xy] = 4
(x + y)[(x + y)/xy] = 4
(x + y)^2 = 4xy
x^2 + 2xy + y^2 = 4x
x^2 - 2xy + y^2 = 0
(x - y)^2 = 0
So, x MUST = y
The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT
Fact 2: (x - 50)^2 = (y - 50^2
Here we can TEST values:
If x = 0 and y = 0 then the answer to the question is YES
If x = 0 and y = 100 then the answer to the question is NO
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
X=Y
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Plug in a value for x and solve for y.vinay1983 wrote:Is x=y?
1. (x+y)* [1/x + 1/y] = 4
2. (x-50)^2 = (y-50)^2
Statement 1: (x+y)* [1/x + 1/y] = 4
Case 1: x=1
(1+y) * (1/1 + 1/y) = 4
1 + 1/y + y/1 + 1 = 4
1/y + y/1 = 2.
Only y=1 will satisfy this equation.
In this case, x=y.
Case 2: x=5
(5+y) * (1/5 + 1/y) = 4
1 + 5/y + y/5 + 1 = 4
5/y + y/5 = 2.
Only y=5 will satisfy this equation.
In this case, x=y.
The implication of these two random cases is that -- regardless of the value of x -- x=y.
SUFFICIENT.
Statement 2: (x-50)² = (y-50)²
If x=51, we get:
(51-50)² = (y-50)²
1 = (y-50)²
y-50 = 1 or y-50 = -1
y=51 or y=49.
Since it's possible that x=y or that x≠y, INSUFFICIENT.
The correct answer is A.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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vinay1983
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Thank you Rich and Mitch(Sort of rhyming isn't it?)
Actually I did what Rich as shown as the method. I got A, but was sceptical about this
(x-y)^2 = 0 Whether I could conclude that x=y.
Now satisfied!
Actually I did what Rich as shown as the method. I got A, but was sceptical about this
(x-y)^2 = 0 Whether I could conclude that x=y.
Now satisfied!
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
