Is z equal to the median of the three positive integers, x, y, and z?
(1) x < y + z
(2) y = z
OA B
Source: GMAT Prep
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Is z equal to the median of the three positive integers, x,
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BTGmoderatorDC
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Jay@ManhattanReview
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Given: x, y, and z are positive integers.BTGmoderatorDC wrote:Is z equal to the median of the three positive integers, x, y, and z?
(1) x < y + z
(2) y = z
OA B
Source: GMAT Prep
Question: Is z equal to the median of x, y, and z?
Let's take each statement one by one.
(1) x < y + z
Case 1: Say x = y = z = 2. Median = 2 = z. The answer is Yes, z is the median of x, y, and z.
Case 2: Say x = 2, y = 1, and z = 3. Median = 2 = x. The answer is No, z is not the median of x, y, and z.
No unique answer. Insufficient.
(2) y = z
Case 1: Say x is the smallest integer, then y or z is the median. The answer is Yes, z is the median of x, y, and z.
Case 2: Say x is the largest integer, then y or z is the median. The answer is Yes, z is the median of x, y, and z.
Case 3: Say x = y = z, then x, y or z is the median. The answer is Yes, z is the median of x, y, and z.
Unique answer. Sufficient.
The correct answer: B
Hope this helps!
-Jay
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fskilnik@GMATH
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\[x,y,z\,\, \geqslant 1\,\,{\text{ints}}\]BTGmoderatorDC wrote:Is z equal to the median of the three positive integers, x, y, and z?
(1) x < y + z
(2) y = z
Source: GMAT Prep
\[{\text{z}}\,\,\mathop = \limits^? \,{\text{Med}}\,\left( {x,y,z} \right)\]
\[\left( 1 \right)\,\,x < y + z\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {x,y,z} \right) = \left( {1,1,1} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\
\,{\text{Take}}\,\,\left( {x,y,z} \right) = \left( {1,2,3} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\
\end{gathered} \right.\]
\[\left( 2 \right)\,\,y = z\,\,\,\, \Rightarrow \,\,\,{\text{Med}}\,\left( {x,y,z} \right) = \,\,\,{\text{Med}}\,\left( {x,z,z} \right) = z\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \]
(The last equality is true if x is equal to z, and it is also true if x is not equal to z.)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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