Problem of the Day

$10,x,30,y,50$

In the above sequence, $x$ and $y$ are integers, and the numbers are arranged in increasing order. What is the value of $y-x$ ?

(1) The median of the sequence is equal to the mean.

(2) $\displaystyle \frac{y+x}{2}=30$

Reveal Answer

Answer

E. Both statements together are insufficient.

See the Solution

Solution

[latexpage]

Statement 1: We already know the median is 30 because we are told the numbers are arranged in increasing order. This tells us the mean is also 30. Therefore, $x+y=60$. This could be true for $x=20, y=40$ in which case $y-x=20$ or $x=29, y=31$, in which case $y-x=2$. INSUFFICIENT.

Statement 2: This essentially gives us the same information from statement 1 in a different form. INSUFFICIENT.

Statements 1&2: Both statements say the same thing and neither is sufficient alone, so they cannot be sufficient together. INSUFFICIENT.

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