Application of Quantity Theory of Money

Quantity Theory of Money
: The quantity equation implies that doubling real GDP will double the price level holding all else constant
True or False? Chapter 8, pp. 193+  (Of Jones Macro Econ, Crisis Update)

Y_{t} X P_{t} = V_{t} X M_{t}

Where Y is real GDP, P is the price level, V is the velocity of money and M is the money supply.

Converting this to grouth rates, we get:
    g_{Y}+g_{P} = g_{V} + g_{M}

We're told to assume that velocity and money supply is constant,
    this implies that g_{V}=0 & g_{M}=0

    g_{Y}+g_{P} = 0

    g_{P} = - g_{Y}

Meaning if Y grows (holding all else constant), the price level must shrink.