Macroeconomics: LM Curve and Money Supply

How about this one: 

“A given increase in the money supply will shift the LM curve farther to the right if money demand is more sensitive to the level of income”. True, false or uncertain? Briefly explain your answer.
Thanks, Katie

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An increase in the money supply shifts the LM curve to the right, raising income and lowering the interest rate. It seems to me that if money demand is more sensitive to the level of income, this will reduce the shift of the LM curve to the right.