We propose a simple method to generate multilingual question and answer pairs on a large scale through the use of a single generative model. These synthetic samples can be used to improve the zero-shot performance of multilingual QA models on target languages. Our proposed multi-task training of the generative model only requires labeled training samples in English, thus removing the need for such samples in the target languages, making it applicable to far more languages than those with labeled data. Human evaluations indicate the majority of such samples are grammatically correct and sensible. Experimental results show our proposed approach can achieve large gains on the XQuAD dataset, reducing the gap between zero-shot and supervised performance of smaller QA models on various languages.