Edit in JSFiddle

  const vm = new Vue({
    el: "#app",
    data: {
      a: Math.floor(Math.random() * 10),
      b: Math.floor(Math.random() * 10),
    },
    methods: {
      c: function(e) {
        if (parseInt(window.prompt(`${this.a} + ${this.b} は?`)) != (this.a + this.b)) {
          e.preventDefault()
          alert("不正解")
        } else {
        e.preventDefault()
        }
      },
    },
  })
<div id="app">
  <form @submit="c" method="POST" action="" ref="form">
    <div class="form-group">
      <div class="col-md-offset-2 col-md-10">
        <button type='submit' class="btn btn-primary" name='action' value='send'>
          送信
        </button>
      </div>
    </div>
  </form>
</div>