Gradle in Android Studio giving error Project sync failed

Replace this

C:\Program Files\Java\jdk1.7.0_40\jre

with

C:\Program Files\Java\jdk1.7.0_40

inside your JAVA_HOME variable

This is a very late answer but I see that a common suggestion is to remove all other jdk's and this is not always the best idea. You might need older jdk's for different projects. You can go into the gradle.properties file for the project and enter the following line (varied based on your version):

org.gradle.java.home=C:/Java/jdk1.8.0_111

If you are using a different jdk just point to a different directory.