60 kg on earth is 60 kg on the moon I'm writing a trivia quiz and intend this question, which dates from a high school physics test I took in 1972. 
An astronaut tips the scale at 60 kg while on earth, what will she be if she steps on the scale on the moon? Answer 60 kg.
Kg measures mass, which is constant.
The question is not in pounds, or ask about weight. Yes, it is a trick question, but I think it is an entertaining one. The point is, I've looked around the internet and the discussion all focus on in common usage, weight is mass and nobody knows what a Newton is.
I'm certain of my answer, but I'd like to be ready for some blowback.
 A: The answer depends on the type of instrument you are allowed to use for the measurement. The two types are:

*

*Weighing Machine type


*Beam Balance type

This instrument (weighing machine) measures the downward force applied by the object and then divides it by $g$. That is if your body applies a force of $W$ on the scale then the scale would show a value of $W/g$. This is because $mg=W$ on earth. But say you are on moon and the machine is celebrated for earth then the body applies applies a force say $W'$ then the reading shown by the scale would be $W'/g$. Now on moon $a=g/6$. Therefore the scale would show a reading of about  $m/6$ i.e., this machine on moon measures $10kg$ for a body of $60kg$ on earth.

This instrument (beam balance) works on the principal of moments and therefore for equal arm length it measures the mass of the body. So if you are using this instrument then the value would be same wethere you are on moon or earth.
A: Unfortunately, scales do not measure mass. They measure the force applied by the mass, under the influence of the local gravity. The fact that they are labelled in "mass" is irrelevant. All that happens is that the readout is "adjusted", so that 588 N is shown as 60 kg.
Hence, on the moon your scales will show about 10 kg.
EDIT
I disagree with the comments: even if you are using balance scales, you are measuring force, not mass. Consider the following 2 graphics


The first shows a normal balance, the second an unequal-arm balance. In the second image, it makes no sense to say that 30 kg balances 60 kg. The balance is achieved by having equal torque (moment of rotation) on both sides. Torque is given by $\tau=r\times F$ where $F$ is force, not mass. Hence balance is achieved by using forces of 588 N and 294 N.
