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The outermost shell of a representative element contains x electrons and the penultimate shell contains y electrons. The number of valence electrons could be:
A. $x + y$
B. $y - x$
C.y
D.x

Answer
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Hint:Basically, a valence electron is an outer shell electron that is associated with an atom. Further, this atom can participate in the formation of a chemical bond. The presence of valence electrons can determine the chemical properties of an element.

Complete step by step answer:
-Generally, the valence electrons are the s and p electrons in the outermost shell whereas the electrons present in the inner shell are known as core electrons. We can track the valence electrons with the help of Lewis structures. These electrons are arranged in different orbitals or shells and are mostly negatively charged particles.
-Further, these electrons are responsible for the interaction between atoms and the formation of chemical bonds. Valence is the number of electrons an atom must lose or gain to attain the nearest noble gas or inert gas electron configuration. Now let’s discuss some properties of valence electrons.
-An atom consisting of a closed shell of valence electrons will usually be chemically inert.
A valence electron can exist in the inner shell of a transition metal.
-A valence electron can either absorb or release energy in the form of a proton.
Now, we have been given that the outermost shell of a representative element contains x electrons and the penultimate shell contains y electrons. So, the number of valence electrons could be x because the number of valence electrons is equal to the number of electrons in the outermost shell.

Hence, option D is correct.

Note:
One way of finding the valence electrons is by checking out the elements placed in the periodic table. Another way to find or determine the valence electron in by knowing the electronic configuration of the element.