Here is a question from the book SAT II Success Biology E/M (where the SAT is the exam taken by the American high school students):

Which of the following statements is true about mutations?

(A) Rates
tend to be very high in most populations.

(B) generally lethal

(C)
irreversible

(D) Only certain gene locations are affected.

(E) source
of genetic variation

In my opinion, we can definitely eliminate A, B, and D.

Then, I struggle between C and E since I think mutations are definitely a source of genetic variation but are as well generally irreversible (I've found evidence on different websites, including this http://hawaiireedlab.com/wpress/?p=154 where the author writes that only some mutations are reversible).

In the end, I think I should have probably gone with E because C can be seen as having some exceptions.

Then, here is the book explanation for this question:

The correct answer is (C). These recent conclusions about
mutations—recall that Darwin did not know of mutations—are all the
reverse of those listed in the choices, with the exception of choice
(C), the correct answer. Rates, in fact, tend to be below in
populations, mutations are generally not lethal, any gene location can
be affected, and they are felt to be the source of genetic variation.
Darwin felt over-production of offspring was the source of potential
variation.

The answer is C here. However, I didn't particularly understand why E wasn't considered a correct answer.

Could you please explain why C, and not E, is correct?

Going through the possible answers

(A) Rates tend to be very high in most populations.

This is a very unclear statement. What does "high" mean? In humans, the average mutation rate per nucleotide is of the order of $10^-8$ (Rahbari et al., 2016). Whether someone wants to call that high or low is up to this person original intuition.

(B) generally lethal

No, that's wrong (Robert et al., 2018)

(C) irreversible

It is a little unclear if by "irreversible" they mean that the function of the gene (or any other functional element) cannot be restored or whether a specific mutation cannot be exactly undo by a future mutation. In both cases, however, it would be wrong!

Mutations that restore the function of a gene (or any other genomic functional element) are called reverse mutations (aka. suppressor mutations; I personally don't know of any difference between the concepts of reverse mutation and suppressor mutation). Most reverse mutations are likely to act via a second mutation that restore the function of the gene rather than undoing the previous mutation. It does not mean however that it is impossible a mutation that perfectly undo a mutation is impossible. Consider a substitution inverting a A into a T. A reverse mutation could do just the opposite.

(D) Only certain gene locations are affected.

Mutation rate vary throughout the genome but all of the genome is subject to some non-zero mutation rate.

(E) source of genetic variation

Yes, mutations are the ultimate source of genetic variation in populations, while genetic drift and directional selection removes variation.

As other users have highlighted in their answers, many mutations (incl. synonymous mutations but not only and soma mutations) do not bring up any the underlying genetic variance of phenotypic traits. These details are however mainly irrelevant though. What matters is that it still remain true that (some) mutations increase genetic variance.

We could also add the complication as to wonder whether by "genetic variance", they meant "genetic variance underlying phenotypic variance" (which is its standard usage) or "genetic variance where one allele is given an arbitrary value and another another (problem arsing for loci with more than 2 alleles segregating). More information about the terminology and the math when it comes to quantifying genetic variance in the post Why is a heritability coefficient not an index of how “genetic” something is?

What I would have answered

The correct answer is (C). These recent conclusions about mutations—recall that Darwin did not know of mutations—are all the reverse of those listed in the choices, with the exception of choice (C), the correct answer. Rates, in fact, tend to be below in populations, mutations are generally not lethal, any gene location can be affected, and they are felt to be the source of genetic variation. Darwin felt over-production of offspring was the source of potential variation.

I disagree. To me, B and D are wrong, A is unclear, C is slightly unclear but wrong in both interpretations I can think of and E is correct. I would have answered E.

About the justification given

Rates, in fact, tend to be below in populations [..]

This piece of sentence is not even grammatically correct. Below what? It highlights that A is unclear.

they are felt to be the source of genetic variation

The term "felt" is poorly chosen here IMO, but this piece of sentence seems to rather give credit to answer E. I think, whoever wrote this answer mistakenly wrote C instead of E

Darwin felt over-production of offspring was the source of potential variation.

Really, who cares about Darwin thoughts on the subject here?! But in any case, this sounds like a misrepresentation of Darwin's ideas. More info can be found in Charlesworth and Charlesworth (2009) and also maybe this post

It depends. A mutation in somatic cells is not a source of genetic variation because they are not inherited by offspring. But mutations in the sex cells is a source of variation. Your answer key does not appear to be sure of the correct answer because it says the reverse of every answer but C is true of mutations but then agrees with answer E. Also unless part of the question is missing, what Darwin thought is not really relevant. Also more offspring means more chances offspring carrying a mutation.

mutations form part of the list responsible for genetic variation hence phenotypic variation. by definition mutation are alteration of genetic code and unpredicted changes in sequence of nucleotides in nucleic acids(level).

so yes mutations are responsible of variation but not all the time and not all mutations actually results in variation. silent mutations are neither harmful nor beneficial they do not improve organisms by any means, on the other hand nonsense mutations are readily harmful they can result in death.

other sources of variation include:
1. independent assortment of chromosomes(meiotic division), as per Mandel's first law of independent assortment.
2. crossing over of bivelents
3. environmental changes, which subsequently lead to beneficial mutations.