C should be the answer. "that" in C refers to "The distribution of mass" and after repacling it, the sentence will look like "The distribution of mass within the core of the Earth, like the distribution of mass of the mantle surrounding the core....." seems correct. Whereas in E, 'mantle "that" surrounds the core' suggests that core has many mentles which is not correct.

What is the OA?
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B it is!!!

comparing distribution of mass of core and mantle
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The distribution of mass within the core of the Earth,like the mantle that surrounds the core, has been deduced from the orbital behavior of the Earth andthe motions of satellites controlled by the Earth’s gravity.

(A) the mantle that surrounds the core
(B) that within the mantle surrounding the core
(C) that of the mantle surrounding the core
(D) the mantle the core surrounds
(E) the distribution of mass within the mantle that surrounds the core


The contention seems to be between (B) and (C). 'That' is clearly correct in both cases, as it refers to 'the distribution of mass.' The main difference between the two answers is (B) has '...within the mantle' and (C) has 'of the mantle.'

Notice that the non-underlined part has 'the distribution of mass within the core...' There needs to be parallelism here, in the sense that we want to be comparing '...mass within the core...' to 'that within the mantel'. Therefore the answer is (B).

Hope that helps .
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B is the answer.But note that E is also gramatically correct .But B is more concise and hence the answer .
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A and D incorrectly refer to the earth’s mantle, rather than the distribution of mass within it.
E is very wordy.
C is also wrong, it has a //ism break.

So, B is the right answer.