The GRE likes to put overlapping sets problems in the data interpretation questions. We recognize this as an overlapping set since you can be a Catholic, or a Democrat, or both, or neither. The easiest way to solve these is with an overlapping sets matrix. It looks like a tic-tac-toe game but with an extra row and an extra column. It would be easy to show with pictures but they're not allowed in the answers so I'll have to describe them.

The 3 columns can be labeled "Catholic", "Not Catholic", and "Total". The 3 rows can be labeled "Democrat", "Not Democrat", and "Total". On the test, I'd label them C, NC, and T, and D, ND, and T, respectively. Good enough. Now we fill it in.

We know there are 100 senators total. This goes in the lower right box, or the T-T box. We also have been told that 5 senators are Catholic Democrats, which we then put in the upper left box, or the C-D box. Now we just fill in boxes till we get the middle box, or the NC-ND box. Every column's first two boxes add to the bottom box, and every row's first two boxes add to the rightmost box.

So if we look in the table we can see that there are 62 Democrats, and 38 Republicans, (or Not Democrats). This fills in the rightmost column. Since we know there are 62 Democrats and 5 Catholic Democrats, we can fill in the Not Catholic Democrat box with 57. If we look up the total Catholic Senators, we find that there are 12 total. Since there are 5 Catholic Democrats and 12 Catholics total, there must be 7 Catholic Not Democrats. Finally, since there are 7 Catholic Not Democrats and 38 total Not Democrats, there must be 31 Not Democrat Not Catholics. So the answer is D.
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I think the best way to solve this is a Venn diagram. Catholic+Democrats=5. Only Catholics = 12-5=7. Only democrats =62-5=57. So neither Catholic nor Democrat is 100 -(5+7+57)= 31.
Answer is D.

For anyone who finds the above confusing, note that they are noting the number of Catholic Senators and Democrat Senators in the Venn diagram (well, other user uses a table), so their technique works quite well.

still confusing !!!

The formula is as follows:

Total = n(Catholic) + n(Democrat) + neither - both

100 = (12-5) + (62-5) + neither - 5 -----------> neither = 41

where am I wrong?

As 5 are catholic democratic, republican democratic are 12-5=7

So, here we have to solve that, only republican who are neither democratic nor catholic
So, Answer is 38-7=31

we are looking for the # of neither democrats nor catholics and in other words, the # of republican, non catholics

using a table:

bolded means it's in the given, in parentheses we deduct from given

democrats | republicans | total
senator catholics. 5. | (12-5=7) | 12 (from table)
non senator cath (62-5=57). | (88-57=31) | (100-12=88)
total. 62 | (100-62=38) | =100 senators