A total of 774 doctorates in mathematics were granted to United States

We know that the doctorates granted went down from 1972-1973 school year to the 1986-1987 school year.
In terms of variable, it went down from W to w.

We are asked about the decrease. => \(\frac{W-w}{W}*100\).

The numbers 774 and 362 are distractions which have no role in the question. So statement 2 is not sufficient.

(1) \(\frac{1}{10} < \frac{W}{774} < \frac{1}{9}\)

\(\frac{1}{10}=\frac{77.4}{774} < \frac{W}{774} < \frac{1}{9}=\frac{86}{774}\)

So W can be any value from 78 to 85, both inclusive.
Nothing about w.
Insufficient

(2) W = w + 5
W-w=5, but we require value of W in \(\frac{W-w}{W}*100\).

Is \(\frac{W-w}{W}*100<10.......\frac{5}{W}<\frac{1}{10}.......W>50\).

So using statement II, we will have answer yes if W>50, otherwise No.
But we do not know the exact value of W.
Insufficient


Combined
From statement II, the answer will be yes if W>50, and statement I gives range of W greater than 50.
So answer is always yes.
Sufficient

C

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