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1960 x
1975 2x
1985 Y

what is x

1) Y= 2*2x does not answer x
2) Y -2x = 4.5 can not solve for x

but with 1 and 2 to gather

4x = 4.5 +2x

Both togather are sufficient!
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1960 = x
1975 = 2x
1984 = y

St1: y = 4x. Can not find out x. So INSUFF

St2: y = 2x+4.5. Can not find out x. So INSUFF

Combined: two variables and two equations. Solve for x

4x = 2x + 4.5
x = 2.25
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so the translation of the second statement is x+x+4.5?
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From May 1, 1960, to May 1, 1975, the closing price of a share of stock X doubled. What was the closing price of a share of stock X on May 1, 1960?

(1) From May 1, 1975 to May 1, 1984, the closing price of a share of stock X doubled.
(2) From May 1, 1975 to May 1, 1984, the closing price of a share of stock X increased by $4.50

so the translation of the second statement is x+x+4.5?

Yes. If we assume that the price in 1960 was $x, then the price in 1975 would be $2x. From (2) the price in 1984 was 2x+4.5.
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