In 1984 a certain union had a total of 15,600 members. . . .

[VJesus12]

In 1984 a certain union had a total of 15,600 members. Was the percent increase in the total number of members in the union from 1984 to 1985 greater than that from 1985 to 1986 ?

(1) From 1984 to 1985 the total number of members in the union increased by 781, and from 1985 to 1986 the total number of members in the union again increased by 781.

(2) In 1985 the union had a total of 16,381 members, and in 1986 the union had a total of 17,162 members.

The OA is D.

Experts, I don't know why statement (1) is sufficient. May you help me?

[ErikaPrepScholar]

Hey VJesus12,

Let's go ahead and write down what we know from statement 1:

1984 -- 15,600 members
+781 members
1985 -- ? members
+781 members
1986 -- ? members

Using this information we could go ahead and calculate that in 1985, there were 15,600 + 781 members and that in 1986, there were 15,600 + 781 + 781 members. Then we could find the percent increase for each set of years with the equation $$\frac{change}{initial\ value}$$ .

HOWEVER, we don't need to do that! We know that change = 781 for both sets of years. However, we know that the initial value is smaller in 1984 (15,600) than in 1985 (15,600 + 781). So the change is a larger percent of the initial value in 1984 than of the initial value in 1985. So we know that the union increased by a greater percent in 1984 than it did in 1985, making Statement 1 sufficient.

Let me know if you'd like me to break this down in more detail!