Many graduate schools require applicants to take a certain test. Those taking the test receive three scores:
a verbal reasoning score,
a quantitative reasoning score,
an analytical writing score.
Let average verbal reasoning score represent by v
Let average quantitative reasoning score represent by q
Let average analytical writing score represent by a
In 2013, the average quantitative reasoning score exceeded the average verbal reasoning score by 1.3 points
i.e.,
Average quantitative reasoning score - average verbal reasoning = 1.3
q - v = 1.3 ...(1)
The average verbal reasoning score exceeded the analytical writing score by 150.5 points.
i.e.,
Average Reasoning score - average analytical writing = 150.5
v - a = 150.5 ...(2)
The sum of the three average scores was 305.9.
i.e.,
v + q + a = 305.9 ...(3)
Simplify the equation (1), (2) and (3) to get the value of q,v and a;
Add equation (1) and (2)
(q-v) + (v-a) = 1.3 + 150.5
q + a = 151.8 ....(4)
Substitute the value of (q+a=151.8) in the equation (3);
v + q + a = 305.9
v + 151.8 = 305.9
v = 305.9 - 151.8
v = 154.1
Substitute the value of v = 154.1 in the equation (2);
v - a = 150.5
154.1 -a = 150.5
a = 154.1 - 150.5
a = 3.6
Now, substitute the value of a = 3.6 in the equation (4)
q + a = 151.8
q + 3.6 = 151.8
q = 151.8 - 3.6
q = 148.2
Answer :
The average verbal reasoning score was 154.1
The average quantitative reasoning score was 148.2
The average analytical writing score was 3.6