Last year a state senate consisting of only Republican and Democrat members had 20 more Republican members than

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Last year a state senate consisting of only Republican and Democrat members had 20 more Republican members than Democrat members. This year the senate has the same number of members as last year, but it has 2 fewer Republican members than last year. If this year the number of Republican members is 2/3 the number of senate members, how many members does the senate have this year?

(A) 33
(B) 36
(C) 42
(D) 45
(E) 48


OA E

Source: Official Guide

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BTGmoderatorDC wrote:
Tue Jun 30, 2020 7:25 pm
Last year a state senate consisting of only Republican and Democrat members had 20 more Republican members than Democrat members. This year the senate has the same number of members as last year, but it has 2 fewer Republican members than last year. If this year the number of Republican members is 2/3 the number of senate members, how many members does the senate have this year?

(A) 33
(B) 36
(C) 42
(D) 45
(E) 48

OA E

Source: Official Guide
Say, last year, there were R no. of republicans and D no. of Democrats, so the total no. of members = R + D.

Also, we know that R = D + 2 ---(1)

Given that this year, the no. of members is the same as that in the last year, so, this year, the no.of members = (R + D)

Also, we know that No. of republicans = R – 2, so the no. of Democrats = D + 2.

Also, it is given that R – 2 = 2/3 of (R + D)

From equation (1), we get

R – 2 = 2/3 of (R + D)
D + 20 – 2 = 2/3 of (D + 20 + D)

D = 14 and R = 34, so R + D = 14 + 34 = 48

Correct answer: E

Hope this helps!

-Jay
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