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

This topic has expert replies
Legendary Member
Posts: 1223
Joined: Sat Feb 15, 2020 2:23 pm
Followed by:1 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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

Answer: E
Source: Official guide

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770
BTGModeratorVI wrote:
Thu Nov 05, 2020 7:56 am
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

Answer: E
Source: Official guide
Let D = the number of Democrats LAST YEAR
Let R = the number of Republicans LAST YEAR

Last year a state senate consisting of only Republican and Democrat members had 20 more Republican members than Democrat members
In other words: the number of Republicans = (the number of Democrats) + 20
In other words: R = D + 20

This year the senate has the same number of members as last year, but it has 2 fewer Republican members than last year.
So, R - 2 = the number of Republicans THIS YEAR

Important: Since the Senate still has the same number of members as last year, there must be 2 additional Democrats this year (to account for the fact there are 2 fewer Republicans).
So, D + 2 = the number of Democrats THIS YEAR

If this year the number of Republican members is 2/3 the number of senate members
Important: If Republicans account for 2/3 of the senate, then Democrats must account for the remaining 1/3 of senate. Since 2/3 is TWICE 1/3, we can say: (the number of Republicans this year) = 2(the number of Democrats this year).
In other words: R - 2 = 2(D + 2)
Expand the right side: R - 2 = 2D + 4
Add 2 to both sides to get: R = 2D + 6


How many members does the senate have this year?
We now have the following system:
R = D + 20
R = 2D + 6

Since both equations are set equal to R, we can write: D + 20 = 2D + 6
Solve to get: D = 14

To find the corresponding value of R, we can take: R = D + 20
Replace D with 14 to get: R = 14 + 20 = 34
So, R = 34

Since R + D = the total number of senators LAST YEAR, and since the Senate has the same number of members THIS YEAR, we can conclude that:
The total number of Senators THIS YEAR = R + D = 14 + 34 = 48

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7294
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members
BTGModeratorVI wrote:
Thu Nov 05, 2020 7:56 am
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

Answer: E
Source: Official guide
Solution:

We can let D = the number of Democrat senators last year; thus, D + 20 = the number of Republican senators last year, D + 2 = the number of Democrat senators this year, and D + 20 - 2 = D + 18 = the number of Republican senators this year. We can create an equation for this year as follows:

(D + 18) / (2D + 20) = 2/3

3(D + 18) = 2(2D + 20)

3D + 54 = 4D + 40

14 = D

Therefore, the total number of senators this year is 2(14) + 20 = 48.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage