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Updated on: 12 Apr 2026, 10:10
Originally posted by MartyMurray on 18 Jan 2026, 22:21.
Last edited by MartyMurray on 12 Apr 2026, 10:10, edited 3 times in total.
Last edited by MartyMurray on 12 Apr 2026, 10:10, edited 3 times in total.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
70% (02:49) correct
30%
(03:00)
wrong
based on 116
sessions
History
Date
Time
Result
Not Attempted Yet
In a house of representatives, twice as many representatives are focused on improving education as are focused on preserving the environment. If 40 percent are focused on both improving education and preserving the environment and 30 members are focused on neither, what is the minimum possible total number of representatives in the house?
(A) 100
(B) 130
(C) 150
(D) 160
(E) 190
Source: Marty Murray Coaching
(A) 100
(B) 130
(C) 150
(D) 160
(E) 190
Source: Marty Murray Coaching
19 Jan 2026, 05:56
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say total = 100x
total environment= p
total educ = 2p
both = 40x
neither = 30
only envirn= p - 40x
only edu = 2p - 40x
p-40x + 40x + 2p - 40x + 30 = 100x
3p + 30 = 140x
now we know that both has 40x and total environment has P
so the maximum people in both category will be 40x itself.
so p = 40x
we can use this into equ.
120x + 30 = 140x
x = 3/2
total = 100(3/2)
150
total environment= p
total educ = 2p
both = 40x
neither = 30
only envirn= p - 40x
only edu = 2p - 40x
p-40x + 40x + 2p - 40x + 30 = 100x
3p + 30 = 140x
now we know that both has 40x and total environment has P
so the maximum people in both category will be 40x itself.
so p = 40x
we can use this into equ.
120x + 30 = 140x
x = 3/2
total = 100(3/2)
150
MartyMurray
19 Jan 2026, 09:34
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I solved this somewhat differently. I used the Double Matrix method for two overlaping sets and used that to write the equation:
X-40+30=100-2x
Solving for X = total no. of people who support the environment. This number must be an integer.
The equation simplifies to x = 110/3, which itself isn't an integer quotient.
Reviewing the answer choices, answer 150 is the smallest amount that when multiplied by 1.10 gives a numerator divisible by 3.
So ANS = C.
X-40+30=100-2x
Solving for X = total no. of people who support the environment. This number must be an integer.
The equation simplifies to x = 110/3, which itself isn't an integer quotient.
Reviewing the answer choices, answer 150 is the smallest amount that when multiplied by 1.10 gives a numerator divisible by 3.
So ANS = C.
