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Bunuel
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The ratio of Democrats to Republicans in a certain state legislature 25 Dec 2020, 08:30
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5% (low)

Question Stats:

95% (01:01) correct 5% (01:46) wrong based on 63 sessions

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The ratio of Democrats to Republicans in a certain state legislature is 5:7. If the legislature has 156 members, all of whom are either Democrats or Republicans (but not both), what is the difference between the number of Republicans and the number of Democrats?

(A) 14
(B) 26
(C) 35
(D) 37
(E) 49
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B
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The ratio of Democrats to Republicans in a certain state legislature 25 Dec 2020, 09:42
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Bunuel
The ratio of Democrats to Republicans in a certain state legislature is 5:7. If the legislature has 156 members, all of whom are either Democrats or Republicans (but not both), what is the difference between the number of Republicans and the number of Democrats?

(A) 14
(B) 26
(C) 35
(D) 37
(E) 49
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Given: Ratio of Democrats to Republicans in a certain state legislature = 5:7.
Legislature has 156 members.
Democrats + Republicans = 12x = 156.
x = 13.
Democrats = 65, Republicans = 91.
Difference = 91-65 = 26.
Answer is B.
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The ratio of Democrats to Republicans in a certain state legislature 25 Dec 2020, 13:30
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D/R = 5/7, so 12*x= 156, x= 156/12 = 13

R-D= 2*x= 2*13= 26.

So, I think B. :)
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The ratio of Democrats to Republicans in a certain state legislature 26 Dec 2020, 20:13
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Considering, the ratio is an easier approach to solve such type of question.
Given, \(\frac{D}{R}=\frac{5}{7}\)

Also, \(D+R = 156 \)

\(=> 5+7-->156\)
\(=> 1-->13\)

\(7-5=2*13=26\)

Ans B
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The ratio of Democrats to Republicans in a certain state legislature 27 Dec 2020, 07:17
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Given

    • The ratio of Democrats to Republicans in a certain state legislature is 5:7.
    • The legislature has 156 members, all of whom are either Democrats or Republicans (but not both).


To Find

    • The difference between the number of Republicans and the number of Democrats.

Approach and Working Out


    • Democrats: Republican = 5: 7
      o The difference = 2 (7 – 2) out of 12 (7 + 5)

    • The answer = \(\frac{2}{12} \)× 156
      o = 26


Correct Answer: Option B
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