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For the positive integers a, b, c, and d, a is half of b, wh
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23 Jun 2018, 12:24
23 Jun 2018, 12:24
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50% (01:36) correct
49% (02:05) wrong based on 104 sessions
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For the positive integers a, b, c, and d, a is half of b, which is one-third of c. The value of d is three times the value of c.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(\frac{a+b}{c}\) |
\(\frac{a+b+c}{d}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
For the positive integers a, b, c, and d, a is half of b, wh
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13 Jan 2024, 00:15
13 Jan 2024, 00:15
2
We are given
\(a=\frac{1}{2}b\)
\(b=\frac{1}{3}c\)
\(d = 3c\)
Expressing all variables in terms of \(a\)
\(a=\frac{1}{2}b => b=2a\)
\(\underline{b=2a}\)
\(b=\frac{1}{3}c => c=3b\)
\(c=3b=3(2a)=6a\)
\(\underline{c=6a}\)
\(d=3c\)
\(d=3c=3(6a)=18a\)
\(\underline{d=18a}\)
Now, we insert the values into both quantities
\(\text{Quantity A} = \dfrac{a+b}{c} = \dfrac{a+2a}{6a} = \dfrac{3a}{6a} = \dfrac{3}{6}=\dfrac{1}{2}\)
\(\text{Quantity B} = \dfrac{a+b+c}{d} = \dfrac{a+2a+6a}{18a} = \dfrac{9a}{18a} = \dfrac{9}{18} = \dfrac{1}{2}\)
BOTH quantities are EQUAL.
Answer is C.
\(a=\frac{1}{2}b\)
\(b=\frac{1}{3}c\)
\(d = 3c\)
Expressing all variables in terms of \(a\)
\(a=\frac{1}{2}b => b=2a\)
\(\underline{b=2a}\)
\(b=\frac{1}{3}c => c=3b\)
\(c=3b=3(2a)=6a\)
\(\underline{c=6a}\)
\(d=3c\)
\(d=3c=3(6a)=18a\)
\(\underline{d=18a}\)
Now, we insert the values into both quantities
\(\text{Quantity A} = \dfrac{a+b}{c} = \dfrac{a+2a}{6a} = \dfrac{3a}{6a} = \dfrac{3}{6}=\dfrac{1}{2}\)
\(\text{Quantity B} = \dfrac{a+b+c}{d} = \dfrac{a+2a+6a}{18a} = \dfrac{9a}{18a} = \dfrac{9}{18} = \dfrac{1}{2}\)
BOTH quantities are EQUAL.
Answer is C.
General Discussion
Re: For the positive integers a, b, c, and d, a is half of b, wh
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23 Jun 2018, 12:37
23 Jun 2018, 12:37
1
sandy wrote:
For the positive integers a, b, c, and d, a is half of b, which is one-third of c. The value of d is three times the value of c.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(\frac{a+b}{c}\) |
\(\frac{a+b+c}{d}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
As per the statement
Let b= 4 so that a= 2 , c = 12 and d=36
Therefore for statement 1 we have=
\(\frac{6}{12} = \frac{1}{2}\)
For statement 2 we have
\(\frac{18}{36} = \frac{1}{2}\)
So option C
