GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
For the positive integers a, b, c, and d, a is half of b, wh
[#permalink]
23 Jun 2018, 12:24
23 Jun 2018, 12:24
1
Expert Reply
2
Bookmarks
00:00
Question Stats:
50% (01:40) correct
49% (02:02) wrong based on 110 sessions
Hide Show timer Statistics
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
[#permalink]
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
[#permalink]
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
