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# For the positive integers a, b, c, and d, a is half of b, wh

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Retired Moderator
Joined: 07 Jun 2014
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GRE 1: Q167 V156
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For the positive integers a, b, c, and d, a is half of b, wh [#permalink]  23 Jun 2018, 12:24
Expert's post
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Question Stats:

44% (01:23) correct 55% (01:56) wrong based on 61 sessions
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.

 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.
[Reveal] Spoiler: OA

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Sandy
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VP
Joined: 20 Apr 2016
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Re: For the positive integers a, b, c, and d, a is half of b, wh [#permalink]  23 Jun 2018, 12:37
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KUDOS
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.

 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
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Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3037 [0], given: 394

Re: For the positive integers a, b, c, and d, a is half of b, wh [#permalink]  18 Jul 2018, 07:07
Expert's post
Explanation

The following relationships are given: $$a =\frac{b}{2}$$, $$b = \frac{c}{3}$$ , and d = 3c. Pick one variable and put everything in terms of that variable. For instance, variable a:
b = 2a
c = 3b = 3(2a) = 6a
d = 3c = 3(6a) = 18a

Substitute into the quantities and simplify.

Quantity A: $$\frac{a+b}{c}=\frac{a+2a}{6a}=\frac{1}{2}$$

Quantity B: $$\frac{a+b+c}{d}=\frac{a+2a+6a}{18a}=\frac{1}{2}$$.

The two quantities are equal.
_________________

Sandy
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Re: For the positive integers a, b, c, and d, a is half of b, wh   [#permalink] 18 Jul 2018, 07:07
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