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The inflation index for the year 1989 relative to the year

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The inflation index for the year 1989 relative to the year  [#permalink]

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New post 26 Dec 2012, 03:34
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The inflation index for the year 1989 relative to the year 1970 was 3.56, indicating that, on the average, for each dollar spent in 1970 for goods, $3.56 had to be spent for the same goods in 1989. If the price of a Model K mixer increased precisely according to the inflation index, what was the price of the mixer in 1970 ?

(1) The price of the Model K mixer was $102.40 more in 1989 than in 1970.
(2) The price of the Model K mixer was $142.40 in 1989.
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Re: The inflation index for the year 1989 relative to the year  [#permalink]

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New post 26 Dec 2012, 03:38
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The inflation index for the year 1989 relative to the year 1970 was 3.56, indicating that, on the average, for each dollar spent in 1970 for goods, $3.56 had to be spent for the same goods in 1989. If the price of a Model K mixer increased precisely according to the inflation index, what was the price of the mixer in 1970 ?

Given that (price in 1989) = (price in 1970)*3.65.

(1) The price of the Model K mixer was $102.40 more in 1989 than in 1970 --> (price in 1989) = (price in 1970) + 102.4, We have two distinct linear equations with two unknowns, thus we can solve for both. Sufficient.

(2) The price of the Model K mixer was $142.40 in 1989 --> (price in 1989) = 142.4 --> (price in 1970) = (price in 1989)/3.65 = 142.4/3.65. Sufficient.

Answer: D.
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The inflation index for the year 1989 relative to the year  [#permalink]

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New post 03 Nov 2014, 21:29
S1 suggests proportion: 1/3.56=x/x+102.40, so we can easily find variable x. Sufficient

S2 suggests another proportion: 1/3.56=x/142.40, we can find x too. Sufficient

PS. Checking gives us x=40 in both statements, but we do not need counting value in this type of DS


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Re: The inflation index for the year 1989 relative to the year  [#permalink]

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New post 23 Nov 2014, 12:26
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Bunuel wrote:
Given that (price in 1989) = (price in 1970)*3.65.

(1) The price of the Model K mixer was $102.40 more in 1989 than in 1970 --> (price in 1989) = (price in 1970) + 102.4, We have two distinct linear equations with two unknowns, thus we can solve for both.Sufficient.

(2) The price of the Model K mixer was $142.40 in 1989 --> (price in 1989) = 142.4 --> (price in 1970) = (price in 1989)/3.65 = 142.4/3.65. Sufficient.

Answer: D.


Hi,
I didn't understand this part, is there any theory behind two distinct linear equation with two unknowns?
Please feel free to share any resources :)
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Re: The inflation index for the year 1989 relative to the year  [#permalink]

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New post 09 Dec 2015, 13:26
Let´s call
a = 1970
b = 1989

Given information
b/a = 3.56/1

Statement 1
b - a = 102.4
We have 2 different, linear equations. Therefore, we can solve. Sufficient.

Statement 2
b = 142.4
We have 2 different, linear equations. Therefore, we can solve. Sufficient.

OA = D
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Re: The inflation index for the year 1989 relative to the year  [#permalink]

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New post 19 May 2016, 06:53
Walkabout wrote:
The inflation index for the year 1989 relative to the year 1970 was 3.56, indicating that, on the average, for each dollar spent in 1970 for goods, $3.56 had to be spent for the same goods in 1989. If the price of a Model K mixer increased precisely according to the inflation index, what was the price of the mixer in 1970 ?

(1) The price of the Model K mixer was $102.40 more in 1989 than in 1970.
(2) The price of the Model K mixer was $142.40 in 1989.


Solution:

We are given that the inflation for the year 1989 relative to the year 1970 was 3.56, which means the price of an item in 1989 was 3.56 times the price of the same item in 1970. We are also given that the price of a Model K mixer increased according to the given inflation index, and from that we must determine the price of the mixer in 1970.

If we let x = the price of the Model K mixer in 1970, then the price of the Model K mixer in 1989 is 3.56x. Thus, we must determine the value of x.

Statement One Alone:

The price of the Model K mixer was $102.40 more in 1989 than in 1970.

Using the information in statement one, we can create the following equation:

3.56x = 102.40 + x

We see that we have enough information to determine the value of x. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

The price of the Model K mixer was $142.40 in 1989.

Using the information in statement two we can create the following equation:

3.56x = 142.40

We see that we have enough information to determine the value of x.

Answer: D
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Re: The inflation index for the year 1989 relative to the year  [#permalink]

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New post 08 Nov 2018, 10:14
Walkabout wrote:
The inflation index for the year 1989 relative to the year 1970 was 3.56, indicating that, on the average, for each dollar spent in 1970 for goods, $3.56 had to be spent for the same goods in 1989. If the price of a Model K mixer increased precisely according to the inflation index, what was the price of the mixer in 1970 ?

(1) The price of the Model K mixer was $102.40 more in 1989 than in 1970.
(2) The price of the Model K mixer was $142.40 in 1989.

\({{{\rm{pric}}{{\rm{e}}_{\,70}}} \over {{\rm{price}}{\,_{89}}}} = {1 \over {3.56}}\,\,\,\,\,\,\left( * \right)\)


\(?\,\, = {\rm{pric}}{{\rm{e}}_{\,70}}\)


\(\left( 1 \right)\,\,\,{\rm{pric}}{{\rm{e}}_{\,89}} - {\rm{pric}}{{\rm{e}}_{\,70}} = 102.40\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,3.56 \cdot {\rm{pric}}{{\rm{e}}_{\,70}} - {\rm{pric}}{{\rm{e}}_{\,70}} = 102.40\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.\,\)


\(\left( 2 \right)\,\,\,{\rm{pric}}{{\rm{e}}_{\,89}} = 142.40\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,3.56 \cdot {\rm{pric}}{{\rm{e}}_{\,70}}\, = 142.40\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\,\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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