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The price of the item in January 2007 was k, which is a 15% increase

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The price of the item in January 2007 was k, which is a 15% increase [#permalink] New post   08 Apr 2021, 20:12
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The price of the item in January 2007 was \(K\), which is a 15% increase from the price of the same item in January 2006.

Quantity A
Quantity B
Price of the item in January 2006
\(0.85K\)


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.
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The price of the item in January 2007 was k, which is a 15% increase [#permalink] New post   09 Apr 2021, 02:37
Quote:
K, which is a 15% increase from the price of the same item in January 2006

If price of the item in Jan 2006 is S, then K = 1.15 S

We have to compare S and 0.85K.
Therefore, let's convert S into K.
\(S = \frac{K}{1.15}\)

\(S = K * \frac{100 }{ 115} \)

\(S = K * \frac{20 }{ 23}\)

\(0.85 * K = \frac{85 }{ 100} * K = \frac{17 }{ 20 }* K\)

To compare fractions \(\frac{20}{23}, and \frac{17 }{ 20}\), cross-multiply.

\(20 * 20 > 17 * 20\)
So, \(\frac{20 }{ 23} * K > \frac{17 }{ 20} * K\)

or S > 0.85 K

Hence, A is the correct answer.
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Re: The price of the item in January 2007 was k, which is a 15% increase [#permalink] New post   09 Apr 2021, 23:10
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Let the price in 2006 be 100

So, the price in 2007 will 15/100*100 = 15
100+15= 115
So K will be 115

Quantity A = 100

Quantity B = 0.85K
0.85*115= 97.75


Hence Quantity A > Quantity B
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Re: The price of the item in January 2007 was k, which is a 15% increase [#permalink] New post   26 May 2022, 10:45
Let the price in 2006 be x

K=x+0.15x=1.15x
x=0.8696K

If we assume the price in 2006 x=100, then K=115

87% > 85%

Answer is (A)
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Re: The price of the item in January 2007 was k, which is a 15% increase [#permalink] New post   20 Nov 2023, 18:47
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The price of the item in January 2007 was k, which is a 15% increase [#permalink]
20 Nov 2023, 18:47
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