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From January 1, 2002 to July 1, 2002, the median household

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From January 1, 2002 to July 1, 2002, the median household  [#permalink]

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New post Updated on: 03 Jul 2014, 08:01
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From January 1, 2002 to July 1, 2002, the median household income in Country X increased by 2%. What was the median household income in Country X on January 1, 2002?

(1) From July 1, 2001 to January 1, 2002, the median household income in Country X increased by 4%.

(2) From July 1, 2001 to January 1, 2002, the median household income in Country X increased by $1,020.

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Originally posted by Gnpth on 03 Jul 2014, 07:47.
Last edited by Bunuel on 03 Jul 2014, 08:01, edited 1 time in total.
Edited the question.
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Re: From January 1, 2002 to July 1, 2002, the median household  [#permalink]

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New post 03 Jul 2014, 08:16
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From January 1, 2002 to July 1, 2002, the median household income in Country X increased by 2%. What was the median household income in Country X on January 1, 2002?

{Medan July 1, 2001} = x.
{Medan January 1, 2002} = y.

We want to find y.

(1) From July 1, 2001 to January 1, 2002, the median household income in Country X increased by 4%.

y = 1.04x.

Not sufficient.

(2) From July 1, 2001 to January 1, 2002, the median household income in Country X increased by $1,020.

y = x + 1,020.

Not sufficient.

(1)+(2) We can solve y = 1.04x and y = x + 1,020, to find y. Sufficient.

Answer: C.

P.S. Info about July 1, 2002 is irrelevant.
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Re: From January 1, 2002 to July 1, 2002, the median household  [#permalink]

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New post 27 Nov 2018, 10:01
Let's denote each median income (M) by its timing, such that the two figures mentioned in the question stem are represented as MJan 02 and MJul 02. The stem tells us that MJul 02 = 1.02(MJan 02), but not much else, so move on to the statements.

Statement (1): insufficient. This tells us something about the ratio of M for July 2001 and January 2002 (MJul 01 x 1.04 =MJan 02 ), but it gives no actual numbers. Thus, we cannot determine the median income in January 2002. Eliminate (A) and (D).

Statement (2): insufficient. This tells us the dollar amount of the increase in M from July 2001 to January 2002 (MJan 02 = MJul 01 + $1,020), but without knowing the value of MJul 01, we can't find the value of MJan 02. Eliminate choice (B).

Statements (1) and (2): sufficient. Statement (2) gives us the dollar amount of the increase in M from July 01 to January 02, and statement (1) tells us that this amount represented a 4% increase. So $1,020 = 0.04(MJul 01); from here, you could solve for MJul 01, and add $1,020 to find MJan 02. The correct answer choice is (C)

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Re: From January 1, 2002 to July 1, 2002, the median household   [#permalink] 27 Nov 2018, 10:01
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