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# At the beginning of the year, an item had a price of A. At the end of

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Manager
Joined: 12 Jan 2019
Posts: 121
At the beginning of the year, an item had a price of A. At the end of  [#permalink]

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05 Apr 2019, 02:54
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25% (medium)

Question Stats:

76% (02:21) correct 24% (02:24) wrong based on 21 sessions

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At the beginning of the year, an item had a price of A. At the end of January, the price was increased by 60%. At the end of February, the new price was decreased by 60%. At the end of March, the new price was increased by 60%. At the end of April, the new price was decreased by 60%. On May 1st, the final price was approximately what percent of A?

(A) 41%

(B) 64%

(C) 100%

(D) 136%

(E) 159%
Manager
Joined: 12 Jan 2019
Posts: 121
Re: At the beginning of the year, an item had a price of A. At the end of  [#permalink]

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05 Apr 2019, 02:54
The trap answer is 100%: a percent increase and percent decrease by the same percent do not cancel out.

Let’s say that the A = \$100 at the beginning of the year.

End of January, 60% increase. New price = \$160

End of February, 60% decrease: that’s a decrease of 60% of \$160, so that only 40% of \$160 is left.

10% of \$160 = \$16

40% of \$160 = 4(16) = \$64

That’s the price at the end of February.

End of March, a 60% increase: that’s a increase of 60% of \$64.

10% of \$64 = \$6.40

60% of \$64 = 6(6 + .40) = 36 + 2.4 = \$38.40

Add that to the starting amount, \$64:

New price = \$64 + \$38.40 = \$102.40

End of April, 60% decrease: that’s a decrease of 60% of \$102.40, so that only 40% of \$102.40 is left.

At this point, we are going to approximate a bit. Approximate \$102.40 as \$100, so 40% of that would be \$40. The final price will be slightly more than \$40.

Well, what is slightly more than \$40, as a percent of the beginning of the year price of \$100? That would be slightly more than 40%.

Re: At the beginning of the year, an item had a price of A. At the end of   [#permalink] 05 Apr 2019, 02:54
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