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The price of a left-handed widget increased 20 percent in 1981 and 10

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The price of a left-handed widget increased 20 percent in 1981 and 10  [#permalink]

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New post 22 Feb 2018, 20:53
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E

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  45% (medium)

Question Stats:

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The price of a left-handed widget increased 20 percent in 1981 and 10 percent in 1982. By approximately what percent would the price at the end of 1982 have to be decreased to restore the price of the widget to its pre-1981 price?

(A) 40%

(B) 35%

(C) 30%

(D) 26%

(E) 24%
Spoiler: OA

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The price of a left-handed widget increased 20 percent in 1981 and 10  [#permalink]

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New post 22 Feb 2018, 21:50
Bunuel wrote:
The price of a left-handed widget increased 20 percent in 1981 and 10 percent in 1982. By approximately what percent would the price at the end of 1982 have to be decreased to restore the price of the widget to its pre-1981 price?

(A) 40%

(B) 35%

(C) 30%

(D) 26%

(E) 24%


Assume the price of the left-handed widget to be $100 before 1981.

In 1981 the price went up by 20% and the price went up by 20% in 1982
The cost of the left-handed widget in 1982 is 1.1*(1.2(100)) = $132

In order to restore the price to its pre-1981 price, we would need to
bring down the cost of $32, which is a decrease of \(\frac{32}{132}*100 = \frac{3200}{132} = 24\)%(Option E)
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Re: The price of a left-handed widget increased 20 percent in 1981 and 10  [#permalink]

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New post 23 Feb 2018, 02:09
Bunuel wrote:
The price of a left-handed widget increased 20 percent in 1981 and 10 percent in 1982. By approximately what percent would the price at the end of 1982 have to be decreased to restore the price of the widget to its pre-1981 price?

(A) 40%

(B) 35%

(C) 30%

(D) 26%

(E) 24%


100 - 120 - 132

now 132 must decrease to 100 = 32/132 x 100 = 24%

(E) imo
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Re: The price of a left-handed widget increased 20 percent in 1981 and 10  [#permalink]

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New post 23 Feb 2018, 16:57
lets say the price was 100 pre-1981

< 1981 1981 1982

100 120 132


to bring back to original <1981 price

% decrease = \(\frac{{change}}{{original value}}\) * 100

= \(\frac{32}{132}\) * 100
=> \(< \frac{1}{4}\) *100
=> < 25%

IMO E
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Re: The price of a left-handed widget increased 20 percent in 1981 and 10  [#permalink]

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New post 24 Feb 2018, 02:11
pushpitkc wrote:
Bunuel wrote:
The price of a left-handed widget increased 20 percent in 1981 and 10 percent in 1982. By approximately what percent would the price at the end of 1982 have to be decreased to restore the price of the widget to its pre-1981 price?

(A) 40%

(B) 35%

(C) 30%

(D) 26%

(E) 24%


Assume the price of the left-handed widget to be $100 before 1981.

In 1981 the price went up by 20% and the price went up by 20% in 1982
The cost of the left-handed widget in 1982 is 1.1*(1.2(100)) = $132

In order to restore the price to its pre-1981 price, we would need to
bring down the cost of $32, which is a decrease of \(\frac{32}{132}*100 = \frac{3200}{132} = 24\)%(Option E)


Hi ,

If u have used the formula of percent decrease i.e

Change / original

then why u used 132 as original and not 100?
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Re: The price of a left-handed widget increased 20 percent in 1981 and 10  [#permalink]

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New post 26 Feb 2018, 15:38
rocko911 wrote:
pushpitkc wrote:
Bunuel wrote:
The price of a left-handed widget increased 20 percent in 1981 and 10 percent in 1982. By approximately what percent would the price at the end of 1982 have to be decreased to restore the price of the widget to its pre-1981 price?

(A) 40%

(B) 35%

(C) 30%

(D) 26%

(E) 24%


Assume the price of the left-handed widget to be $100 before 1981.

In 1981 the price went up by 20% and the price went up by 20% in 1982
The cost of the left-handed widget in 1982 is 1.1*(1.2(100)) = $132

In order to restore the price to its pre-1981 price, we would need to
bring down the cost of $32, which is a decrease of \(\frac{32}{132}*100 = \frac{3200}{132} = 24\)%(Option E)


Hi ,

If u have used the formula of percent decrease i.e

Change / original

then why u used 132 as original and not 100?
(last-previous)/previous. Here, 132 is previous


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Re: The price of a left-handed widget increased 20 percent in 1981 and 10  [#permalink]

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New post 27 Feb 2018, 03:48
Bunuel wrote:
The price of a left-handed widget increased 20 percent in 1981 and 10 percent in 1982. By approximately what percent would the price at the end of 1982 have to be decreased to restore the price of the widget to its pre-1981 price?

(A) 40%

(B) 35%

(C) 30%

(D) 26%

(E) 24%


Its E.
Pre-1981 = 100
1981 = 120 [20 % increase]
1982 = 132 [10 % increase]

% decrease from 1982 to Pre-1981 = \(\frac{100 - 132}{132}\)
= 32/132 ~ a little < 1/4
~ 24 %
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Re: The price of a left-handed widget increased 20 percent in 1981 and 10  [#permalink]

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New post 27 Feb 2018, 04:06
I find that throwing in some smart numbers will be helpful.

Pre-1981 = $100
1981 = $100 x 1.2 = $120
1982 = $120 x 1.1 = $132

In order to return to $100,

\(\frac{132-100}{132}*100 = \frac{32}{132}*100 = approx \frac{30}{130}*100 =\) approx 23%

Nearest is (E) 24%
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Re: The price of a left-handed widget increased 20 percent in 1981 and 10  [#permalink]

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New post 28 Feb 2018, 11:10
Bunuel wrote:
The price of a left-handed widget increased 20 percent in 1981 and 10 percent in 1982. By approximately what percent would the price at the end of 1982 have to be decreased to restore the price of the widget to its pre-1981 price?

(A) 40%

(B) 35%

(C) 30%

(D) 26%

(E) 24%


We can let the original price = 100.

After the two increases the new price would be 1.2 x 1.1 x 100 = 132. We can let n = the percent decrease and create the equation:

(100 - n)/100 x 132 = 100

13,200 - 132n = 10,000

3,200 = 132n

24 ≈ n

Answer: E
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Re: The price of a left-handed widget increased 20 percent in 1981 and 10   [#permalink] 28 Feb 2018, 11:10
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