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

Question

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%

(A) 40% 
(B) 35%
(C) 30%
(D) 26%
(E) 24%

pushpitkc · Answer

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)

Hatakekakashi · Answer

100 - 120 - 132

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

(E) imo

chetna14 · Answer

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

rocko911 · Answer

Hi ,

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

Change / original

then why u used 132 as original and not 100?

KeySky22 · Answer

(last-previous)/previous. Here, 132 is previous

Sent from my iPhone using  GMAT Club Forum mobile app

Sash143 · Answer

Its E. 
Pre-1981 = 100
1981 = 120  
1982 = 132

% decrease from 1982 to Pre-1981 =  \frac{100 - 132}{132} 
 = 32/132 ~ a little < 1/4
 ~ 24 %

Wongderful · Answer

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%

ScottTargetTestPrep · Answer

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

luisdicampo · Answer

Deconstructing the Question

The price increased  20% in 1981  and then  10% in 1982 . 
We must find the percent decrease needed to return to the original price.

Step-by-step

Let the original price be:

100

After 20% increase:

100 	imes 1.20 = 120

After 10% increase:

120 	imes 1.10 = 132

Required decrease to return to 100:

132 - 100 = 32

Percent decrease relative to current price:

\frac{32}{132} \approx 0.242 \approx 24\%

Answer: 24%

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

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