The price of a left-handed widget increased 20% in 1981 and 10% 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%
OA: E
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Can't find the correct solution for this one. Any help?
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GMATGuruNY
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Let the original price = 100.fambrini wrote:The price of a left-handed widget increased 20% in 1981 and 10% 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%
OA: E
After a 20% increase, the 1981 price = 100 + (20% of 100) = 100+20 = 120.
After a 10% increase, the 1982 price = 120 + (10% of 120) = 120+12 = 132.
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?
Percent decrease from 132 to 100 = (difference)/(larger) * 100 = (32/132) * 100 = (8/33) * 100 = 8 * (100/33) ≈ 8 * 3 = 24.
The correct answer is E.
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Let the original price = $100fambrini wrote:The price of a left-handed widget increased 20% in 1981 and 10% 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%
OA: E
The price increased 20% in 1981
20% of $100 = $20
So, the new price = $100 + $20 = $120
The price increased 10% in 1982
10% of $120 = $12
So, the new price = $120 + $12 = $132
To get back to the original $100, the latest price ($132) must be decreased by $32
$32/$132 ≈ 24.2%
Answer: E
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Jeff@TargetTestPrep
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fambrini wrote:The price of a left-handed widget increased 20% in 1981 and 10% 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%
OA: E
We can let the pre-1981 price of the widget = x.
Thus, after a 20% increase in price, in 1981, the new price is 1.2x.
After a 10% increase in price, in 1982, the new price is 1.1(1.2x) = 1.32x.
We need to determine by approximately what percentage would the price at the end of 1982 have to be decreased to restore the price of the widget to its pre-1981 price. We can create the following equation in which n = the percentage decrease.
(1.32x)(1 - n/100) = x
(1.32x)[(100-n)/100] = x
We can convert 1.32 to a fraction and cancel out the x's, so we have:
(132/100)[(100-n)/100] = 1
(100-n)/100 = 100/132
Cross-multiplying gives us:
132(100 - n) = 10,000
13,200 - 132n = 10,000
132n = 3200
n = 3200/132 ≈ 24
Answer:E
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Matt@VeritasPrep
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The easiest way for me:
x * (1.2) * (1.1) * (something) = x
x * (6/5) * (11/10) * (something) = x
Divide both sides by x:
6/5 * 11/10 * something = 1
Something = 1/(6/5 * 11/10)
Something = 1/(66/50) = 50/66 = 25/33
So we'd have to multiply by 25/33 to get back to the original price. 25/33 = 1 - 8/33, so our price would decrease by 8/33, or 24/99, or ≈ 24%.
x * (1.2) * (1.1) * (something) = x
x * (6/5) * (11/10) * (something) = x
Divide both sides by x:
6/5 * 11/10 * something = 1
Something = 1/(6/5 * 11/10)
Something = 1/(66/50) = 50/66 = 25/33
So we'd have to multiply by 25/33 to get back to the original price. 25/33 = 1 - 8/33, so our price would decrease by 8/33, or 24/99, or ≈ 24%.
