During a two-week period, the price of an ounce of silver increased by

SOLUTION

During a two-week period, the price of an ounce of silver increased by 25 percent by the end of the first week and then decreased by 20 percent of this new price by the end of the second week. If the price of silver was x dollars per ounce at the beginning of the two-week period, what was the price, in dollars per ounce, by the end of the period?

(A) 0.8x
(B) 0.95x
(C) x
(D) 1.05x
(E) 1.25x

The price by the end of the period = (x*1.25)*0.8 = x.

Answer: C.

Initial Price = x

25% increase\(= \frac{125x}{100}\)

20% decrease\(= \frac{125x}{100} * \frac{80}{100} = x\)

Answer = C

1 Week : (1.25)x
2nd Week : (0.80)(1.25)x
x
C

Alternate approach when two successive rate changes are given:
final change is =25+(-20)+ (25)(-20)/100 =0

Hence, no change in price after two week.

Hi All,

We're told that during a two-week period, the price of an ounce of silver INCREASED by 25 percent by the end of the first week and then DECREASED by 20 percent of this new price by the end of the second week. We're asked, if the price of silver was X dollars per ounce at the beginning of the two-week period, then what was the price, in dollars per ounce, by the end of the period. This question can be approached in a number of different ways; you might find it easiest to convert the percents to fractions and simplify the calculation all at once.

Starting value of an ounce of silver = X
After the 25% increase in price --> (5/4)(X)

The 20% decrease in price means that the value of the silver was 80% of the prior price...
After the 20% decrease of the new price --> (4/5)(5/4)(X)

The product of (4/5) and (5/4) is 20/20 = 1, so we're left with (1)(X) as the price at the end of the 2-week period.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

By the end of the 2-week period, the price was:

x * 1.25 * 0.8 = x

Answer: C

I've often seen the relationship of 25% and 20% being used on GMAT quant.

It's good to remember that if we increase the original value by 25% then we need to decrease the new value by 20% to get the original value.

Similarly, if we decrease the original value by 20% then we must increase the new value by 25% to get the original value

During the first week, the price of silver increased by 25 percent:
Price at the end of the first week = x + (25/100) * x = x + 0.25x = 1.25x

During the second week, the price of silver decreased by 20 percent of the new price:
Price at the end of the second week = 1.25x - (20/100) * 1.25x = 1.25x - 0.25x = 1x = x

Therefore, the price of silver per ounce by the end of the two-week period is x dollars, which corresponds to option (C) in the given choices.

Week 1 = 1.25 (X) - 25% Increase
Week 2 = 1.25 (X) - [1.25(X) * 0.2] (20 % Decrease) => 1.25 (X) - 0.25(X) => X

Price,in dollars per ounce, by the end of the period= X
Option (C).