Problem Solving

BTGmoderatorLU wrote:Source: GMAT Prep

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 OA is C.

Price by the end of the first week = 125% of x = 1.25x;
Price by the end of the second week = 80% of 1.25x = x

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorLU wrote:Source: GMAT Prep

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 OA is C.

Another approach is to test a "nice" value x
A great value would be $80 (since we get $100 after we increase $80 by 25%)

So, x = $80
In other words, the price of silver was $80 per ounce at the beginning of the two-week period.

During a two-week period, the price of an ounce of silver increased by 25 percent by the end of the first week. . . .
So, the price at the end of the first week = $80 + 25% of $80
= $80 + $20
= $100

. . . . and then decreased by 20 percent of this new price by the end of the second week.
So, the price at the end of the second week = $100 - 20% of $100
= $100 - $20
= $80

Hey, that's the value we started with (x = $80)
So, when we use x = $80 for the question, the resulting answer to the question is $80 (aka x)

Answer: C

Cheers,
Brent

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: C

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

BTGmoderatorLU wrote:Source: GMAT Prep

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

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

x * 1.25 * 0.8 = x

Answer: C