SAT Math : SAT Mathematics
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Example Questions
Example Question #4 : Percent Of Change
A stock for YUM was trading at 
We will use the formula 
compute the terms in the parentheses:
If we rewrite the term in parentheses to match the form of the original formula, we can find the rate without having to do extra computation.
So, the rate is a decrease by 0.784%, which we round to 0.8%
Example Question #4 : Percent Of Change
A circle has its radius increased by 
Cannot be determined with the information given.
If we use r to denote the original radius of the circle, then according to the formula:
the new radius R, is given by
Therefore, the new area is:
Or
Since (pi)r2 is the area of the original circle, the rate of the increase is 21%
Example Question #3 : Percent Of Change
At a certain store, prices for all items were assigned in January. Each month after that, the price was 20% less than the price the previous month. If the price of an item was x dollars in January, approximately what was the price in dollars of the item in June?
0.12x
0.81x
0.66x
0.51x
0.33x
0.33x
The question tells us that the price in January was x. To find the price in February, we decrease the price of x by 20%, which is the same as taking 80% of x. (In general, a P% decrease of a number is the same as (100 – P)% times that number). Continue to take 0.8 times the previous month's price to find the next month's price until we have the price for June, as follows:
January Price: x
February Price: 0.8 * January Price = 0.8x
March Price: 0.8 * February Price = 0.8 * 0.8x = 0.82 * x
April Price: 0.8 * March Price = 0.8 * 0.8 * 0.8x = 0.83 * x
May Price: 0.8 * April Price = 0.8 * 0.8 * 0.8 * 0.8x = 0.84 * x
June Price: 0.8 * May Price = 0.8 * 0.8 * 0.8 * 0.8 * 0.8x = 0.85 * x; therefore, the price in June was 0.85 ≈ 0.328 ≈ 0.33 times the original price.
Example Question #1993 : Psat Mathematics
The sale of a tablet decreased from $500 to $450. By what percentage did the cost decrease?
20%
1%
15%
5%
10%
10%
Set up the following ratio
50/500 = n/100
The cost of the tablet decreased by $50. The original cost is $500; therefore, 50 is the numerator and 500 is the denominator on the left side of the ratio.
Since a percentage is a part of a whole, n symbolizes the the percentage decrease.
To solve for n, you can cross multiply. So, 50(100) = n(500).
n = 10%
Example Question #1994 : Psat Mathematics
On Monday, the price of a shirt costs x dollars. On Tuesday, the manager puts the shirt on sale for 10% off Monday's price. On Wednesday, the manager increases the price of the shirt by 10% of Tuesday's price. Describe the change in price from Monday to Wednesday.
1% decrease
10% increase
1% increase
10% decrease
No change
1% decrease
To find the cost on Tuesday, take 10% off Monday's price. In other words, find 90% of Monday's price. This is simply 0.9x. If we are to now add 10% of this value back onto itself to find Wednesday's price, we want 100% + 10%, or 110% of 0.9x.
1.1(0.9x) = 0.99x
This value is 1% smaller than x.
Example Question #1 : How To Find The Percent Of Decrease
If the length of a rectangle is increased by thirty percent, which of the following most closely approximates the percent by which the rectangle's width must decrease, so that the area of the rectangle remains unchanged?
21
30
25
23
17
23
Example Question #1996 : Psat Mathematics
If the price of a TV was decreased from $3,000 to $1,800, by what percent was the price decreased?
50%
20%
40%
60%
30%
40%
The price was lowered by $1,200 which is 40% of $3,000.
Example Question #1997 : Psat Mathematics
If a rectangle's length decreases by fifteen percent, and its width decreases by twenty percent, then by what percent does the rectangle's area decrease?
36
35
40
32
45
32
Let's call the original length and width of the rectangle 
The initial area, 
Next, let 
We are asked to find the change in the area, which essentially means we want to compare 
First, we are told that the length is decreased by fifteen percent. We can think of the full length as 100% of the length. If we take away fifteen percent, we are left with 100 – 15, or 85% of the length. In other words, the final length is 85% of the original length. We can represent 85% as a decimal by moving the decimal two places to the left.
Similarly, if we decrease the width by 20%, we are only left with 80% of the width.
We can now express the final area in terms of 
Lastly, let's apply the formula for percent of change, which will equal the change in the area divided by the original area. The change in the area is equal to the final area minus the original area.
percent change = 
=
=
The negative sign indicates that the rectangle's area decreased. The change in the area was a decrease of 32%.
The answer is 32.
Example Question #1998 : Psat Mathematics
The cost of a load of laundry is reduced by 
The original reduction brings the total to 
Example Question #1 : Percent Of Change
The cost of a shirt in January is 
We must know the original cost to find the answer
The best way to answer this question is to plug in a number for n. Since you are working with percentages, it may be easiest to use 100 for n.
We know that in the month of February, the cost of this shirt was decreased by 10%. Because 10% of 100 is $10, the new cost of the shirt is $90.
In March, the cost of the shirt decreased another 10%. 10% of 90 is 9, so the cost of the shirt is now $81.
To find the total percentage decrease, you must divide 81 by 100 and subtract it from 1.
1 – (81/100) = 1 – 0.81 = 0.19
The total decrease was 19%.
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