<p>A reservoir is at full capacity at the beginning of summer. By the first day of fall, the level in the reservoir is 30 percent below full capacity. Then during the fall, a period of heavy rains increases the level by 30 percent. After the rains, the reservoir is at what percent of its full capacity
Can somebody give an explanation for the Answer this is from Kaplan sat book, thanks!</p>
<p>91 percent i assume, first of all it says the reservoir is at its full capacity which is 100 percent then its level decreased by 30 percent so the new level is 70 percent then it increased by 30 percent which is (1.30 * .70 =.91)</p>
<p>Why did we multiply by 1.30 rather than .3 of 70 and then adding it ?? That’s why I posted this question… Thanks… Both ways are right but I just wanna know where did u get 1.3 from! Thanks.</p>
<p>^Because there is a 30 percent increase.</p>
<p>You can do it that way too:</p>
<p>0.3 * .7 = .21. Add that to 70% (.7) to get the total after the rain. Same number: .91.</p>
<p>I edit it the way I do it which is .3*70 and then adding it to 70 that’s gonna give me 91 but do we Add 1 when it’s an increase and then subtract 1 when it’s a decrease or what??
@PusatShrade. @SAT97TAKER. </p>
<p>@Student3500</p>
<p>If a quantity x is increased by 30% then that is equivalent to adding 30% of x (same as 0.3x) and adding it to the original which is x, or x+0.3x=1.3x. In other words after the 30% increase, the quantity x is 130% of x or 1.3x. It is really important to learn this because it can save you time. </p>
<p>Now when we decrease this same quantity 1.3x by 30%, we first compute 30% of 1.3x which is 0.39x and subtract this from 1.3x and is equal to 1.3x-0.39x or 0.91x. However, this would be equivalent to taking 70% of the quantity 1.3x or 0.7(1.3x)=0.91x. </p>
<p>What this means is that an increase of 30% followed by a decrease of 30% is equivalent to a single decrease of 9%. This type of language is common on the SAT. </p>
<p>Once you become comfortable with these operations, then it is easy to do this question in one shot:
An increase of 30% gives a multiplier of 1.3 and a decrease of 30% gives a multiplier of 0.7, therefore the final quantity is equal to a multiplier of (1.3)(0.7)=0.91 or 91% of the original. </p>
<p>Finally, one can also do this problem by assuming the initial quantity to be equal to 100, and that makes this question easy. However, there are cases on the SAT where one needs to know the underlying algebra. </p>
<p>I have attached one such difficult problem from the Official SAT question. Please see the attached image below:
[Percent</a> Question from Official SAT](<a href=“http://www.screencast.com/t/gihAsR7riia"]Percent”>http://www.screencast.com/t/gihAsR7riia)</p>
<p>Cheers</p>
<p>^Answer is A. Was that the last question of a 16-question section</p>
<p>@SATQuantum thanks ur answer really helped me and for the question u put for me i A because it’s the closest answer but the thing that I wasn’t sure of is why did they put a 1- t/100 isn’t it supposed to be multiplied only by t/100 like why is it subtracted by one first, thanks so much</p>
<p>@Student3500 -</p>
<p>Is it possible that you are having a vocabulary issue rather than a math issue? Suppose something costs $100. If the price is reduced “to” 30%, then the new price is $30. But if the price is reduced “BY” 30% then the new price is $100 - $30 = $70. That’s where the (1-t/100) you were asking about comes from.</p>
<p>Yes, the answer is indeed A. This is the last question from one of the math sections in an official SAT test.</p>
<p>@Student3500
The initial price of the book was b dollars, this was discounted or reduced by x percent. This means the discount was (x/100)b and this would then needs to be subtracted from the initial price of x dollars. In other words the price after the first discount is equal to b - (x/100)b, which on factoring is equivalent to b[1 - (x/100)]. This is exactly what we did in the original problem where if something is decreased by 30% then we can write as b[1-(30/100)] = b[1-0.3]=b(0.7) or 70% of the original. </p>
<p>In general, one should be able to do the following operations quickly:</p>
<p>1) A quantity x is increased by 40%, what is the new quantity? 1.4x
2) A quantity x is decreased by 20%, what is the new quantity? 0.8x
3) A quantity x is decreased by p%, what is the new quantity? x[1 - (p/100)]
4) A price x is first increased by p%, then this new price is decreased by q%, what is the new quantity?
x[1 + (p/100)][1 - (q/100)]</p>
<p>Here is another percentage question, Level 4, from an old SAT test. </p>
<p>[Percentage:</a> Level 4 Question](<a href=“http://www.screencast.com/t/skJCGWPho8m"]Percentage:”>http://www.screencast.com/t/skJCGWPho8m)</p>
<p>Cheers</p>
<p>^B right?</p>
<p>Yes, it is B indeed.</p>
<p>@SATQuantum can u give me the link for a lot more sat math questions like these… Thanks man !!</p>
<p>@Student3500</p>
<p>Here are some official SAT questions on percents. Enjoy.</p>
<p>Question#1: If x and y are positive, which of the following represents x percent of y?
A) 0.01xy
B) 0.1xy
C) xy
D) 10xy
E) 100xy </p>
<p>Question#2: The price of a telephone was first increased by 10 percent and then the new price was decreased by 25 percent. The final price was what percent of the initial price?
A) 78%
B) 80%
C) 82.5%
D) 85%
E) 87.5%</p>
<p>Question#3: What is the least possible integer for which 20 percent of that integer is greater than 1.2 ?
A) 2
B) 3
C) 4
D) 6
E) 7</p>
<p>Question#4: If n is positive and 50/n equals n percent of 50, what is the value of n ?
A) 1
B) 5
C) 10
D) 50
E) 100</p>
<p>Question#5: If 30 percent of 40 percent of a positive number is equal to 20 percent of w percent of the same number, what is the value of w ?
A) 80
B) 60
C) 50
D) 15
E) 10 </p>
<p>Question#6: In a certain shop, items were put in a showcase and assigned prices for January. Each month after that, the price was 10 percent less than the price for the previous month. If the price of an item was p dollars for January, what was the price for April?
A) 0.4p
B) 0.6p
C) 0.6561p
D) 0.7p
E) 0.729p</p>
<p>Question#7(Grid in): If a+2b is equal to 125 percent of 4b, what is the value of a/b?</p>
<h1>1. A</h1>
<h1>2. D</h1>
<h1>3. D</h1>
<h1>4. E</h1>
<h1>5. B</h1>
<h1>6. D</h1>
<h1>7. 3</h1>
<p>Correct?? @SATQuantum and what do you think… Did I improve or not? As for my 1st question… And thanks man for these questions…</p>
<h1>1: A</h1>
<h1>2: C</h1>
<h1>3: E</h1>
<h1>4: E</h1>
<h1>5: B</h1>
<h1>6: E</h1>
<h1>7: 3</h1>
<p>Answers: 1(A), 2©, 3(E), 4©, 5(B), 6(E), 7(3)</p>
<p>@Student3500 Missed 2, 3, 4, and 6</p>
<p>Try them again and read them very carefully.</p>
<p>@SATQuantum i got all of them right ( iam srry it seems that iam an intruder ) but can u post some really tough geometric questions ( caz this is my weakest point ) </p>
<p>@SATQuantum
Lol… I was in a rush when I did them… I just checked them out and yes I made sure and solved all of them except for number 3 I didn’t quite understand what they really want from the question… And thanks so much again !! Plus I would appreciate it If u can give me more questions involving the sat graphs like the f(x).</p>