ACT math question (of the day)...

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1

<p>Three years ago men made up two out of every three internet users in America. Today the ratio of male to female users is about 1 to 1. In that time the number of American females using the internet has grown by 30,000,000, while the number of males who use the internet has grown by 100%. By how much has the total internet-user population increased in America in the past three years? </p>

<pre><code> a. 50,000,000
b. 60,000,000
c. 80,000,000
d. 100,000,000
e. 200,000,000
</code></pre>

<p>Can someone explain? I didnt understand the website's explanation..its very confusing to me.</p>

<p>correct answer is:</p>

<p>a.</p>

2

<p>The question just requires the manipulation of simultaneous equations. The “three years” and all is just extraneous information. Say “x” is males and “y” is females. The subscript is used to denote whether the variable represents the before growth or after growth figure.</p>

<p>Originally (x1/y1) = 2, because for every 2 men there’s one women (hence 2/3).
After growth (x2/y2) = 1, because for every 1 man there’s one woman (hence 1/1).</p>

<p>You know in the second equation x2 = 2*x1 because males increase by 100%
You know in the second equation y2 = y1 + 30,000,000 because females increase by 30 million.</p>

<p>You want to know how much the male population has increased (and add that to the female population growth to identify total growth), thus you solve for x1.</p>

<p>You know x1 = 2*y1 from the first equation.
Substitute as such into y1 + 30,000,000.</p>

<p>Thus;
(x1/2) + 30 million = 2<em>x1,
30 million = 1.5</em>x1
x1 = 20million</p>

<p>And if the male growth rate is 100%, you know that the nominal figure is 20 million.
30 million + 20 million = 50 million —> choice A.</p>

<p>The steps as written in this equation might look in depth and long but it’s just a quick manipulation of simultaneous equations with bigger numbers. Should take between 20 seconds and 30 seconds for most people, I’d think. In fact, if you’re one who cuts it close on time, this is a good problem to save time on. Because the numbers are fairly easily to mentally manipulate you can do it in your head much more quickly. Since there aren’t too many steps it won’t be too complicated and you might even have lower chances of error. Took me much less time eyeballing the problem and figuring it out in my head than it did to actually do the steps deliberately.</p>

3

<p>Wouldn’t it be (x1/y1)=2/3 for the first equation? Because men over women would need to be a two to three ratio?</p>

4

<p>No, because men made up 2/3 of the TOTAL internet users. </p>

<p>So actually that is:</p>

<p>(x/(x+y)) = (2/3)</p>

<p>Hence if x = 2, x+y =3. Thus y = 1, so x/y = 2</p>

<p>That’s the math… but actually you can intuitively understand it because if men made up 2/3 of the population you would need half of that more to have 1. Hence my answer.</p>

5

<p>Ahhh I see now, thanks for clarifying</p>

6

<p>i appreciate the explanation but ill have to look at it again since it still appears a bit fuzzy to me.</p>

7

<p>lol that’s pretty hard. I would miss that if it was on the ACT</p>

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<p>i agree lol</p>

9

<p>You can do this question much more quickly, accurately, and easily by thinking before you pick variables and solve. This is how:</p>

<pre><code>1st there were more men than woman on the internet. Than, after the number of woman increased by 30,000,000 and men by 100%, the ration of men to woman were 1:1, so the numbers were equal. Obviously, there was a greater increase in the number of woman than men (because otherwise there would still be more men than woman.)
</code></pre>

<p>Once we know there was a greater increase of woman who used the internet, we can look at the answer choices.</p>

<p>If it was E, there was a total increase of 200,000,000, or 170,000,000 men and 30,000,000 woman. This means there was a greater increase of men than woman, which is wrong.</p>

<p>If it was D, the total increase was 100,000,000, or 70,000,000 men and only 30,000,000 woman, which again cannot be the answer.</p>

<p>By now you may be able to see that the only conceivable answer is A, or 50,000,000 of total increase. This means that 30,000,000 were woman and 20,000,000 were men, which is the only answer choice where there is a greater increase of woman than of men.</p>

<p>Let me know what you think.</p>

10

<p>i kind of understand what you’re saying, but the problem confuses me when it gives this part of the information, as you said “after the number of woman increased by 30,000,000 and men by 100%, the ration of men to woman were 1:1, so the numbers were equal.” The 100% and the 1:1 ratio part confuses me, like exactly what does that mean and how can i use it in the problem?</p>

<p>(i might be sounding like a complete idiot…)</p>

11

<p>the grow by 100% part means the number of males was multiplied by 1 (100%=1), and this product was added to the previous total number of males.</p>

<p>1:1 means 1 divided by 1. Which equals 1. This means that the new number of males divided by the number of females equals 1, which means the males are equal in number to the females.</p>

12

<p>Where did you get this question? I’m kinda scared now…</p>

13

<p>Thank you duster, I understand it now!</p>

<p>@practical: It was an ACT Math Question of the Day =/</p>

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<p>Where do you get ACT questions of the day??</p>

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<p>google this : ACT math question of the day</p>