<p>If x > 2^1,000 , which of the following is greatest?</p>
<p>A - (x+2)^2 -2
B - (x-2)^2 + 2
C - (x/2)^2
D - (2x)^2/2
E - (x^2 + 2)/2</p>
<p>Can somebody explain the answer to me please?</p>
<p>Pick a number that’s bigger than 2^1000 and plug it into the answers</p>
<p>If you don’t want to plug in values for X, I have a decent way to think it out.
Basically, you know that x is some ridiculously high number.</p>
<p>to prove A and B wrong, a high number +/- 2 will not make much difference when it is squared. The +/-2 at the end is also insignificant. You can almost say that A and B are about the same.</p>
<p>you can eliminate C because big number cut in half and then squared will be less than A or B. </p>
<p>D, on the other hand, creates a much bigger number than A or B. If x is already a huge number and you double it, then square it, it’ll be 4 times the value of (x^2). When this mounstrous number is divided by 2, it is still larger than A or B.</p>
<p>So currently, D is the biggest number. Now let’s look at E.</p>
<p>For E, you’re squaring x and then adding 2. so basically it’s just squaring x. Then you divide by 2. This will be less than D, because doubling a big number will make it much bigger than adding 2 to it. </p>
<p>Final Answer: D</p>
<p>its not b cus the 4 isnt enough to make up for hte difference of hte squares (a v b)</p>
<p>its not e cus its smaller than A
c is also smaller than A</p>
<p>d, as u wrote it, features poor parentheses and lacks brackets</p>
<p>if it is ((2x)^2)/2, then it is bigger than A
if not, the answer is A</p>
<p>just think about it, dividing by 2 is just subtracting 1 from the exponent</p>
<p>so if x = 2^1001, (2^1001)^2–the +2 is negligible-- is 2^2002–the -2 is also neglegible</p>
<p>A=2^2002</p>
<p>D= ((2x)^2)/2
(2^1002)^2 is 2^2004</p>
<p>then divided by 2</p>
<p>will make it 2^2003</p>
<p>still about twice as large as A</p>
<p>
</p>
<p>You cannot plug in numbers for this type of problem because doing so only tells you something about one particular number, not the entire set of numbers greater than 2^1000.</p>
<p>
</p>
<p>No. Exponents come before division, so you don’t need parentheses around the term with an exponent.</p>
<hr>
<p>All you have to do is simplify, and you’ll get:</p>
<p>(A) x^2 + 4x + 2
(B) x^2 - 4x + 2
(C) x^2/4
<a href=“D”>b</a> 2x^2<a href=“E”>/b</a> x^2/2 + 1</p>
<p>(C) and (E) are smaller than (D) because the term x^2 is being divided as opposed to being multiplied. The +1 in (E) is negligible.</p>
<p>(B) is smaller than (A) because it is subtracting 4x as opposed to adding 4x.</p>
<p>Between (A) and (D), (D) is bigger:</p>
<p>(A)
(2^1000)^2 + <a href=“4”>b</a>(2^1000)** + 2 =
2^2000 + <a href=“2%5E2”>b</a>(2^1000)** + 2 = </p>
<p>2^2000 + 2^1002 + 2</p>
<p>(D)
2(2^1000)^2 =
2*2^2000 =
(2^1)(2^2000) =
2^2001 =
(2^1)(2^2000) = 2(2^2000) =</p>
<p>2^2000 + 2^2000</p>
<p>2^2000 + 2^2000 > 2^2000 + 2^1002 + 2</p>
<p>^ You pretty much still plugged in. And if you can’t think about the logic quick enough, your best strategy is plugging in a number. And if two answers are equal, then you quickly pick another number</p>
<p>@elau0493: Well, if you plug in 3 for x, then choice A comes out to be larger. </p>
<p>@crazybandit: At the same time, elau0493 is correct because you are plugging in numbers, which could possibly become misleading as you said. Plus, you used 2^1000 for x, but the problem says x > 2^1,000. Can you elaborate with your explanation a little more, please?</p>
<p>P.S. When you break choice A down after plugging in 2^1000, it becomes 2^2000 + 2^1002 + 2. When you break choice D down, it becomes 2^2001. So, when you compare 2^2000 + 2^1002 + 2 and 2^2001, obviously choice A seems larger, but it’s not. So what I’m saying is that if I was given this problem during the test, I would have most likely chosen A after breaking them both down to those two values. Is there any way to avoid this trick the CB used on us?</p>
<p>Let’s just agree on the fact that only A and D are larger than x^2 and therefore larger than the other.s</p>
<p>We have
A. (x+2)^2 -2 = x^2 + 4x+2
D. (2x)^2/2 = x^2 + x^2</p>
<p>So, is x^2 > 4x + 2?</p>
<p>The positive solution to x^2 - 4x is 4, which is obviously less than 2^1000 so x^2 is larger than 4x (or 4x+2) and therefore D must be the answer…</p>