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Although you've got the correct answer, I just want to add that those three lines marked in green are unnecessary time waste. When you can approximate (3^2 - 1) as 3^2, you can definitely approximate (3^8 - 1) as 3^8.srcc25anu wrote:1. x > 3^12 - 3^4
x > 3^4 (3^8 - 1)
x > 3^4 * (3^4 + 1) * (3^4 - 1)
x > 3^4 * (3^4 + 1) * (3^2 + 1) * (3^2 - 1)
x > 3^4 * ~3^4 * ~3^2 * ~3^2
x > ~3^12
Target question: Is x > 3^10 ?kevincanspain wrote:Is x > 3^10 ?
(1) x > 3^12 - 3^4
(2) x > 10^5
Brent@GMATPrepNow wrote:Target question: Is x > 3^10 ?kevincanspain wrote:Is x > 3^10 ?
(1) x > 3^12 - 3^4
(2) x > 10^5
Statement 1: x > 3^12 - 3^4
We need to compare 3^12 - 3^4 with 3^10.
If 3^12 - 3^4 > 3^10, then we can be certain that x > 3^10
Here's the "number sense" approach.
First, let's ignore the 3^4 for a moment.
Notice that 3^12 is WAYYYY bigger than 3^10
In fact, since 3^12 = (3^2)(3^10), we can see that 3^12 is 9 TIMES the value of 3^10
As such, subtracting 3^4 from 3^12 is going to have little effect on 3^12.
In other words, we can be quite certain that 3^12 - 3^4 > 3^10, which means x > 3^12 - 3^4 > 3^10, in which case we can be certain that x > 3^10
For those who don't like the number sense approach, here's a quick proof.
First recognize that x > 3^12 - 3^4 > 3^12 - 3^10
Now examine 3^12 - 3^10
3^12 - 3^10 = 3^10(3^2 - 1) = 3^10(8)
Since 3^10(8) > 3^10, we can write:
x > 3^12 - 3^4 > 3^12 - 3^10 > 3^10
From here, we can be certain that x > 3^10
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: x > 10^5
Since 3^2 = 9 and 4^2 = 16, we can say that (3.something^2) = 10
Now replace 10 with (3.something^2)
We get: x > (3.something^2)^5
Simplify: x > (3.something)^10
Since (3.something)^10 > 3^10, we can write: x > (3.something)^10 > 3^10
From here, we can be certain that x > 3^10
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = D
Cheers,
Brent
That would be true if each statement gave us the actual value of x. However, each statement is an inequality (not an equation) and does not give us the value of x.chrislacolla wrote:all of the calculations unnecessary in this case. each statement gives you a value of x- regardless of what that value is, it will allow you answer the original yes/no question. it doesn't matter whether it's yes or no, just that you can answer it given whatever the expressions in 1 and 2 simplify to.
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