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.... 7^(x + 2)/49 > 1koby_gen wrote:Is ( 7^(X+2) ) / 49 > 1 ?
(1) 7^(x+2) > 1/49
(2) 7^(x-1) > 1/49
Quick note - simplifying (x+2)>2, the question rephrase should be "is x>0"? In this problem it does not change the end result however.Anurag@Gurome wrote:.... 7^(x + 2)/49 > 1koby_gen wrote:Is ( 7^(X+2) ) / 49 > 1 ?
(1) 7^(x+2) > 1/49
(2) 7^(x-1) > 1/49
=> 7^(x + 2) > 49 = 7^2
=> (x + 2) > 2
=> x > 2
Hence, the problems is asking whether x is greater than 2 or not.
Thanks Whitney.Whitney Garner wrote:Quick note - simplifying (x+2)>2, the question rephrase should be "is x>0"?
Whitney Garner wrote:Quick note - simplifying (x+2)>2, the question rephrase should be "is x>0"? In this problem it does not change the end result however.Anurag@Gurome wrote:.... 7^(x + 2)/49 > 1koby_gen wrote:Is ( 7^(X+2) ) / 49 > 1 ?
(1) 7^(x+2) > 1/49
(2) 7^(x-1) > 1/49
=> 7^(x + 2) > 49 = 7^2
=> (x + 2) > 2
=> x > 2
Hence, the problems is asking whether x is greater than 2 or not.
A question for the OP - what is the source of this question? It tests solid theory but the set-up seems a bit off for the GMAT.
Thanks!
Whit
It actually can be simplified further. If we leave everything on the left side we can investigate the 2 cases that seem to arise from |7|^2. We'll start with the positive case:Night reader wrote:rather hesitating to post this one ...
( 7^(X+2) ) / 49 > 1 ---> 7^(x+2)>|7|^2 ? can not be further simplified
49/49 will be 1 regardless of the underlying values used to create those 49s. To put this in a slightly different perspective - if I asked you for 81/81, you would not have to first ask if one was 9^2 and the other (-9)^2 or answer +1 or -1; the answer would simply be 1. If the numerator was made of (-9)(-9) and the denominator by (9)(9), the answer would only be 1 because the negatives will be paired and will cancel. We only have to worry about the mod or underlying sign of 7 if we are trying to pull out only one of the 7s in the denominator - but we are treating them as a whole. We can think about it in the following way:Night reader wrote:Whit, (7^x)*49 in the numerator and 49 in the denominator are two different numbers in the mods
one is 7^2 from original source number, and the other is 49 - we don't know the original number
further to equate the powers one needs to have the same baseline number on both sides (left and right)
we have +ve 7 on the left and -ve 7 on the right in case when |7|=-7
So when I said can't be further simplified, it was meant that this expression breaks down to two expressions exactly:
7^(x+2)>|7|^2 AND |7|>7 {+ve} --> 7^(x+2)>7^2 This we can simplify and write as x+2>2
7^(x+2)>|7|^2 AND |7|>-7 {-ve} --> 7^(x+2)>-7^2 Here we can't write as x+2>2 because the baseline numbers are of the different values 7 and -7
OR in the more straightforward way
7^(x+2)/|7|^2 >1 --> for |7| -ve, 7^(x+2)<-7^2 AND for |7| +ve, 7^(x+2)>7^2 ... actually this would be the correct way, as we can not multiply inequality to the mod. What do you think?
Be careful, because I can rewrite (-7)^2 as (-1)^2 times (7)^2 and this is a legal move. And since (-1)^2 = 1, that term effectively disappears.Night reader wrote:7^(x+2)>|7|^2 AND |7|>-7 {-ve} --> 7^(x+2)>-7^2 Here we can't write as x+2>2 because the baseline numbers are of the different values 7 and -7
Anurag@Gurome wrote:.... 7^(x + 2)/49 > 1koby_gen wrote:Is ( 7^(X+2) ) / 49 > 1 ?
(1) 7^(x+2) > 1/49
(2) 7^(x-1) > 1/49
=> 7^(x + 2) > 49 = 7^2
=> (x + 2) > 2
=> x > 0
Hence, the problems is asking whether x is greater than 0 or not.
Statement 1: 7^(x + 2) > 1/49 = 7^(-2)
Implies, (x + 2) > -2
=> x > -4
Not sufficient
Statement 2: 7^(x - 1) > 1/49 = 7^(-2)
Implies, (x - 1) > -2
=> x > -1
Not sufficient
1 & 2 Together: x > -1
Not sufficient.
The correct answer is E.
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