hi tommy,
Quantity A Quantity B
1 /(1/2+1/4+1/8) & 1/2+1/4+1/8
Compare and don't calculate strategy.Please explain.
How is 1/2+1/4+1/8 is less than 1/2?
thank you
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- nruthya.rajagopal
- Students
- Posts: 18
- Joined: Wed Dec 28, 2011 4:17 pm
- rheyn
- Students
- Posts: 7
- Joined: Tue Oct 23, 2012 3:59 pm
Re: quantitative comparison and Data interpretation-guide 6
Hey Nruthya!
I'm not Tommy but:
Quantity A Quantity B
1 /(1/2+1/4+1/8) 1/2+1/4+1/8
The book says " 1/2+1/4+1/8 < 1/2+(1/4+1/4) (which equals 1),
so 1/2+1/4+1/8 < 1.
'Stuff' divided by a fraction means that 'stuff' is multiplied with the reciprocal of that fraction.
As you know that 1/2+1/4+1/8 is <1, its reciprocal must be >1. Therefore, A > B.
Hopefully I'm right....
Robert =)
I'm not Tommy but:
Quantity A Quantity B
1 /(1/2+1/4+1/8) 1/2+1/4+1/8
The book says " 1/2+1/4+1/8 < 1/2+(1/4+1/4) (which equals 1),
so 1/2+1/4+1/8 < 1.
'Stuff' divided by a fraction means that 'stuff' is multiplied with the reciprocal of that fraction.
As you know that 1/2+1/4+1/8 is <1, its reciprocal must be >1. Therefore, A > B.
Hopefully I'm right....
Robert =)
- tommywallach
- Manhattan Prep Staff
- Posts: 1917
- Joined: Thu Mar 31, 2011 11:18 am
Re: quantitative comparison and Data interpretation-guide 6
Hey Nruthya/Robert!
Robert is absolutely right with his explanation here. The only thing he may have glossed is how you know that 1/2 + 1/4 +1/8 is less than 1 without calculating. The truth is, this requires a bit of logic, and I'm not entirely sure the logic is all that much faster than calculating, assuming you're a reasonably fast calculator.
Logic: Believe it or not, the logic of this addition is akin to what is known as Zeno's Paradox in logic. Namely, if you walk halfway towards a wall, then half again, then half again, logic seems to dictate you'll never actually reach it, merely keep halving the distance forever. Now, in real life, we know this isn't true (except on the atomic level). But in math, it is true. If you add in halves like this one does (1/4 = one half of 1/2, 1/8 = one half of 1/4, etc.), you'll never actually reach one.
Calculation: Common denominator 1/8 + 2/8 + 4/8 = 7/8, reciprocal = 8/7
HOWEVER, the fact that this question can be done very simply with calculation is not the point. This is an opportunity to practice your ability to do logic without calculation. Even if it isn't faster on THIS question, it will certainly be faster on SOME questions, so you want to be sure to practice it.
Hope that helps, and thanks for chiming in, Robert! It's always fun to have more voices!
-t
Robert is absolutely right with his explanation here. The only thing he may have glossed is how you know that 1/2 + 1/4 +1/8 is less than 1 without calculating. The truth is, this requires a bit of logic, and I'm not entirely sure the logic is all that much faster than calculating, assuming you're a reasonably fast calculator.
Logic: Believe it or not, the logic of this addition is akin to what is known as Zeno's Paradox in logic. Namely, if you walk halfway towards a wall, then half again, then half again, logic seems to dictate you'll never actually reach it, merely keep halving the distance forever. Now, in real life, we know this isn't true (except on the atomic level). But in math, it is true. If you add in halves like this one does (1/4 = one half of 1/2, 1/8 = one half of 1/4, etc.), you'll never actually reach one.
Calculation: Common denominator 1/8 + 2/8 + 4/8 = 7/8, reciprocal = 8/7
HOWEVER, the fact that this question can be done very simply with calculation is not the point. This is an opportunity to practice your ability to do logic without calculation. Even if it isn't faster on THIS question, it will certainly be faster on SOME questions, so you want to be sure to practice it.
Hope that helps, and thanks for chiming in, Robert! It's always fun to have more voices!
-t
- nruthya.rajagopal
- Students
- Posts: 18
- Joined: Wed Dec 28, 2011 4:17 pm
Re: quantitative comparison and Data interpretation-guide 6
@robert , thanks for correcting my question
@tommy, exact gloss which i was looking for.thank u:)
i hope i used the word gloss properly... correct?
@tommy, exact gloss which i was looking for.thank u:)
i hope i used the word gloss properly... correct?
- tommywallach
- Manhattan Prep Staff
- Posts: 1917
- Joined: Thu Mar 31, 2011 11:18 am
Re: quantitative comparison and Data interpretation-guide 6
Hey Nruthya,
Interestingly, we are using two different definitions of gloss!
Verb
1) To treat something a little too briefly, often with intention to deceive -- "He glossed over what he was doing in Thailand in the first place."
2) A brief explanation of something. "The president doesn't have time for anything more than a gloss of the situation in Israel."
: )
-t
Interestingly, we are using two different definitions of gloss!
Verb
1) To treat something a little too briefly, often with intention to deceive -- "He glossed over what he was doing in Thailand in the first place."
2) A brief explanation of something. "The president doesn't have time for anything more than a gloss of the situation in Israel."
: )
-t
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