The grammer of "as [adj] as " in math

Question

Hi ! I am confused

: When we say " a point that is twice as far from P as from Q " How we knew that : the length from the point to P = 2 of the length from the point to Q ? Because I read the following example (in the picture ) and understood the opposite (that length from the point to Q = 2 of the length from the point to P ) . In general : how to translate this expression "twice as as " into a math equation ? Is there a rule ? How we know the order ? example : OG13 PS 43

GMATinsight · Answer

a point that is twice as far from P as from Q means that

If the point talked about in the question is R

then, PR = 2*RQ

It's a simple English language and not a rule...

foryearss · Answer

Ok , this is simple , but for me i need a rule , : 
the following sentence is more confusing to me : 
"The retailer has less than twice as many radios as clocks " 
so R : radios , C : clocks 
the sentence means : 
R< 2 C 
 or
C< 2 R

thanks  GMATinsight

ccooley · Answer

First, this is a really smart question to ask. This is one of the most common translation mistakes I see people make on Quant, and a lot of people don't ever realize that they made a mistake. The fact that you've noticed this mistake is a good sign. My best tip is to write down the equation you think is right, then try some numbers. You want an equation where the same numbers make sense in the equation, as in the problem itself. If the retailer has less than twice as many radios as clocks, what are some numbers of radios and clocks that might make sense? 10 radios and 3 clocks: that doesn't make sense, since there are more than twice as many radios. 10 radios and 6 clocks: that makes sense. The number of radios is less than twice the number of clocks. 10 radios and 10 clocks: that makes sense as well. The number of radios is the same as the number of clocks, so it's definitely less than twice as many. Which of your equations (inequalities, really) works with these numbers? Try plugging in R = 10 and C = 6. Those numbers should work, if you have the right equation. First equation: R < 2C 10 < 2(6) 10 < 12 That's good! Second equation: C < 2R 6 < 2(10) 6 < 20 That's good too! So, we haven't figured it out just yet. Let's try plugging in some numbers that shouldn't work. R = 10 and C = 3 shouldn't work, since 10 is more than twice as many as 3, not less than twice as many . First equation: R < 2C 10 < 2(3) 10 < 6 Good! That doesn't work, and it shouldn't. Second equation: C < 2R 3 < 2(10) 3 < 20 Uh-oh. This works, and we didn't want it to. So, C < 2R is wrong. Because R < 2C works when you expect it to, and doesn't work when you don't expect it to, that's the correct translation. Once you do this enough times, you won't have to actually write down the numbers and the different equations - you'll be able to do it very quickly.

The grammer of "as [adj] as " in math

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