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by ketkoag » Thu Jul 16, 2009 9:02 am
please confirm whether "between" in this question means excluding the limits or including them..i excluded the limits and then proceed further..
In general whenever "between" is mentioned and nothing else then we have to exclude the limiting numbers, right?
that means if i consider statement 1, then i will not consider value of y to be 40 or 45, right?
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by Bryant@VeritasPrep » Thu Jul 16, 2009 10:01 am
incorrect-- if a number is between 40 and 45, it can indeed include the number 40 or the number 45.
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by Ian Stewart » Thu Jul 16, 2009 10:51 am
bryantmichaels wrote:incorrect-- if a number is between 40 and 45, it can indeed include the number 40 or the number 45.
No, that's not true. OG11, page 112: "To say that the number n is between 1 and 4 on the number line means that n > 1 and n < 4." If the endpoints are to be included in the range, the question will say "inclusive".

In the original question, S1 tells you that:

40/6 < y < 45/6

Statement 2 tells you that 19/3 < y < 23/3, or equivalently that


38/6 < y < 46/6

Combined, we only know that 40/6 < y < 45/6. So we can't find y; y could be 41/6, or y could be 43/6, for example.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by ketkoag » Fri Jul 17, 2009 11:16 am
Ian Stewart wrote:
bryantmichaels wrote:incorrect-- if a number is between 40 and 45, it can indeed include the number 40 or the number 45.
No, that's not true. OG11, page 112: "To say that the number n is between 1 and 4 on the number line means that n > 1 and n < 4." If the endpoints are to be included in the range, the question will say "inclusive".

In the original question, S1 tells you that:

40/6 < y < 45/6

Statement 2 tells you that 19/3 < y < 23/3, or equivalently that


38/6 < y < 46/6

Combined, we only know that 40/6 < y < 45/6. So we can't find y; y could be 41/6, or y could be 43/6, for example.
thanks Ian..
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by Bryant@VeritasPrep » Fri Jul 17, 2009 6:36 pm
ok so now I am confused. I can see where in linear space, when dealing with whole numbers, we could ignore the "endpoints," but when dealing with the product of two numbers where the numbers are not required to be whole, I don't see how "pick a number between 40 and 45 would not include 40 and 45 since 40.000000000000001 would be between the two and also 44.999999999999999
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by PussInBoots » Sun Jul 19, 2009 9:28 pm
bryantmichaels wrote:ok so now I am confused. I can see where in linear space, when dealing with whole numbers, we could ignore the "endpoints," but when dealing with the product of two numbers where the numbers are not required to be whole, I don't see how "pick a number between 40 and 45 would not include 40 and 45 since 40.000000000000001 would be between the two and also 44.999999999999999
40.000000000001 and 44.99999999999 are between 40 and 45 just as 41, 42, or 43.3204230982130948012938402193840. 40.000000001 is not 40 and 44.999999999 is not 45. That being said, I highly doubt GMAT will go past 3 decimal numbers.
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by Ian Stewart » Mon Jul 20, 2009 4:14 am
bryantmichaels wrote:ok so now I am confused. I can see where in linear space, when dealing with whole numbers, we could ignore the "endpoints," but when dealing with the product of two numbers where the numbers are not required to be whole, I don't see how "pick a number between 40 and 45 would not include 40 and 45 since 40.000000000000001 would be between the two and also 44.999999999999999
If a number x is described, on the GMAT, as being 'between 40 and 45', that simply means that 40 < x < 45. Sure, x can be as close as you like to 40; x could be 40.000000000000001, for example. That number isn't equal to 40; it's larger than 40, and the distance between it and 40 is 0.000000000000001.
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