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For all numbers t, let //t// be defined as the greatest integer less
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For all numbers t, let //t// be defined as the greatest integer less than or equal to t. Is //k// evenly divisible by 2? (1) 5 < k < 6 (2) //k + 2.3// = 7 Source: Knewton
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Originally posted by martie11 on 26 Nov 2010, 15:03.
Last edited by Bunuel on 06 Feb 2019, 04:00, edited 3 times in total.
Edited the question




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Re: For all numbers t, let //t// be defined as the greatest integer less
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01 Feb 2014, 04:28




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Re: For all numbers t, let //t// be defined as the greatest integer less
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26 Nov 2010, 15:26
Thanks for the reply stanford2012.
Looking at statement b... Slight correction in your inequality: 4.7 ≤ k < 5.7. With this inequality, we see that k can be 4.7, 4.8, 4.9, etc. Hence, if k < 5 then //k// = 4, which is divisible by 2. However, if k = 5.2, then //k// = 5, which is not divisible by 2.
Hence insufficient.
Correct answer is A. Updated post with OA.



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Re: For all numbers t, let //t// be defined as the greatest integer less
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27 Nov 2010, 20:39
martie11 wrote: Source: Knewton
For all numbers t, let //t// be defined as the greatest integer less than or equal to t. Is //k// evenly divisible by 2?
a) 5 < k < 6 b) //k + 2.3// = 7
Solution to follow...interested to see how people interrupt this question. S1: 5< k < 6 means //k// = 5. Not divisible by 2. Sufficient. S2: //k+2.3// = 7 means 8 > k+2.3 >= 7. therefore 5.7 > k >=4.7 and //k// = 4 or 5. Not Sufficient. Answer: A
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Re: For all numbers t, let //t// be defined as the greatest integer less
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26 Nov 2010, 15:15
Statement A: Tells you that k is somewhere between 5 and 6. Based on the definition of the question stem /k/ is thus 5, which is not evently divisible by 2.
=> Sufficient
Statement B:Tells you that the following inequality has to hold: 7 < k + 2.3 < 8 => 4.7 < k < 5.7 => /k/ has to equal 5, which is not evenly divisible.
=> Sufficient
Hence, solution D is correct.



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Re: For all numbers t, let //t// be defined as the greatest integer less
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26 Nov 2010, 23:25
krishnasty wrote: martie11 wrote: Source: Knewton
For all numbers t, let //t// be defined as the greatest integer less than or equal to t. Is //k// evenly divisible by 2?
a) 5 < k < 6 b) //k + 2.3// = 7
Solution to follow...interested to see how people interrupt this question. Can somebody please explain me what '//' symbol implies over here??  Consider KUDOS if you like my post!It's my interpretation that this is equivalent to the "floor" of the number. In this case, say you have x = 11.3. Now the question tries to confuse you: // x // is equal to the greatest integer less than or equal to x, in other words: // x // > the largest integer <= x In this case x = 11.3, so the largest number that is <= 11.3 is 11. So // x // = 11. Note, if x = 11, then by definition, // x // = 11. I think the concept itself is fairly straightforward, it's the wording that is awkward.... HTHs.



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Re: For all numbers t, let //t// be defined as the greatest integer less
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27 Nov 2010, 02:15
krishnasty wrote: martie11 wrote: Source: Knewton
For all numbers t, let //t// be defined as the greatest integer less than or equal to t. Is //k// evenly divisible by 2?
a) 5 < k < 6 b) //k + 2.3// = 7
Solution to follow...interested to see how people interrupt this question. Can somebody please explain me what '//' symbol implies over here??  Consider KUDOS if you like my post!Stem defines some function, represented by the symbol \(////\), as the function which rounds down any number to an integer value: \(//3.4//=3\), \(//2//=2\), \(//7.5//=8\), ... Check similar question for practice: howxbecomefractionifitsbeensaidaninteger94687.htmlHope it helps.
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Re: For all numbers t, let //t// be defined as the greatest integer less
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27 Nov 2010, 08:59
hmmmmmm........... much clear now....thanks!!



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Re: For all numbers t, let //t// be defined as the greatest integer less
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31 Dec 2010, 11:11
Sat.1 5<k<6 mean any integer n.m. between 5 to 6. 5 is possible integer value.and 5 isn't evenly divisible by 2. suffucient



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Re: For all numbers t, let //t// be defined as the greatest integer less
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18 Dec 2012, 01:29
Rule: //t// is the greatest integer less than or equal to t Problem: Is //k// evenly divisible by 2?
(1) 5 < k < 6 //k// = 5 which is not divisible by 2 SUFFICIENT. (2) //k + 2.3// = 7 8 > k + 2.3 >= 7 5.7 > k > 4.7 if k = 4, YES if not, NO INSUFFICIENT.
Answer: A



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Re: For all numbers t, let //t// be defined as the greatest integer less
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11 Sep 2014, 19:11
Can somebody explain to me why statement B //k + 2.3// = 7 become this 8 > k + 2.3 >= 7 ? I am confused ...



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Re: For all numbers t, let //t// be defined as the greatest integer less
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12 Sep 2014, 04:51
shelrod007 wrote: Can somebody explain to me why statement B //k + 2.3// = 7 become this 8 > k + 2.3 >= 7 ? I am confused ... The function rounds down any number to an integer value: \(//3.4//=3\), \(//2//=2\), \(//7.5//=8\), ... So, //x// = 7, means that 7 <= x < 8. Any number from this range when rounded down gives 7. Check other Rounding Functions Questions in our Special Questions Directory.
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Re: For all numbers t, let //t// be defined as the greatest integer less
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19 Dec 2015, 06:54
Statement 1 gives k to be 5. Sufficient Statement 2, on solving, gives two answers 3 and 4. Insufficient Hence A
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Re: For all numbers t, let //t// be defined as the greatest integer less
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25 Apr 2016, 04:54
Bunuel wrote: krishnasty wrote: martie11 wrote: Source: Knewton
For all numbers t, let //t// be defined as the greatest integer less than or equal to t. Is //k// evenly divisible by 2?
a) 5 < k < 6 b) //k + 2.3// = 7
Solution to follow...interested to see how people interrupt this question. Can somebody please explain me what '//' symbol implies over here??  Consider KUDOS if you like my post!Stem defines some function, represented by the symbol \(////\), as the function which rounds down any number to an integer value: \(//3.4//=3\), \(//2//=2\), \(//7.5//=8\), ... Check similar question for practice: howxbecomefractionifitsbeensaidaninteger94687.htmlHope it helps. 7 < k + 2.3 < 8 I'm confuse how they got this



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Re: For all numbers t, let //t// be defined as the greatest integer less
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25 Apr 2016, 05:02
sabxu1 wrote: Bunuel wrote: Stem defines some function, represented by the symbol \(////\), as the function which rounds down any number to an integer value: \(//3.4//=3\), \(//2//=2\), \(//7.5//=8\), ... Check similar question for practice: howxbecomefractionifitsbeensaidaninteger94687.htmlHope it helps. 7 < k + 2.3 < 8 I'm confuse how they got this The function rounds down any number to an integer value: \(//3.4//=3\), \(//2//=2\), \(//7.5//=8\), ... So, //x// = 7, means that 7 <= x < 8. Any number from this range when rounded down gives 7. Check other Rounding Functions Questions in our Special Questions Directory.
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Re: For all numbers t, let //t// be defined as the greatest integer less
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16 May 2016, 22:50
Bunuel , I didn't get why B is not sufficient . Could you please explain.
So, //x// = 7, means that 7 <= x < 8. Any number from this range when rounded down gives 7.
When any number in this range rounds down to 7 , then
//k+2.3//=7
7<=k+2.3<8
4.7<=k<5.7
So K will rounds down either 4 or 5 . Right . That is what you mean ??
That's why B not sufficient ?
Thanks Regards



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Re: For all numbers t, let //t// be defined as the greatest integer less
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16 May 2016, 23:08
parvgugnani wrote: Bunuel , I didn't get why B is not sufficient . Could you please explain.
So, //x// = 7, means that 7 <= x < 8. Any number from this range when rounded down gives 7.
When any number in this range rounds down to 7 , then
//k+2.3//=7
7<=k+2.3<8
4.7<=k<5.7
So K will rounds down either 4 or 5 . Right . That is what you mean ??
That's why B not sufficient ?
Thanks Regards Yes, you have understood the logic perfectly..
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Re: For all numbers t, let //t// be defined as the greatest integer less
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07 Aug 2017, 10:21
I did understand st 1. Pretty clear But for statement two, how do we know that //k + 2.3 // 7 is basically 8>=7. How do we deduce that there was an 8 as well? It doesn't state anywhere that k is a value between 8 and 7 > after all, //t// was less than equal to t Would appreciate some detail on interpreting this, thank you



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Re: For all numbers t, let //t// be defined as the greatest integer less
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18 Sep 2018, 09:10
This seems to me a very high quality question. Couldn't really get statement B until I read the comments. Thanks for wonderful explanation Bunuel.
As for statement 1, it always rounds down to 5 and hence not divisible by 2 and hence is sufficient to answer the question.



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Re: For all numbers t, let //t// be defined as the greatest integer less
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10 Oct 2018, 13:49
the question is lacking of auxiliary info: how do we know //k values can be operated by decimals...




Re: For all numbers t, let //t// be defined as the greatest integer less
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