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Manager  Joined: 26 Apr 2010
Posts: 95
Concentration: Strategy, Entrepreneurship
Schools: Fuqua '14 (M)
For all numbers t, let //t// be defined as the greatest integer less  [#permalink]

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51 00:00

Difficulty:   75% (hard)

Question Stats: 57% (01:59) correct 43% (01:53) wrong based on 874 sessions

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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

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
Math Expert V
Joined: 02 Sep 2009
Posts: 60778
Re: For all numbers t, let //t// be defined as the greatest integer less  [#permalink]

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2
5
Manager  Joined: 26 Apr 2010
Posts: 95
Concentration: Strategy, Entrepreneurship
Schools: Fuqua '14 (M)
Re: For all numbers t, let //t// be defined as the greatest integer less  [#permalink]

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7
2

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  [#permalink]

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2
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.

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PS: Correct me if I am wrong.
##### General Discussion
Manager  Joined: 02 Apr 2010
Posts: 92
Re: For all numbers t, let //t// be defined as the greatest integer less  [#permalink]

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5
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.
Manager  Joined: 26 Apr 2010
Posts: 95
Concentration: Strategy, Entrepreneurship
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Re: For all numbers t, let //t// be defined as the greatest integer less  [#permalink]

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1
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.
Math Expert V
Joined: 02 Sep 2009
Posts: 60778
Re: For all numbers t, let //t// be defined as the greatest integer less  [#permalink]

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2
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: how-x-become-fraction-if-its-been-said-an-integer-94687.html

Hope it helps.
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Re: For all numbers t, let //t// be defined as the greatest integer less  [#permalink]

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hmmmmmm........... much clear now....thanks!!
Intern  Joined: 08 Jun 2010
Posts: 48
Re: For all numbers t, let //t// be defined as the greatest integer less  [#permalink]

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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
Senior Manager  Joined: 13 Aug 2012
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Concentration: Marketing, Finance
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Re: For all numbers t, let //t// be defined as the greatest integer less  [#permalink]

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1
1
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.

Manager  Joined: 23 Jan 2013
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Re: For all numbers t, let //t// be defined as the greatest integer less  [#permalink]

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Can somebody explain to me why statement B //k + 2.3// = 7 become this 8 > k + 2.3 >= 7 ?

I am confused ... Math Expert V
Joined: 02 Sep 2009
Posts: 60778
Re: For all numbers t, let //t// be defined as the greatest integer less  [#permalink]

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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  [#permalink]

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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  [#permalink]

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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: how-x-become-fraction-if-its-been-said-an-integer-94687.html

Hope it helps.

7 < k + 2.3 < 8
I'm confuse how they got this
Math Expert V
Joined: 02 Sep 2009
Posts: 60778
Re: For all numbers t, let //t// be defined as the greatest integer less  [#permalink]

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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: how-x-become-fraction-if-its-been-said-an-integer-94687.html

Hope 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  [#permalink]

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1
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
Math Expert V
Joined: 02 Aug 2009
Posts: 8322
Re: For all numbers t, let //t// be defined as the greatest integer less  [#permalink]

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1
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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Joined: 15 Jan 2017
Posts: 322
Re: For all numbers t, let //t// be defined as the greatest integer less  [#permalink]

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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 Manager  G
Joined: 14 Jan 2017
Posts: 120
Location: India
Re: For all numbers t, let //t// be defined as the greatest integer less  [#permalink]

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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.
Manager  B
Joined: 12 Mar 2018
Posts: 106
Re: For all numbers t, let //t// be defined as the greatest integer less  [#permalink]

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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   [#permalink] 10 Oct 2018, 13:49

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