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

Question

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

vaibhavtripathi · Accepted Answer

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

martie11 · Answer

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.

stanford2012 · Answer

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.

krishnasty · Answer

Can somebody please explain me what '//' symbol implies over here??

Bunuel · Answer

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.

krishnasty · Answer

hmmmmmm........... :idea:

much clear now....thanks!!

Bunuel · Answer

Similar questions to practice: if-denotes-the-least-integer-greater-than-or-equal-to-x-132223.html if-denotes-the-greatest-integer-less-than-or-equal-to-x-94687.html for-all-numbers-t-let-t-be-defined-as-the-greatest-105416.html is-x-an-odd-integer-1-x-2-2x-99856.html for-all-z-denotes-the-least-integer-greater-than-or-110561.html denotes-to-be-the-least-integer-no-less-than-x-is-130841.html for-all-numbers-t-let-t-be-defined-as-the-greatest-105416.html if-is-the-greatest-integer-less-than-or-equal-to-x-what-144277.html how-x-become-fraction-if-its-been-said-an-integer-94687.html awkward-ds-105416.html help-data-sufficiency-equation-and-inequalities-99856.html if-denotes-the-greatest-integer-less-than-or-equal-to-x-94687.html denotes-to-be-the-least-integer-no-less-than-x-is-130841.html is-the-greatest-integer-less-than-or-equal-to-the-real-n-154006.html if-denotes-the-greatest-integer-less-than-or-equal-to-z-162078.html if-denotes-the-least-integer-greater-than-or-equal-to-x-132223.html is-the-greatest-integer-less-than-or-equal-to-the-real-n-154006.html Hope it helps.

shelrod007 · Answer

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

Bunuel · Answer

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 .

sabxu1 · Answer

7 < k + 2.3 < 8 
I'm confuse how they got this

Bunuel · Answer

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 .

parvgugnani · Answer

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

chetan2u · Answer

Yes, you have understood the logic perfectly..

Kritisood · Answer

Hi  Bunuel   VeritasKarishma

can we not do this like this:

//k + 2.3// = 7

=> //k// +//2.3// = 7
=> //k// + 2= 7
=> //k// = 5
 therefore //k// isnt divisble by 2. Whats wrong in this?

KarishmaB · Answer

With functions, it is not necessary that 
f(a+b) = f(a) + f(b)

For example, if the function is defined as f(x) = x^2, then
(a + b)^2 is not equal to a^2 + b^2

So you cannot say //a + b// = //a// + //b//

Also, if //x// = 7, in what range can the value of x lie? x can be anything from 7 to less than 8 because //7// = 7
//7.34// = 7
//7.987685// = 7
and so on...

So 7 <= k + 2.3 < 8

Hope this helps.

arunbhati · Answer

Hi Sir,

Can you explain me how it will 4.7 in statement 2

Bunuel · Answer

Because if //k + 2.3// = 7, then k + 2.3 must be at least 7 but less than 8.

So:
7 ≤ k + 2.3 < 8

Subtract 2.3 from all sides:
4.7 ≤ k < 5.7

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

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