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BhishmaNaidu99
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For all numbers t, let //t// be defined as the greatest integer less 20 Jan 2020, 22:26
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Given //t// <= t

for 5<k<6, //k// = 5 , therefore //k// is not divisible by 2. sufficient

for // K+2.3// = 7

7< K + 2.3 < 8
4.7<K<5.7
so for 4.7 to 5 , K = 4 and for 5 to 5.7 , k = 5 , for k= 4 , yes and for K=5 no , not sufficient

Statement A is sufficient
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For all numbers t, let //t// be defined as the greatest integer less 11 Mar 2020, 09:52
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Bunuel
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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 ... :?

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.

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?
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For all numbers t, let //t// be defined as the greatest integer less 12 Mar 2020, 01:03
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Kritisood
Bunuel
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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 ... :?

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.

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?

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.
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For all numbers t, let //t// be defined as the greatest integer less 14 Aug 2020, 12:19
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mbaiseasy
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

Reviving an old thread... can I kindly clarify an item?

I completely understand these equations:
8 > k + 2.3 >= 7
5.7 > k >= 4.7

However, given these, how can we assume that K = 4 when it's clearly said that K>=4.7?

If I take the solution set above, then
K = 4.7 --> NOT EVENLY DIVISIBLE BY 2
K = 5 --> NOT EVENLY DIVISIBLE BY 2
K = 5.7 --> NOT EVENLY DIVISIBLE BY 2

Any number from the solution set seems to be non-divisible by 2. If that's the case, then B should be sufficient.

Please let me know what I am missing

------------------------------------------------------------

EDIT: I get it now. I misunderstood the question. The question is asking for // K // and not for K. Hence B is not sufficient.
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For all numbers t, let //t// be defined as the greatest integer less 04 May 2021, 20:52
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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

//k// = 5 ALWAYS

5 is not divisible by 2

Sufficient

(2) //k + 2.3// = 7

k = 5 --> //5 + 2.3 = 7.3// = 7 NO
k = 4.9 --> //4.9 + 2.3 = 7.2 // = 7 YES

Insufficient

A
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For all numbers t, let //t// be defined as the greatest integer less 04 May 2021, 21:08
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1) 5 < k < 6 means //k// must be 5.
5 is not divisible by 2
Sufficient

2) For //u// = 7, 8>u>=7
8 > k+2.3 >= 7
5.7 > k >= 4.7
Because //k// can equal 5 (for values 5.7 to 5) or 4 (4.7 to 4.9999999), //k// may or may not be divisible by 2.
Insufficient.

Answer: A.
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For all numbers t, let //t// be defined as the greatest integer less 27 Oct 2021, 03:55
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mbaiseasy
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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For all numbers t, let //t// be defined as the greatest integer less 03 Mar 2022, 06:14
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(2) //k + 2.3// = 7...

Hi! Statement (1) is fine but can someone please explain break it down for my simple mind, how did we enter the inequality realm in (2) mentioned here? Thanks in advance.
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For all numbers t, let //t// be defined as the greatest integer less Updated on: 23 Nov 2022, 08:07
Originally posted by aishwarysoni on 23 Nov 2022, 08:02.
Last edited by aishwarysoni on 23 Nov 2022, 08:07, edited 1 time in total.
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I have a question Bunuel:

I evaluated "//k+2.3//" as//k// + //2.3//

//2.3// = 2

Implying that, //k// = 7 - 2 = 5

Why is this interpretation incorrect?

Edit: I understand why and this question can be ignored.

f(a+b) need not be equal to f(a) = f(b)
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For all numbers t, let //t// be defined as the greatest integer less 23 Nov 2022, 08:05
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aishwarysoni
I have a question Bunuel:

I evaluated "//k+2.3//" as//k// + //2.3//

//2.3// = 2

Implying that, //k// = 7 - 2 = 5

Why is this interpretation incorrect?

I think your doubt is already answered here: https://gmatclub.com/forum/for-all-numb ... l#p2473413

Hope it helps.
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For all numbers t, let //t// be defined as the greatest integer less 17 Dec 2024, 16:04
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