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# [V] denotes the greatest integer less than or equal to 'V'. 'V' is a p

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Joined: 19 Oct 2018
Posts: 1446
Location: India
[V] denotes the greatest integer less than or equal to 'V'. 'V' is a p  [#permalink]

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16 Jun 2019, 15:02
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Difficulty:

75% (hard)

Question Stats:

42% (02:05) correct 58% (02:34) wrong based on 31 sessions

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[V] denotes the greatest integer less than or equal to 'V'. 'V' is a positive integer and $$[\frac{V}{5}]-[\frac{V}{7}]=1$$.
If the minimum value of 'V' is 'a' and the maximum value of 'V' is 'b'. What is the value of (a+b)?

A. 33
B. 34
C. 35
D. 40
E. 42
Director
Joined: 16 Jan 2019
Posts: 555
Location: India
Concentration: General Management
WE: Sales (Other)
[V] denotes the greatest integer less than or equal to 'V'. 'V' is a p  [#permalink]

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18 Jun 2019, 22:37
5
V is a positive integer, therefore $$[\frac{V}{5}]−[\frac{V}{7}]=1$$ at minimum value of V should be $$1-0$$

Therefore V should be at least 5, $$a=5$$

Now looking at the answer choices, the maximum value for V should be among 28, 29, 30, 35 and 37.

When V=28, $$[\frac{V}{5}]−[\frac{V}{7}]=5-4=1$$

When V=29, $$[\frac{V}{5}]−[\frac{V}{7}]=5-4=1$$

When V=30, $$[\frac{V}{5}]−[\frac{V}{7}]=6-4=2$$

We can conclude here that V can be maximum 29 and so $$b=29$$ but just to check,

When V=35, $$[\frac{V}{5}]−[\frac{V}{7}]=7-5=2$$

When V=37, $$[\frac{V}{5}]−[\frac{V}{7}]=7-5=2$$

Therefore, $$a+b=5+29=34$$

Hit Kudos if this helped!
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Math Expert
Joined: 02 Aug 2009
Posts: 8310
Re: [V] denotes the greatest integer less than or equal to 'V'. 'V' is a p  [#permalink]

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16 Jun 2019, 22:08
nick1816 wrote:
[V] denotes the greatest integer less than or equal to 'V'. 'V' is a positive integer and $$[\frac{V}{5}]-[\frac{V}{7}]=1$$.
If the minimum value of 'V' is 'a' and the maximum value of 'V' is 'b'. What is the value of (a+b)?

A. 33
B. 34
C. 35
D. 40
E. 42

$$[\frac{V}{5}]-[\frac{V}{7}]=1$$

Minimum
When $$\frac{V}{5}$$ just crosses 0.5, while $$\frac{V}{7}$$ remains below 0.5..
This means V can be 3, SO A=3

Maximum
$$[\frac{V}{5}]-[\frac{V}{7}]<2$$, as we can have the difference just below 2, but the answer still as 1, for example 4.5 and 6.4999.
Here 4.5 will become 5, while 6.4999 will come down to 6 and answer will be 1.
$$[\frac{V}{5}]-[\frac{V}{7}]<2............[V]\frac{1}{5}]-\frac{1}{7}<2..........[V]<35$$

Let us check for the values below it..
(1) 34.....$$[\frac{34}{5}]-[\frac{34}{7}]=1........[6.8]-[4.9]=7-5..NO$$
(2) 33.....$$[\frac{33}{5}]-[\frac{33}{7}]=1........[6.6]-[4.7]=7-5..NO$$
(3) 32.....$$[\frac{32}{5}]-[\frac{32}{7}]=1........[6.4]-[4.6]=6-5=1..YES$$
SO B=32

A+B=3+32=35

c
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Joined: 03 Jun 2019
Posts: 22
Re: [V] denotes the greatest integer less than or equal to 'V'. 'V' is a p  [#permalink]

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05 Jul 2019, 22:17
chetan2u wrote:
nick1816 wrote:
[V] denotes the greatest integer less than or equal to 'V'. 'V' is a positive integer and $$[\frac{V}{5}]-[\frac{V}{7}]=1$$.
If the minimum value of 'V' is 'a' and the maximum value of 'V' is 'b'. What is the value of (a+b)?

A. 33
B. 34
C. 35
D. 40
E. 42

$$[\frac{V}{5}]-[\frac{V}{7}]=1$$

Minimum
When $$\frac{V}{5}$$ just crosses 0.5, while $$\frac{V}{7}$$ remains below 0.5..
This means V can be 3, SO A=3

Maximum
$$[\frac{V}{5}]-[\frac{V}{7}]<2$$, as we can have the difference just below 2, but the answer still as 1, for example 4.5 and 6.4999.
Here 4.5 will become 5, while 6.4999 will come down to 6 and answer will be 1.
$$[\frac{V}{5}]-[\frac{V}{7}]<2............[V]\frac{1}{5}]-\frac{1}{7}<2..........[V]<35$$

Let us check for the values below it..
(1) 34.....$$[\frac{34}{5}]-[\frac{34}{7}]=1........[6.8]-[4.9]=7-5..NO$$
(2) 33.....$$[\frac{33}{5}]-[\frac{33}{7}]=1........[6.6]-[4.7]=7-5..NO$$
(3) 32.....$$[\frac{32}{5}]-[\frac{32}{7}]=1........[6.4]-[4.6]=6-5=1..YES$$
SO B=32

A+B=3+32=35

c

chetan2u

Shouldn't [v] be converted to the next largest integer as per the question. So why are we following the rounding rule of largest if >=.5 and smallest if <0.5.
So if [v]=0.45 then shouldn't it be converted to 1 rather than 0 as it is the largest integer? Sorry if am asking a stupid question, but this one striked without any plausible explanation that proves the other way...!!!

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Re: [V] denotes the greatest integer less than or equal to 'V'. 'V' is a p   [#permalink] 05 Jul 2019, 22:17
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