If ⌈n⌉ denotes the least integer greater than or equal to n and ⌈n/2 -

Question

If ⌈n⌉ denotes the least integer greater than or equal to n and ⌈n/2 - n/3⌉= -1 which of the following could be the value of n ?

A) -10
B) - 5
C) 5
D) 10
E) 15

Bunuel · Accepted Answer

We are given that function ⌈ ⌉ rounds UP a number to the nearest integer, for example:

= 2  since 2 is the least integer which is no less than 1.5;

=0  since 0 is the least integer which is no less than -0.5;

= 1  since 1 itself is the least integer which is no less than 1;
...

Back to the question:

⌈\frac{n}{2 }- \frac{n}{3}⌉= -1 ;

⌈\frac{3n-2n}{6 }⌉= -1 ;

⌈\frac{n}{6 }⌉= -1

Since function ⌈x⌉ denotes the least integer greater than or equal to x, then n/6 must be  -2 < \frac{n}{6} \leq -1  (any number from -2 to -1, when rounds UP to the nearest integer gives -1)

-2 < \frac{n}{6} \leq -1

-12 < n \leq -6

Answer: A.

chetan2u · Answer

For your solution...
Simplify the term..⌈ \frac{n}{2} - \frac{n}{3} ⌉= -1...... \frac{n}{6} ]=-1
As ⌈n⌉ denotes the least integer greater than or equal to n,  \frac{n}{6}\leq{-1}.....n\leq{-6}

Only A possible..

You could also substitute value of n from choices
 \frac{n}{6} ]=-1

A) -10...... \frac{n}{6} ]= \frac{-10}{6} ]=-1.67..Immediate greater integer = -1..YES
B) - 5...... \frac{n}{6} ]= \frac{-5}{6} ]=-0.8..Immediate greater integer =  0
eq{-1} 
C) 5...... \frac{n}{6} ]= \frac{5}{6} ]=0.8..Immediate greater integer =  1
eq{-1} 
D) 10...... \frac{n}{6} ]= \frac{10}{6} ]=1.67..Immediate greater integer =  2
eq{-1} 
E) 15...... \frac{n}{6} ]= \frac{15}{6} ]=2.5..Immediate greater integer =  3
eq{-1}

A

BrushMyQuant · Answer

⌈n⌉ denotes the least integer greater than or equal to n and  ⌈\frac{n}{2} - \frac{n}{3}⌉ = -1 and we need to find which of the following could be the value of n

⌈\frac{n}{2} - \frac{n}{3}⌉  = -1
 ⌈\frac{3n}{6} - \frac{2n}{6}⌉  = -1
=>  ⌈\frac{n}{6}⌉  = -1

Let's take each option choice and check which one satisfies this

A) -10 
=>  ⌈\frac{-10}{6}⌉  = -1
=>  ⌈\frac{-10}{6}⌉  ~ ⌈-1.6⌉ = -1 ( as -1 is just greater than -1.6) -1 =>   TRUE  
In Test, we don't need to solve further. But I am solving to complete the solution

B) -5 
=>  ⌈\frac{-5}{6}⌉  = -1
=>  ⌈\frac{-5}{6}⌉  ~ ⌈-0.8⌉ = 0 ( as 0 is just greater than -0.8) ≠ -1 =>   FALSE

C) 5 
=>  ⌈\frac{5}{6}⌉  = -1
=>  ⌈\frac{5}{6}⌉  ~ ⌈0.8⌉ = 1 ( as 1 is just greater than -0.8) ≠ -1 =>   FALSE

D) 10 
=>  ⌈\frac{10}{6}⌉  = -1
=>  ⌈\frac{10}{6}⌉  ~ ⌈1.6⌉ = 2 ( as 2 is just greater than 1.6) ≠ -1 =>   FALSE

E) 15 
=>  ⌈\frac{15}{6}⌉  = -1
=>  ⌈\frac{15}{6}⌉  ~ ⌈3.5⌉ = 4 ( as 4 is just greater than 3.5) ≠ -1 =>   FALSE

So,  Answer will be A .
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

https://www.youtube.com/watch?v=b7JoMX0gk8M

bumpbot · Answer

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If ⌈n⌉ denotes the least integer greater than or equal to n and ⌈n/2 -

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