og 12 ed #143ps

nafiul9090 wrote:If [x] is the greatest integer less than or equal to x,
what is the value of [–1.6] + [3.4] + [2.7] ?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7


how could i ace this type of problem .........help needed

-2+3+2= 3 hence A
[x] will give the value of greatest integer to the left of the x on the number line.

[-1.6]; x =-1.6; therefore [-1.6] will give the value of greatest integer which is at the lest of -1.6 which is -2; similarly we can see for 3.4 it is 3 and for 2.7 it is 2.

First understand the question.
"If [x] is the greatest integer less than or equal to x"
What do you make of this statement?
The greatest integer possible that should be either equal to the given number of less than. More specifically it should not be greater than the given number.

For eg. Let us try to find [3]. It has to be 2,3 or 4. It cannot be 4 because [X] cannot be greater than X itself.
Is it 2 or 3? It has be 3 because 3 satisfies the given criteria. It is less than or equal to the given number.

Now what is [3.1]
Again, it cannot be 4, because 4 > 3.1
Is it 3? Yes! it is because 3 is an integer and it is < 3.1. Satisfies the question.

Now what is [2.9]
Is it 3? No! 3 > 2.9.
Is it 2? Yes it is. It satisfies the condition.

What about negative numbers?
Try [-1.5]
Is it -1? No because -1 > -1.5 (negative numbers)
Is it -2? Yes it is. it is an integer and it is < -1.5.


Now if the concept is clear.

Let us move to the question. It asks you to add three [] values.
Find each value separately.

[-1.6] = -2 Logic same as above.
[3.4] = 3
[2.7] = 2

So add all these three together.
-2 + 3 + 2 = 3.

Answer is A.

Did I help you? Let me know!

guys its crystal clear right now

manpsingh87 wrote:

nafiul9090 wrote:If [x] is the greatest integer less than or equal to x,
what is the value of [–1.6] + [3.4] + [2.7] ?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7


how could i ace this type of problem .........help needed

-2+3+2= 3 hence A
[x] will give the value of greatest integer to the left of the x on the number line.

[-1.6]; x =-1.6; therefore [-1.6] will give the value of greatest integer which is at the lest of -1.6 which is -2; similarly we can see for 3.4 it is 3 and for 2.7 it is 2.

But why to the left? [/u]

fr743 wrote:

manpsingh87 wrote:

nafiul9090 wrote:If [x] is the greatest integer less than or equal to x,
what is the value of [–1.6] + [3.4] + [2.7] ?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7


how could i ace this type of problem .........help needed

-2+3+2= 3 hence A
[x] will give the value of greatest integer to the left of the x on the number line.

[-1.6]; x =-1.6; therefore [-1.6] will give the value of greatest integer which is at the lest of -1.6 which is -2; similarly we can see for 3.4 it is 3 and for 2.7 it is 2.

But why to the left? [/u]

In general, if n is an integer and x is any real number between n and n+1
i.e. n<=x<(n+1), then [x]=n;

this is the mathematical definition of greatest integer function i can also explain that through graph but that is of no use..in order to solve question on greatest integer function just remember the rule explained by me above..!!

i hope it helps..!!!