What is the greatest integer that is less than

Question

What is the greatest integer that is less than:  -|\sqrt{3}-3|  ?

A. -3

B. -2

C. -1

D. 0

E. 1

Bunuel · Accepted Answer

What is the greatest integer that is less than:  -|\sqrt{3}-3|  ?

A. -3
B. -2
C. -1
D. 0
E. 1

Since  \sqrt{3} < 3 , then  \sqrt{3} - 3 < 0 , and thus   |\sqrt{3} - 3| = -(\sqrt{3} - 3) .

Hence,   -|\sqrt{3} - 3| = \sqrt{3} - 3 . Next, since  \sqrt{3} ≈ 1.7 , we have  \sqrt{3} - 3 ≈ 1.7 - 3 = -1.3 .

The greatest integer that is less than -1.3 is -2.

Answer: B.

ChandlerBong · Answer

Asked:  greatest integer that is less than -| \sqrt{3}  -3|

Solution:

We know  \sqrt{3}  = 1.732

On solving, we get -|1.723 - 3| = -|-1.268| = -1.268 (As on opening the mod, we still have a negative sign)

Hence, the greatest integer less than -1.268 would be -2.

Answer:  B.

BrushMyQuant · Answer

We need to find What is the greatest integer that is less than: \(-|\sqrt{3}-3|\)

We know that |x| = -x when x < 0
=> \(-|\sqrt{3}-3|\) = - (-(\(\sqrt{3}\)-3)) [ as \(\sqrt{3}\)-3 < 0 \

= \(\sqrt{3}\)-3 = 1.7-3 = -1.3

=> Greatest integer less than -1.3 = -2

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Absolute Values

GMATinsight · Answer

Greatest integer less than  -|\sqrt{3} - 3| 
= Greatest integer less than  -|1.7 - 3| 
= Greatest integer less than  -|-1.3| 
= Greatest integer less than  -1.3  = -2

Answer: Option B

rakshith97 · Answer

Can someone explain to me why it is not -3?

DanTheGMATMan · Answer

Pretty straightforward problem:

https://www.youtube.com/watch?v=z_fCdWx2N7g

des5631 · Answer

I'm having trouble with understanding why the answer wouldn't be -3? Can someone explain to me the "greatest integer" relation to "rounding down" in the context of negative numbers... Think I'm getting tripped up with language. Thanks!

Bunuel · Answer

Here is  a complete and detailed solution .

To elaborate even more, we need to round down a number to the closest integer  less  than that number. Here's how it works:
 
The greatest integer that is  less than  4.7 is 4;
The greatest integer that is  less than  -12.1 is -13, because -13 is the greatest integer less than -12.1;
The greatest integer that is  less than  -8 is - 9, because -9 is the greatest integer less than -8.

Thus, the greatest integer that is less than -1.3 is -2.

Hlope it's clear.

For more information, you can check out these links:

13. Functions 
     Theory   
 How to Interpret Unfamiliar Symbols 
 Functions on GMAT 
 A Closer Look at GMAT Function Questions 
     Questions   
 Operations/functions defining algebraic/arithmetic expressions 
 Rounding Functions Problems 
 Various Functions Problems 
  DS Questions 
 PS Questions

For more check below:
 ALL YOU NEED FOR QUANT ! ! ! 
 Ultimate GMAT Quantitative Megathread

Hope this helps.

mm92325 · Answer

I was also stuck with this .
Think: what integers are less than -1.268?
They are -2, -3, -4...

But we want the greatest among these integers — the closest integer that is still less than -1.268.
 • -2 is less than -1.268, and
 • -3 is also less than -1.268, but -3 is smaller than -2.

Since we want the greatest such integer, we pick -2, not -3.

FSingh · Answer

I took the following approach...

−|3√−3| = - |1.7-3|
= -|1.3|

On the number line -2 is greatest integer that is less than -1.3

Number line thinking helped me not get mixed up with the answer choices

GmatKnightTutor · Answer

Being extra careful to not make a careless error with questions like this may be helpful. It may help to think of our target as the CLOSEST integer on the number line to the LEFT of the expression's value.

-|\sqrt{3}-3|

- | ~1.7 – 3 |
- | -(~1.3)|
- (~1.3)

Basically, the value of the expression is approximately -1.3

The closest integer to the left on the number line would therefore be -2

(B) is your answer.

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What is the greatest integer that is less than

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What is the greatest integer that is less than

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