For all numbers n, the symbol [n] denotes the greatest integer less

Question

For all numbers n, the symbol denotes the greatest integer less than or equal to n. What is the value of + + ? A. 3 B. 4 C. 5 D. 6 E. 8 2024-01-29_11-43-37.png

Bunuel · Answer

+   +   =

=   +   +   =

= 1 + 2 + 2 =

= 5.

Answer: C.

Danou · Answer

Could you elaborate? I don't understand the question/answer.

bb · Answer

Hi. if a number is Square Root of 5, which technically is 2.23, that means   = 2, since it has to be the largest integer that is lesser or equal to n. Does that make sense?
It is a bit convoluted, but you can figure it out after trying the question a bit. 
Hope it helps.

Bunuel · Answer

The square brackets in this question represent the 'floor function', which rounds down a number to the closest integer less than or equal to that number. Here's how it works:

= 4, because 4 is the greatest integer less than or equal to 4.7;
  = 7, because 7 is the greatest integer less than or equal to 7;
  = -13, because -13 is the greatest integer less than or equal to -12.1;
  = - 8, because -8 is the greatest integer less than or equal to -8.

Since √2 ≈ 1.4, then   = 1, because 1 is the greatest integer less than or equal to 1.4;
Since √5 ≈ 2.2, then   = 2, because 2 is the greatest integer less than or equal to 2.2;
Since √7 ≈ 2.6, then   = 2, because 3 is the greatest integer less than or equal to 2.6.

Hope 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.

GMATinsight · Answer

Given,     denotes the greatest integer less than or equal to n

Now,   = the greatest integer less than or equal to √2 = the greatest integer less than or equal to 1.4 = 1
Similarly,   = the greatest integer less than or equal to √5 = the greatest integer less than or equal to 2.2 = 2
Similarly,   = the greatest integer less than or equal to √7 = the greatest integer less than or equal to 2.7 = 2

i.e.   +   +   = 1+2+2 = 5

Answer: Option C

SergejK · Answer

It's easier to check for squares of larger and smaller integers if one doesn't see right away what the square routes of those numbers are.

1^2<sqrt(2)<2^2, hence 1
2^2<sqrt(5)<3^2, hence 2
2^2<sqrt(7)<3^2, hence 2

1+2+2=5

For all numbers n, the symbol [n] denotes the greatest integer less

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For all numbers n, the symbol [n] denotes the greatest integer less

Prep Toolkit

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