How many bits of computer memory will be required to store the integer

Question

How many bits of computer memory will be required to store the integer x, where x = -  \sqrt{810,000}  if each digit requires 4 bits of memory and the sign of x requires 1 bit?

(A) 25 
(B) 24 
(C) 17 
(D) 13 
(E) 12

Skywalker18 · Accepted Answer

x = -  \sqrt{810,000} 
 = - 900
Each digit requires 4 bits of memory and sign of x requires 1 bit
Total number of bits of computer memory required = 4*3 + 1
= 13

Answer D

ydmuley · Answer

Hi -  carcass  - Could you please check the validity of the question? I think either the question is incorrect or the answer options are not matching.

Your question only contains x = -  \sqrt{810,000}

Carcass · Answer

The question is correct. I checked it out

ydmuley · Answer

Hello  carcass , may be I am wrong. however, however for me this problem looks exactly similar to the problem in GMAT PLUS where the question is:

{-}\sqrt{810,000} - \sqrt{810,000}

Followed by this option

(A) 25 
(B) 24 
(C) 17 
(D) 13 
(E) 12

Answer for the above question is D - 13 and solution is as per below:

-900 - 900 = -1800

As there are three unique digits and each units require 4 bits answer will be  = 4*3 + 1 = 12+1 = 13

======

Coming back to your question, where you have only given  {-}\sqrt{810,000}

Which will be  -900

And answer would be  = 4*2 + 1 = 8+1 = 9

Please confirm if I am wrong.

KarishmaB · Answer

900 has 3 digits. Note that you are not looking for just the unique digits. You need 4 bits to store each of the digit to know the number. Else, if you just store 9 and 0, the number could be 90, 990, 900 ... etc

vaidyasayali24 · Answer

3 unique digits means:- 
 1) 4 bits of memory
 2) sign x requires 
 3) x requires 1 bit

Are these the 3 unique digits for which we did 4*3?

Sent from my MI 5 using  GMAT Club Forum mobile app

boomtangboy · Answer

Hi, Just wanted to understand why we are not considering that the root of 81,000 shall have two values one positive and the other negative. Would appreciate it if anyone could give clarity on this

Bunuel · Answer

\sqrt{...}  is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign ( \sqrt{...} ) always means non-negative square root.

https://gmatclub.com/forum/download/file.php?id=39502 
 The graph of the function f(x) = √x

Notice that it's defined for non-negative numbers and is producing non-negative results.

TO SUMMARIZE:
 When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative root.  That is:

\sqrt{9} = 3 , NOT +3 or -3;
 \sqrt {16} = 2 , NOT +2 or -2;

Notice that in contrast, the equation  x^2 = 9  has TWO solutions, +3 and -3. Because  x^2 = 9  means that  x =-\sqrt{9}=-3  or  x=\sqrt{9}=3 .

adkikani · Answer

Bunuel

Is highlighted text same as taking absolute modulus?

x^2 = 9

Taking square root on both sides, we get |x| = 9 or x = 3 or x = -3.

Bunuel · Answer

Absolutely. Since  \sqrt{x^2}=|x| , then  x^2 = 9  is equivalent to |x| = 3, which gives x = 3 or x = -3.

Vubar · Answer

Would there be any problem with tackling this question like this (i.e., is there any faulty logic, or would it lead me to get a more difficult question incorrect)?

810,000 has 6 digits. The 81 will come from 9 squared (single digit). The 4 zeros will come from essentially 100 squared. So its square root will have 3 digits.

3*4=12. Add 1 bit for the sign = 13 bits.

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How many bits of computer memory will be required to store the integer

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How many bits of computer memory will be required to store the integer

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