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

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carcass
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How many bits of computer memory will be required to store the integer [#permalink] New post   03 Jul 2017, 13:41
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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
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D
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ydmuley
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Re: How many bits of computer memory will be required to store the integer [#permalink] New post   03 Jul 2017, 13:51
carcass wrote:
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


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 = - \(\sqrt{810,000}\)
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Re: How many bits of computer memory will be required to store the integer [#permalink] New post   03 Jul 2017, 13:55
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The question is correct. I checked it out
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Re: How many bits of computer memory will be required to store the integer [#permalink] New post   03 Jul 2017, 14:05
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carcass wrote:
The question is correct. I checked it out


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.
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Re: How many bits of computer memory will be required to store the integer [#permalink] New post   03 Jul 2017, 20:31
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carcass wrote:
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


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
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Re: How many bits of computer memory will be required to store the integer [#permalink] New post   03 Jul 2017, 21:06
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ydmuley wrote:
carcass wrote:
The question is correct. I checked it out


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.


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
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Re: How many bits of computer memory will be required to store the integer [#permalink] New post   13 Mar 2018, 20:42
ydmuley wrote:
carcass wrote:
The question is correct. I checked it out


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.

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
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Re: How many bits of computer memory will be required to store the integer [#permalink] New post   13 Mar 2018, 21:39
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VeritasPrepKarishma wrote:
ydmuley wrote:
carcass wrote:
The question is correct. I checked it out


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.


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


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
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Re: How many bits of computer memory will be required to store the integer [#permalink] New post   13 Mar 2018, 21:44
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boomtangboy wrote:
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


\(\sqrt{...}\) 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.


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;
\(\sqrt[4]{16} = 2\), 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 \(x=\sqrt{9}=3\).
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Re: How many bits of computer memory will be required to store the integer [#permalink] New post   13 Mar 2018, 22:18
Bunuel

Quote:
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 \(x=\sqrt{9}=3\)


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.
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Re: How many bits of computer memory will be required to store the integer [#permalink] New post   13 Mar 2018, 22:29
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adkikani wrote:
Bunuel

Quote:
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 \(x=\sqrt{9}=3\)


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.


Absolutely. Since \(\sqrt{x^2}=|x|\), then \(x^2 = 9\) is equivalent to |x| = 3, which gives x = 3 or x = -3.
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Re: How many bits of computer memory will be required to store the integer [#permalink] New post   20 Dec 2021, 06:21
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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Re: How many bits of computer memory will be required to store the integer [#permalink] New post   13 Mar 2024, 05:32
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Re: How many bits of computer memory will be required to store the integer [#permalink]
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