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GRE Whiz Representative
Joined: 25 May 2022
Posts: 25
Given Kudos: 1
The sum of all the digits of 1/(5^5 * 2^9) when it is written in
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Updated on: 06 Sep 2022, 04:05
Updated on: 06 Sep 2022, 04:05
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Question Stats:
78% (01:07) correct
21% (01:16) wrong based on 19 sessions
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Quantity A |
Quantity B |
The sum of all the digits of \(\frac{1}{(5^5 × 2^9)}\) when it is written in decimal format |
The sum of all the digits of \(\frac{1}{(5^6 ×2^{10})}\) when it is written in decimal format |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Source: GREWhiz
Originally posted by SaquibHGREWhiz on 29 Aug 2022, 05:36.
Last edited by SaquibHGREWhiz on 06 Sep 2022, 04:05, edited 2 times in total.
Last edited by SaquibHGREWhiz on 06 Sep 2022, 04:05, edited 2 times in total.
Re: The sum of all the digits of 1/(5^5 * 2^9) when it is written in
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29 Aug 2022, 05:53
29 Aug 2022, 05:53
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1
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Hi
Please when a QCQ question is posted follow the way to format it. It is quite easy here
https://gre.myprepclub.com/forum/how-to-po ... tml#p31620
Just put the two quantities inside the tag [quantity]
Put it in simple terms: When you are going to create a new Quantitative Comparison Question you only need two set up the two quantities to push the tag button.
Insert your values INSIDE the parenthesis
screenshot.819.jpg [ 87.32 KiB | Viewed 1550 times ]
Add always the answer choices
Ask if you need further assistance
carcass
Please when a QCQ question is posted follow the way to format it. It is quite easy here
https://gre.myprepclub.com/forum/how-to-po ... tml#p31620
Just put the two quantities inside the tag [quantity]
Put it in simple terms: When you are going to create a new Quantitative Comparison Question you only need two set up the two quantities to push the tag button.
Insert your values INSIDE the parenthesis
Attachment:
screenshot.819.jpg [ 87.32 KiB | Viewed 1550 times ]
Quote:
[quantity]( quantity A goes here )( quantity B goes here)[/quantity]
Add always the answer choices
Ask if you need further assistance
carcass
GRE Whiz Representative
Joined: 25 May 2022
Posts: 25
Given Kudos: 1
Re: The sum of all the digits of 1/(5^5 * 2^9) when it is written in
[#permalink]
Updated on: 06 Sep 2022, 03:00
Updated on: 06 Sep 2022, 03:00
1
Expert Reply
Solution:
Quantity A:
We have \(\frac{1}{5^5\times 2^9}\)
\(⇒\frac{1}{5^5\times 2^5\times 2^4}\)
\(⇒\frac{1}{5^5\times 2^5}\times \frac{1}{2^4}\)
\(⇒\frac{1}{10^5}\times \frac{1}{2^4}\)
\(⇒\frac{1}{10^5}\times 0.0625\)
\(⇒0.000...625\) (0 as a digit doesn't matter because we are talking about sum here)
Quantity B:
We have \(\frac{1}{5^6\times 2^{10}}\)
\(⇒\frac{1}{5^6\times 2^6\times 2^4}\)
\(⇒\frac{1}{5^6\times 2^6}\times \frac{1}{2^4}\)
\(⇒\frac{1}{10^6}\times \frac{1}{2^4}\)
\(⇒\frac{1}{10^6}\times 0.0625\)
\(⇒0.000...625\) (0 as a digit doesn't matter because we are talking about sum here)
We see that we have the same non-zero digits in both \(\frac{1}{5^5\times 2^9}\) and \(\frac{1}{5^6\times 2^{10}}\)
Hence the right answer is Option C
Quantity A:
We have \(\frac{1}{5^5\times 2^9}\)
\(⇒\frac{1}{5^5\times 2^5\times 2^4}\)
\(⇒\frac{1}{5^5\times 2^5}\times \frac{1}{2^4}\)
\(⇒\frac{1}{10^5}\times \frac{1}{2^4}\)
\(⇒\frac{1}{10^5}\times 0.0625\)
\(⇒0.000...625\) (0 as a digit doesn't matter because we are talking about sum here)
Quantity B:
We have \(\frac{1}{5^6\times 2^{10}}\)
\(⇒\frac{1}{5^6\times 2^6\times 2^4}\)
\(⇒\frac{1}{5^6\times 2^6}\times \frac{1}{2^4}\)
\(⇒\frac{1}{10^6}\times \frac{1}{2^4}\)
\(⇒\frac{1}{10^6}\times 0.0625\)
\(⇒0.000...625\) (0 as a digit doesn't matter because we are talking about sum here)
We see that we have the same non-zero digits in both \(\frac{1}{5^5\times 2^9}\) and \(\frac{1}{5^6\times 2^{10}}\)
Hence the right answer is Option C
Originally posted by SaquibHGREWhiz on 29 Aug 2022, 12:08.
Last edited by SaquibHGREWhiz on 06 Sep 2022, 03:00, edited 2 times in total.
Last edited by SaquibHGREWhiz on 06 Sep 2022, 03:00, edited 2 times in total.
