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Ratio of the number of two digit integers

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Ratio of the number of two digit integers [#permalink] New post 11 Sep 2018, 05:40
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Question Stats:

45% (01:17) correct 54% (02:53) wrong based on 11 sessions
Quantity A
Quantity B
Ratio of the number of two-digit integers whose squares are three-digit numbers to the number of two-digit integers whose squares is a four-digit number
\(\frac{1}{3}\)


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.
[Reveal] Spoiler: OA

Last edited by Carcass on 11 Sep 2018, 10:04, edited 1 time in total.
Edited by Carcass
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Re: Ratio of the number of two digit integers [#permalink] New post 11 Sep 2018, 10:04
Expert's post
Please format the questions according to the rules of the board

https://greprepclub.com/forum/qq-how-to ... -2357.html

It is easy. Thank you for your collaboration.

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Re: Ratio of the number of two digit integers [#permalink] New post 11 Sep 2018, 10:09
Expert's post
Not a good question.

The two numbers (according to statement A) are 10 and 32, which ratio is < 1/3.

However, I could pick other numbers that satisfy the QA condition and the answer would be A.

See here for good questions https://greprepclub.com/forum/greprepcl ... -3523.html

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Re: Ratio of the number of two digit integers [#permalink] New post 11 Sep 2018, 10:59
The answer is correct.

The numbers 10........31 have squares of 3digit .These are 22 numbers.

32......99 have squares of 4 digit.These are 68 numbers.


So we are comparing, 22/68 and 1/3

So the answer is B.:)
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Re: Ratio of the number of two digit integers [#permalink] New post 12 Sep 2018, 02:49
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AchyuthReddy wrote:
Quantity A
Quantity B
Ratio of the number of two-digit integers whose squares are three-digit numbers to the number of two-digit integers whose squares is a four-digit number
\(\frac{1}{3}\)


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.




Two-digit integers are 10 - 99
number of two-digit integers whose squares are three-digit numbers: 22 ( that is 10^2 = 100 and 31^2 = 961, the integers between this two numbers will also have 3-digit number as square)


number of two-digit integers whose squares is a four-digit number: 68 (that is 32^2 = 1024 and 99^2 = 9801, the integers between this two numbers will also have 4-digit number as square)
so,\(\frac{22}{68} = \frac{11}{34} < \frac{1}{3}\)

Option B is answer.
Re: Ratio of the number of two digit integers   [#permalink] 12 Sep 2018, 02:49
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Ratio of the number of two digit integers

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