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n is a positive integer between 200 and 500.

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Carcass
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n is a positive integer between 200 and 500. [#permalink] New post   15 Feb 2021, 06:58
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\(n\) is a positive integer between 200 and 500.


Quantity A
Quantity B
The number of possible values of \(n\) with a unit digit of 5
31



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: n is a positive integer between 200 and 500. [#permalink] New post   15 Feb 2021, 07:13
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Hello!!

We can find the number of 5's in units place by simply knowing how many multiples of 5 are there in every 100 numbers.

Thus, we have 20 multiples of 5 from 1-100, even though we are not asked about 1-100 it would be same further.
And from those 20 multiples 10 will have units digit as 5 & 10 will have units digit as 0.
Hence, there are 5 comes 10 times in the units digit in every 100 numbers.
200-300--> 10 times
300-400--> 10 times
400-500--> 10 times

Thus, the total is 30.

Therefore Quantity A< Quantity B

Hope this helps!
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Re: n is a positive integer between 200 and 500. [#permalink] New post   15 Feb 2021, 07:26
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Carcass wrote:
\(n\) is a positive integer between 200 and 500.


Quantity A
Quantity B
The number of possible values of \(n\) with a unit digit of 5
31



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.



Let us say the number is abc

Since, the number is between 200 and 500, we have only 3 values for a (i.e. 2, 3 and 4)

For b, we can 10 values (i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9)

For c, we have only 1 values (i.e. 5)

So, Total numbers = 3 x 10 x 1 = 30

Col. A = 30
Col. B = 31

Hence, option B
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Re: n is a positive integer between 200 and 500. [#permalink] New post   16 Feb 2021, 06:54
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a = 205, l =495, d=10
l=a+(n-1)d
495=205+(n-1)10
290=(n-1)10
29=(n-1)
n=30

option b is correct
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Re: n is a positive integer between 200 and 500. [#permalink] New post   16 Feb 2021, 07:03
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Sometimes using brute force is the best helper out there. Unit digit 5 means the numbers which are going to have 5 in the last position(from left to right).

So, let's consider a batch of 10 number from the range, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210. Only 205 meet our criteria, and there will 30 batches in total, 1 number from each batch is going to meet the criteria.

Now, Qnt A = 30, Qnt B = 31. So, the Answer is B
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Re: n is a positive integer between 200 and 500. [#permalink] New post   16 Feb 2021, 07:54
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Positive integer between 200 to 500 with the units digit being 5.
The list starts with 205 and goes on till 295.
there are a total of 10 numbers in the column with 2 in the hundreds place and 5 in the units.

There will be equal number of integers in the list with 3 and 4 in the hundreds place and 5 in the units place.

therefore 10 x 3=30

Solution: Option B

(In such case I prefer doing the column x rows concept to work out the solutions:
205 305 405
215 - -
225 - -
235 - -
245 - -
255 - -
265 - -
275 - -
285 - -
295 - -

Columns x rows- 3 x 10=30 )
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Re: n is a positive integer between 200 and 500. [#permalink] New post   16 Feb 2021, 14:08
Multiples of 5 end with 0 or 5 alternating...Question has even number range, so we are to sure get an equal number of zero-ending and five-ending multiples...there are (500-200)/5 multiples of 5. Half the 60 end with zero, the other half with 5, so 30.
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Re: n is a positive integer between 200 and 500. [#permalink] New post   16 Feb 2021, 14:12
Multiples of 5 end with 0 or 5 alternating...Question has even number range, so we are to sure get an equal number of zero-ending and five-ending multiples...there are (500-200)/5 multiples of 5. Half the 60 end with zero, the other half with 5, so 30 for A...hence B.
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Re: n is a positive integer between 200 and 500. [#permalink] New post   27 Jul 2022, 04:39
KarunMendiratta wrote:
Carcass wrote:
\(n\) is a positive integer between 200 and 500.


Quantity A
Quantity B
The number of possible values of \(n\) with a unit digit of 5
31



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.



Let us say the number is abc

Since, the number is between 200 and 500, we have only 3 values for a (i.e. 2, 3 and 4)

For b, we can 10 values (i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9)

For c, we have only 1 values (i.e. 5)

So, Total numbers = 3 x 10 x 1 = 30

Col. A = 30
Col. B = 31

Hence, option B



Thank you so much. The best :)
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Re: n is a positive integer between 200 and 500. [#permalink] New post   27 Jul 2022, 11:34
KarunMendiratta wrote:
Carcass wrote:
\(n\) is a positive integer between 200 and 500.


Quantity A
Quantity B
The number of possible values of \(n\) with a unit digit of 5
31



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.



Let us say the number is abc

Since, the number is between 200 and 500, we have only 3 values for a (i.e. 2, 3 and 4)

For b, we can 10 values (i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9)

For c, we have only 1 values (i.e. 5)

So, Total numbers = 3 x 10 x 1 = 30

Col. A = 30
Col. B = 31

Hence, option B


What a clever answer! kudos for you!
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