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Mark’s clothing store uses a bar-code system to identify every item.

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Mark’s clothing store uses a bar-code system to identify every item.  [#permalink]

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New post Updated on: 15 Dec 2019, 21:42
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Mark’s clothing store uses a bar-code system to identify every item. Each item is marked by a combination of 2 letters followed by 3 digits. Additionally, the three-digit number must be even for male products and odd for female products. If all apparel products start with the letter combination AP, how many male apparel items can be identified with the barcode?

A) 100

B) 405

C) 500

D) 729

E) 1000

Originally posted by sjuniv32 on 15 Dec 2019, 10:27.
Last edited by Bunuel on 15 Dec 2019, 21:42, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Mark’s clothing store uses a bar-code system to identify every item.  [#permalink]

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New post 15 Dec 2019, 14:14
It is a happy news that the letter combination is fixed, so we don't need to put it into account.
we just have 3 digits, each should accept up to 10 different possible integers (0 to 9) except the unit digit which can only accept 5 different possibilities to maintain an even number (0,2,4,6,8)
so the maximum identifiable items for men = 10*10*5 = 500
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Re: Mark’s clothing store uses a bar-code system to identify every item.  [#permalink]

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New post 15 Dec 2019, 15:52
sjuniv32 wrote:
:) Mark’s clothing store uses a bar-code system to identify every item. Each item is marked by a combination of 2 letters followed by 3 digits. Additionally, the three-digit number must be even for male products and odd for female products. If all apparel products start with the letter combination AP, how many male apparel items can be identified with the barcode?

A) 100

B) 405

C) 500

D) 729

E) 1000


1st digit = 10 options (0-9 digits)
2nd digit = 10 options (0-9 digits)
3rd digit = 5 options (even digits - 0, 2, 4, 6, 8)
—> Total ways = 10*10*5 = 500

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Re: Mark’s clothing store uses a bar-code system to identify every item.  [#permalink]

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New post 15 Dec 2019, 16:10
men: AP**#
* 0-9
# must be an even digit, therefore 10*10*5=500
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Mark’s clothing store uses a bar-code system to identify every item.  [#permalink]

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New post 10 Jan 2020, 13:48
I see how the statement “each item is marked by a combination of 2 letters followed by 3 digits” implies that any digit will do at any of the three locations.

However, most official GMAT questions I’ve seen that specify “a three digit number” typically exclude “0” as a choice for the hundreds digit.

Not trying to be difficult, but I believe that this distinction is crucial to correctly setting up combinatorics questions on the exam.

Thank you,

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Re: Mark’s clothing store uses a bar-code system to identify every item.  [#permalink]

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New post 28 Mar 2020, 22:42
hi, can someone help me to understand. it says the 3 digit number must be even. Does that mean the entire 3 digit to be even or just the unit number? because no where it says last number should be even?
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Re: Mark’s clothing store uses a bar-code system to identify every item.  [#permalink]

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New post 29 Mar 2020, 01:36
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Hi Geet91,

it will depend only on the Unit digit of the number to be identified as even or odd. for e.g. 12 or 22 is even(Unit digit 2).
In case of above question, we can have such format APXXY where X can be any value from 0 to 9, and Y can be any among 0, 2, 4, 6, 8 to qualify as even number.

Hope it is clear!

Geet91 wrote:
hi, can someone help me to understand. it says the 3 digit number must be even. Does that mean the entire 3 digit to be even or just the unit number? because no where it says last number should be even?

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Re: Mark’s clothing store uses a bar-code system to identify every item.  [#permalink]

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New post 04 Jun 2020, 10:21
In this question, it has to be 3 digit number

units place has to have (0,2,4,6,8) - 5 ways
tens place can numbers between (0 to 9)
Hudred place should have numbers (1to9 ) excluding zero as a three digit number with zero at hundredths place will represent a 2 digit number . eg 024.

shouldn't it be 9*10*5 = 450 ways

Please clarify egmat
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Re: Mark’s clothing store uses a bar-code system to identify every item.   [#permalink] 04 Jun 2020, 10:21

Mark’s clothing store uses a bar-code system to identify every item.

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