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

Question

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

A) 100

B) 405

C) 500

D) 729

E) 1000

Samuel0709 · Answer

Total no of ways of selecting first digit : 10 ( 0-10) 
Total no of ways of selecting second digit : 10 (0-10)
Total no of ways of selecting third digit : 5 (0,2,4,6,8)
Total no of ways : 10 x 10 x 5 = 500 ways

100mitra · Answer

A * P * 100th Digit * 10th Digit * 1 Digit (only even)
1 * 1 * 10 * 10 * 5 = 500 ways

An78w · Answer

@Banuel - how to decide where to include zero as an option for the first place? In this question we’re saying that number of options for the first place is 10 numbers but wouldn’t it make it a Two digit number if we start with 0?

Teitsuya · Answer

"If all apparel products start with the letter combination AP"
Hmmm, maybe I interpreted this message wrongly. 
I though it can formed as "AP" or "PA" as well.

wtstone · Answer

I agree. it specifically used the word "combination" which implies, to me, that it can be "AP" or "PA". I hope that the test won't word a question that leaves room for this ambiguity.

Rainman91 · Answer

Basically the question boils down to asking how many even numbers up to 3 digits are there? 
In GMAT, 0 is considered an even number (But neither a positive nor a negative number). 
1000/2 (since half are even) equals to 500. \

all apparel starts with AP. And we are trying to find number of male apparel products we can include in the store. so question of does not matter. PA is not representative of apparel products.

MegaMBA · Answer

The STATEMENT says 3 Digit Number. 
How can a 3 digit number start with 0? shouldn't the Answer be 1x 9x10x5 = 450 ?

SN_09 · Answer

Even I am thinking the same. Can someone please confirm why we are considering 0 for the Hundredths place in the code?

Bunuel  - if you can please shed some light on this one? Thanks!

Bunuel · Answer

In the setup, the question states, "Each item is marked by a combination of 2 letters followed by  3 digits ," implying that any digit is permissible. Nevertheless, I concur that it would have been clearer if they had followed this with, "Additionally, the last digit must be even for male products and odd for female products."

Chibvike · Answer

"Additionally, the three-digit number must be even for male products and odd for female products."

I think a more appropriate way to phrase this would be "Additionally, **THE PRODUCT** of the three-digit number must be even for male products and odd for female products."

I had mistakenly interpreted it to mean that the three-digit must be even so I did 5*5*5 to represent the number of ways to select the three-digits

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.

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