Just confused!

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How many odd integers between 200 and 600 are there such that their tens digit is even?

A. 20
B. 25
C. 100
D. 150
E. 200

Answer -C

[rakeshd347]

How many odd integers between 200 and 600 are there such that their tens digit is even?

A. 20
B. 25
C. 100
D. 150
E. 200

Answer -C

Think it logically rather than mathematically.

There are 400 integers between 200 and 600. Out of which half will be even and half will be odd. So there are 200 odd integers. Now out of 200 odd integers half will have tens digit even and half will have tens digit odd. So out of 200 only 100 will have tens digit even.

Because we have 5 odd digits (1,3,,5,7,9) and 5 even digits(0,2,4,6,8).

So the correct answer is [/spoiler]C[spoiler][/spoiler]

[Brent@GMATPrepNow]

How many odd integers between 200 and 600 are there such that their tens digit is even?

A. 20
B. 25
C. 100
D. 150
E. 200

Take the task of "building" suitable numbers and break it into stages.

Stage 1: Select a hundreds digit
The hundreds digit must be 2, 3, 4 or 5, so we can complete stage 1 in 4 ways

Stage 2: Select a tens digit
The tens digit must be 0, 2, 4, 6 or 8, so we can complete stage 2 in 5 ways

Stage 3: Select a units digit
The units digit must be 1, 3, 5, 7, or 9, so we can complete stage 3 in 5 ways

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus build a suitable number) in (4)(5)(5) ways ([spoiler]= 100 ways[/spoiler])

Answer: C

Cheers,
Brent

Aside: For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775