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Even integers less then 100?

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Even integers less then 100?

by HPengineer » Sat Nov 27, 2010 8:39 pm
How many positive even integers less then 100 contain digits 4 or 7.

A.) 16
B.)17
C.)18
D.) 19
E.)20

I tried something as follows but am unable to get the correct answer.

first i started with 4

so 4, 40, 42, 44, 46, 48, 24, 64, 84 giving me 9 numbers that have a 4 and are even.


now using 7

70,72,74,76,78, since 7 is not even number it can not be in the second place so we have only 5 numbers

9 number + 5 numbers is only 14... that is not even answer choice... what numbers am i missing?
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by beat_gmat_09 » Sat Nov 27, 2010 8:42 pm
14,34,54,94
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by HPengineer » Sat Nov 27, 2010 8:44 pm
damn it i was fixated on number starting with 4... and 7 only...

Is there any formula i could use here to avoid hicups as such?

thanks for the answer..
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by Laura GMAT Tutor » Sat Nov 27, 2010 9:17 pm
I'd suggest being more systematic. Choose something to list and then stick with it. It ensures you don't forget any, and it makes counting easier. If you have to find a lot more numbers, then you can write out enough to see the pattern, and then just go based on the pattern. There isn't a formula exactly, but if you've done a few of these you're less likely to forget a large group.

In this problem, one way to write the list would be:

First, try the numbers that have 4 at the end:

4,14, 24,34, 44, 54, 64, 74, 84, 94 = 10 ways
Then the numbers that have 4 at the beginning

40, 42, (44), 46, 48, = 4 ways

Then the numbers that have 7 at the end, well none of those are even.

Then the numbers that have 7 at the beginning:
70, 72, (74), 76, 78 = 4 ways
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by rishab1988 » Sun Nov 28, 2010 1:38 am
My approach:

Find all integers ending in 4 [they re all even]

04[same as 4.This is logic],14,24,...94 [This is like counting from 0 to 9 [in tens digit]. Therefore no of integers both inclusive =9-0=9 +1 [for inclusive]=10

Now 40 42 46 48 [Do not count 44 - already included in first list].Total =4

Now 70 72 76 78 =4 [ 74 would be repeated.]

I didn't include any integers that have 7 as their units digit ,for they are all odd.

total integers = 10+4+4 =18
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by anirudhbhalotia » Sun Nov 28, 2010 2:08 am
Very first thing is to read the question very carefully!

It says 4 or 7...not starting with 4 or 7, and also not 4 and 7!

Then I did the manual listing of nos. and counting. Since the range is 100, this is the least complicated way for me and also to not get confused.

For bigger ranges, I am not too sure of the approach.
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