How many odd integers between 200 and 600 are there such

Question

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

Bunuel · Accepted Answer

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

The hundreds digit can take 4 values: 2, 3, 4 and 5;
The tens digit can take 5 values: 0, 2, 4, 6 and 8;
The units digit can take 5 values: 1, 3, 5, 7 and 9;

Total: 4*5*5=100.

Answer: C.

sriharimurthy · Answer

The definition of even and odd covers all integers such that : 
(a) Any number which, when divided by 2, leaves a remainder 0 is EVEN.
(b) Any number which, when divided by 2, leaves a remainder 1 is ODD.

Thus 0, being an integer and satisfying condition (a), is an EVEN number.

bschooladmit · Answer

I guess the easier way to do this would be.

400 numbers between - 200 & 600 
Out of which half would be even, half odd. 
Number of odd = 200. Of this.. the one with even tenth digit would be half again. hence 100.

KevinBrink · Answer

This has got nothing to do with the question, however according to the Sum formula aren't there 399 numbers between 200 and 600, i.e. 599-201 = 398 + 1 = 399????

Bunuel · Answer

It depends whether we include 200 and 600.

There are 401 integers from 200 to 600, both inclusive;
There are 400 integers from 200 to 600, including 600 or 200.
There are 399 integers from 200 to 600, both exclusive.

Hope it's clear.

KevinBrink · Answer

Yes thank you that is what I thought also, but then Asax is wrong? Isn't he or she?!

Bunuel · Answer

I guess asax meant that there are 400 integers from 201 to 600, both inclusive.

KevinBrink · Answer

Ok thanks Bunuel for the clear explanation!

gmatgeek · Answer

even when you exclude 200 and 600 there will be 200 odd numbers and 100 out of which will have tenths digit as even

CEdward · Answer

Total brain fart. Ever get those instances where your brain just stares blankly at the page and nothing is being processed? 6 minutes.

Pattern recognition is key here.

Tens digit is even means 0,2,4,6,8
3-digit integer must also be odd

201 202 203 204 205 206 207 208 209 <--- Only 5 of these satisfy the condition.
221 222 223... <--- Only 5 of these satisfy

For every X00 series where X is 2,3,4,5 there are a total of 25 digits that satisfy the condition

4 x 25 = 100

Answer is C.

bumpbot · Answer

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How many odd integers between 200 and 600 are there such

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How many odd integers between 200 and 600 are there such

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