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PS problem

Expert replies
by vishalwin » Sun Oct 11, 2015 11:29 am
q) How many positive integers less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9?

a)19
b)18
c)17
d)16
e)15

q) How many positive integers less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a multiple of 2 and a positive multiple of 9?

a)19
b)18
c)17
d)16
e)15
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Source: — Problem Solving |

by MartyMurray » Sun Oct 11, 2015 2:56 pm
Positive multiples of 2 that are less than 20 - 2, 4, 6, 8, 10, 12, 14, 16, 18 - 9

Odd multiples of 9 that are less than 20 - 9 - 1

Sum of positive multiple of 2 and positive multiple of 9 - 11, 13, 15, 17, 19 - 5

9 + 1 + 5 = 15

Choose E.
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by Matt@VeritasPrep » Thu Oct 15, 2015 12:07 am
We know we've got 19 positive integers less than 20.

9 of them are multiples of 2: everything from 2*1 to 2*9.

1 of them is an odd multiple of 9.

5 of them are multiples of 2 + 9: 2*1+9 to 2*5+9.

(The nice thing about this counting approach is that it generalizes to something like "How many positive integers less than 10,000,000 are there that have the same qualities?")

So we've got 9 + 1 + 5, or 15 such numbers.
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by vishalwin » Fri Oct 16, 2015 5:54 am
Thanks for the reply.

The confusion arised due to the language of question IN 'either' part.

Can we get questions with wrong usage of either like above in real exam?
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by MartyMurray » Sat Oct 17, 2015 7:25 pm
vishalwin wrote:The confusion arised due to the language of question IN 'either' part.

Can we get questions with wrong usage of either like above in real exam?
I doubt that you would see either used to begin a list of three items on the real exam.

At the same time, the question does seem decipherable even given the unconventional use of either. Maybe you were being a little to technical in the way you read it?
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