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between 10 and 100

by j_shreyans » Fri Mar 06, 2015 10:19 am
If n is an integer between 10 and 100, is the tens digit of n even?

(1) The remainder when n is divided by 4 is equal to the remainder when n is divided by 5.

(2) The only prime factor of n is 3.

i don't understand statement 2.

Please advise.

Thanks,

Shreyans
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by [email protected] » Fri Mar 06, 2015 10:56 am
HI j_shreyans,

In Fact 2, we're told that the ONLY prime factor of N is 3. This means that if we use prime-factorization to break N down into its prime 'pieces', we will only see 3s (and nothing else).

This is actually a significant "restriction", since N is between 10 and 100

N COULD be 27, since 27 = (3)(3)(3)
N COULD be 81 since 81 = (3)(3)(30(3)

N CANNOT be 9, even though 9 = (3)(3)....because 9 is NOT between 10 and 100
N CANNOT be 18, since 18 = (2)(3)(3) and we're told that N only has 3 as a prime factor.

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by dannydb » Tue Jun 14, 2016 5:25 pm
Isn't this question illegal? Don't both statements need to be true for N. Given statement 1, N can only be either 27 or 81.

Given statement 2, N can only be 20, 40, 60, or 80.

In all cases, the tens digit is even, but N does cannot be part of both sets of information. I thought each statement has to be true for the number or variable discussed.
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by [email protected] » Tue Jun 14, 2016 6:59 pm
Hi dannydb,

To answer your immediate question - NO, this question is fine as it is written. While you are correct that the two Facts/Statements in a DS questions cannot contradict one another, the work that you've provided for the first Fact is incomplete. There are MORE numbers that fit that description than just 20, 40, 60 and 80. For example, 81 has the same remainder when divided by 4 as it has when divided by 5.

Based on your examples, you have not done enough

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