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# If 18 < x < 68, is the integer x even?

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Joined: 02 Sep 2009
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If 18 < x < 68, is the integer x even?  [#permalink]

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09 Mar 2016, 13:06
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Difficulty:

75% (hard)

Question Stats:

51% (01:07) correct 49% (01:24) wrong based on 55 sessions

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If 18 < x < 68, is the integer x even?

(1) Neither the tens digit nor the units digits of x is prime.
(2) Sum of the tens digit and units digit of x is prime.

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If 18 < x < 68, is the integer x even?  [#permalink]

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Updated on: 09 Mar 2016, 15:22
According to how i went on solving this, i got the answer as C.

1) neither units nor tens digit is prime.

=> it is composite
=> possible numbers for both - 4,6,8,9
which will give numbers such as 44, 46, 48, 49 - here you get both even and odd => not sufficient

2) Sum of tens and units digit is prime
=> possible tens digit nos - 1,2,3,4,5,6,
possible units digit nos- 1,2,3,5,6,7,8,9,0

=> some of the numbers are - 20,21,25,29,32 .. - here again you get both even and odd => not sufficient

1)+2)
=> possible number for tens and units places - 4,6
possible number for units places - 4,6,8,9
sum of tens and units digits is prime
=> will give only one answer 13 (49; 4+9 =13) odd => x is not even

Originally posted by PSV01 on 09 Mar 2016, 13:24.
Last edited by PSV01 on 09 Mar 2016, 15:22, edited 1 time in total.
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Joined: 15 Feb 2016
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If 18 < x < 68, is the integer x even?  [#permalink]

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Updated on: 12 Mar 2016, 10:17
Bunuel wrote:
If 18 < x < 68, is the integer x even?

(1) Neither the tens digit nor the units digits of x is prime.
(2) Sum of the tens digit and units digit of x is prime.

I was able to do this in half a minute but took me 15 minutes to try to write down the thinking process. Writing confused me

Will give writing a shot nevertheless

Tens can be 2,3,4,5,6 Units can be anything from 0 to 9 plus number 19

Statement 1

Forget 10s digit, the units digit can be 1,4,6,8,9
clearly, x can be odd or ever
Not sufficient

Statement 2

Prime sum options 21,23,25,32 etc
Since these are both odd and even numbers
Not sufficient

Together
realising that 2 can not be the units digit (since it is prime) 4,6,or 8 in units will sum up to prime numbers only when ten's digit is prime. So can't be.

Possible values
19,41,49,61

Only Odd

Hence C

Correction in the posted Question - Neither the tens digit nor the units digit s of x is prime.
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Originally posted by KarishmaParmar on 09 Mar 2016, 13:48.
Last edited by KarishmaParmar on 12 Mar 2016, 10:17, edited 1 time in total.
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Re: If 18 < x < 68, is the integer x even?  [#permalink]

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09 Mar 2016, 15:13
KarishmaParmar

Though you have arrived at the same answer like me Don't forget that 1 is neither prime nor composite
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Re: If 18 < x < 68, is the integer x even?  [#permalink]

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06 Oct 2017, 23:40
PSV01 wrote:
KarishmaParmar

Though you have arrived at the same answer like me Don't forget that 1 is neither prime nor composite

The question says the number is not prime. It does not say that the number is not composite. Hence 1 should be included.
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Re: If 18 < x < 68, is the integer x even?  [#permalink]

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06 Oct 2017, 23:41
KarishmaParmar wrote:
Bunuel wrote:
If 18 < x < 68, is the integer x even?

(1) Neither the tens digit nor the units digits of x is prime.
(2) Sum of the tens digit and units digit of x is prime.

I was able to do this in half a minute but took me 15 minutes to try to write down the thinking process. Writing confused me

Will give writing a shot nevertheless

Tens can be 2,3,4,5,6 Units can be anything from 0 to 9 plus number 19

Statement 1

Forget 10s digit, the units digit can be 1,4,6,8,9
clearly, x can be odd or ever
Not sufficient

Statement 2

Prime sum options 21,23,25,32 etc
Since these are both odd and even numbers
Not sufficient

Together
realising that 2 can not be the units digit (since it is prime) 4,6,or 8 in units will sum up to prime numbers only when ten's digit is prime. So can't be.

Possible values
19,41,49,61- 19 should not be included here. 10 is not a prime.
Only Odd

Hence C

Correction in the posted Question - Neither the tens digit nor the units digit s of x is prime.
Re: If 18 < x < 68, is the integer x even? &nbs [#permalink] 06 Oct 2017, 23:41
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