DS from GMAT Prep software

[Anonymous]

This came on my GMAT practice exam from official software.

An interger greater than 1 that is not prime is called composite. If the two digit integer is greater than 20, is n composite.

1. The tens digit of n is a factor of the units digit of n
2. The tens digit of n is 2.

I chose C. The answer is A. Please explain.

23, 2 not divisible by 3 but for 31 three is factor of 1.

[akshata.udiavar]

For condition one - They have mentioned that ten's digit is a factor of one's digit.
Implying that numbers are - 22 ( 2 is factor of 2 ) , 24 ( 2 is a factor of 4 ) , 26, 28, 33, 36, 39 etc. Thus these numbers are composite as they are not prime.

Condition 2 , gives us 21,22,23,24....29. Of which 23, 29 are prime . Thus insufficient.

IMO - A .

[Anonymous]

Thanks a lot. I was considering it the opposite way for the option 1.

[RonPurewal]

For condition one - They have mentioned that ten's digit is a factor of one's digit.
Implying that numbers are - 22 ( 2 is factor of 2 ) , 24 ( 2 is a factor of 4 ) , 26, 28, 33, 36, 39 etc. Thus these numbers are composite as they are not prime.

Condition 2 , gives us 21,22,23,24....29. Of which 23, 29 are prime . Thus insufficient.

IMO - A .

nicely done.

the reason why none of the numbers in (1) are prime is because they are guaranteed to be multiples of the tens digit.

(this is also the reason for the rather strange restriction that stipulates that the numbers be greater than 20; if the teens were allowed, then some prime numbers would be allowed into the mix.)

[dechanter2003]

hi

I have a question


what about 12, 13, 14...

In those numbers the tens digit of n is a factor of the units digit of n.. but those numbers are not greater than 20.. im confused.

thanks

[RonPurewal]

hi

I have a question


what about 12, 13, 14...

In those numbers the tens digit of n is a factor of the units digit of n.. but those numbers are not greater than 20.. im confused.

thanks

the problem says "if n is greater than 20..." -- in other words, you don't consider numbers unless they are greater than 20. so, the numbers you've listed don't constitute exceptions, because they are not under consideration in this problem in the first place.

[parakh.rahul]

Could we say that this is the application of the rule: a prime number is only divisible by itself or 1?

And since the tens digit is a factor of the units digit of n, it implies that the number is divisible by a number other than itself and 1. Is this reasoning correct?

[RonPurewal]

Could we say that this is the application of the rule: a prime number is only divisible by itself or 1?

And since the tens digit is a factor of the units digit of n, it implies that the number is divisible by a number other than itself and 1. Is this reasoning correct?

yes, although i don't think it's very straightforward to jump from the first statement here to the second without considering enough specific examples to understand the pattern (as has been done by the user named "akshata.udiavar" above). once you look at enough such examples, it should become a lot more clear why the divisibility will always occur.

[rr.hbti]

Hi,

i followed the below approach for stm A:

the number be of the form
AB
= 10A + B (splitting the number)

now here we are told A is a factor of B and AB>20
so the number 10A+B will be of the form A(10+integer).

This shows that AB can be written as integer*integer => non prime => composite.

Please correct if I am wrong.

Thanks.

[RonPurewal]

Hi,

i followed the below approach for stm A:

the number be of the form
AB
= 10A + B (splitting the number)

now here we are told A is a factor of B and AB>20
so the number 10A+B will be of the form A(10+integer).

This shows that AB can be written as integer*integer => non prime => composite.

Please correct if I am wrong.

Thanks.

extremely well done.

[skullz03]

For condition one - They have mentioned that ten's digit is a factor of one's digit.
Implying that numbers are - 22 ( 2 is factor of 2 ) , 24 ( 2 is a factor of 4 ) , 26, 28, 33, 36, 39 etc. Thus these numbers are composite as they are not prime.

Condition 2 , gives us 21,22,23,24....29. Of which 23, 29 are prime . Thus insufficient.

IMO - A .

Why are we not choosing numbers like 21, 25, 27- Here 2 is not a factor of unit digit and yet they are composite. "A" could be wrong?

[tim]

if you are testing statement 1 by picking numbers, the numbers you pick must fit the constraints of the statement. none of your examples do. remember, you must take the statement as a given and try to answer the question at the top of the page, not the other way around..