Gmat Prep Prime and composite

[sdotcruz]

I came across this question in the Gmat Prep software and did not understand the proper manner to solve it.



An Integer greater than 1 that is not prime is called a composite. If the Two-digit integer n 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.




OA will be posted later.

[Gurpinder]

composite number is any number that has more than 2 divisors (1 and itself - which is a prime)

(1) Lets say that N = AB, its saying that b/a=int. this would mean that the number is 22. which is a composite number.

in fact, anytime b/a=int its a composite #.
33 --> 3/3=1
26 --> 6/2=3
28 --> 8/2=4

(2) we don't know anything about the units digit

therefore the answer should be (A).

[Maciek]

Hi all!

IMO A

n is the two-digit integer
n> 20
(1)
let x represent tens and y units
n = x*10 + y

A factor x is the integer that, when multiplied by other factors, gives the integer y.

y/x is the integer
a factor of y is the integer x
a factor of 1 is 1
factors of 2 are 1 and 2
factors of 3 are 1 and 3
factors of 4 are 1 , 2 and 4
factors of 5 are 1 and 5
factors of 6 are 1 , 2, 3 and 6
factors of 7 are 1 and 7
factors of 8 are 1 , 2, 4 and 8
factors of 9 are 1 , 3 and 9
0 has infinite number of factors

n is composite
statement 1 alone is SUFFICIENT

(2)
n = x*10 + y
x = 2

let us plug in numbers
n = 23
it is not a composite, it is prime
n = 24
it is composite
statement 2 alone is INSUFFICIENT

hope it helps!
Best,
Maciek

[Arcane66]

I said A because obviously from B you cannot solve it. Eliminate B & D. A works because just take some prime numbers as an example. Ex: 31. Is 3 a factor of 1? No. Ex: 29. Is 2 a factor of 9? No. Ex: 37. Is 3 a factor if 7? No. Therefore the number is composite.

[GMATGuruNY]

I came across this question in the Gmat Prep software and did not understand the proper manner to solve it.



An Integer greater than 1 that is not prime is called a composite. If the Two-digit integer n 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.

OA will be posted later.

Statement 1:
If the tens digit is a factor of the units digit, then n is divisible by the tens digit and thus is a composite. Sufficient.

Let's examine why.
If n is a 2-digit integer, then n = (multiple of 10) + (units digit):
n = 24 = 20 + 4
n = 39 = 30 + 9
n = 55 = 50 + 5
Note that the multiple of 10 is by definition divisible by the tens digit.
Statement 1 states that the units digit also is divisible by the tens digit.
Thus the sum (the value of n) must be divisible by the tens digit.
Hence n is a composite. Sufficient.

Statement 2:
n = 22. Composite.
n = 23. Not a composite.
Insufficient.

The correct answer is A.

[sanju09]

I came across this question in the Gmat Prep software and did not understand the proper manner to solve it.



An Integer greater than 1 that is not prime is called a composite. If the Two-digit integer n 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.




OA will be posted later.

(1) Since the unit's digit of a two-digit integer n, which is greater than 20, is a multiple of a digit, which is more than 1, then this n is surely a composite. Possible cases, 22, 24, 26, 28, 33, 36, and 39. Sufficient

(2) If tens digit of n is 2, then there are 20 through 29 different possibilities for n, few being primes and few not. Insufficient

[spoiler]A[/spoiler]