Factors

[kop]

Is P divisible by 168??

1) p is divisible by 14
2) p is divisible by 12

Please explain? I solved by taking out prime factors , with that i concluded both statements are enough to answer the question, but that's wrong? . Please explain

[Brent@GMATPrepNow]

Is P divisible by 168??

1) p is divisible by 14
2) p is divisible by 12

Target question: Is P divisible by 168?

A lot of integer property questions can be solved using prime factorization.
For questions involving divisibility, divisors, factors and multiples, we can say:
If N is divisible by k, then k is "hiding" within the prime factorization of N

Examples:
24 is divisible by 3 <--> 24 = (2)(2)(2)(3)
70 is divisible by 5 <--> 70 = (2)(5)(7)
330 is divisible by 6 <--> 330 = (2)(3)(5)(11)
56 is divisible by 8 <--> 56 = (2)(2)(2)(7)

So, for P to be divisible by 168, 168 must be hiding in the prime factorization of P.

Since 168 = (2)(2)(2)(3)(7), we need to determine whether there are AT LEAST three 2's, one 3 and one 7 are hiding in the prime factorization of P. So, let's rephrase our target question . . .

REPHRASED target question: Are three 2's, one 3 and one 7 "hiding" in the prime factorization of P?

Statement 1: p is divisible by 14
Since 14 = (2)(7), we can conclude that one 2 and one 7 are "hiding" in the prime factorization of P.
So, we can't be certain whether or not three 2's, one 3 and one 7 are hiding in the prime factorization of P
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: p is divisible by 12
Since 12 = (2)(2)(3), we can conclude that two 2's and one 3 are "hiding" in the prime factorization of P.
So, we can't be certain whether or not three 2's, one 3 and one 7 are hiding in the prime factorization of P
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that one 2 and one 7 are "hiding" in the prime factorization of P.
Statement 2 tells us that two 2's and one 3 are "hiding" in the prime factorization of P.
So, we can conclude that there are at least TWO 2's, one 3 and one 7 "hiding" in the prime factorization of P.
HOWEVER, our goal is to determine whether there are THREE 2's, one 3 and one 7 "hiding" in the prime factorization of P.
So, we can't be certain whether or not three 2's, one 3 and one 7 are hiding in the prime factorization of P
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

[Uva@90]

Is P divisible by 168??

1) p is divisible by 14
2) p is divisible by 12

Please explain? I solved by taking out prime factors , with that i concluded both statements are enough to answer the question, but that's wrong? . Please explain

Hi Kop,
What you started is correct,
first do the prime factorization,
168 = 2*2*2*3*7
So, Number should have at least three 2's and one 3 and one 7 for divisible by 168.

Statement 1: 14 =2*7
Insufficient.

Statement 2: 12 = 2*2*3
Insufficient.

Combine 1 + 2:
Multiple of both 14 and 12.

Important thing to note here is check both numbers have common factors or not.

Yes it have 14 =2*7 and 12 = 2*2*3

we can number is divisible by 84 = 2*7*2*3 but
we can't say for sure that it is divisible by 168

Hence Insufficient.

Answer is E

Regards,
Uva.

[Brent@GMATPrepNow]

Is P divisible by 168??

1) p is divisible by 14
2) p is divisible by 12

Another approach is to look for counterexamples...

Target question: Is P divisible by 168?
NOTE: 168 = (2)(2)(2)(3)(7)

Statement 1: p is divisible by 14
There are several values of P that satisfy this condition. Here are two:
Case a: P = 168, in which case P is divisible by 168
Case b: P = 84, in which case P is NOT divisible by 168
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: p is divisible by 12
There are several values of P that satisfy this condition. Here are two:
Case a: P = 168, in which case P is divisible by 168
Case b: P = 84, in which case P is NOT divisible by 168
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several values of P that satisfy this condition. Here are two:
Case a: P = 168, in which case P is divisible by 168
Case b: P = 84, in which case P is NOT divisible by 168
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent