Explanation for DS question

[nadib002]

Is p divisible by 168?

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

Could someone please explain an approach to answer this DS question without substituting numbers?

Thank you


P.S. I am not adding the answer choices since they are same for all the DS questions.

[gmatmachoman]

Is p divisible by 168?

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

Could someone please explain an approach to answer this DS question without substituting numbers?

Thank you


P.S. I am not adding the answer choices since they are same for all the DS questions.

step 1: Find the factors of 168 ---->( 2 ,3,7)

Using St 1:

Factors of 14 2,7)

What if the P is a multiple of 3???. SO factors of 14 won't divide P --St 1 is insufficient

Using st 2:

factors of 12 : (2,3)
What if p is a multiple of 7?? So factors of 12 wont divide P--St 2 is insufficient

Combining St1 & St2:
U an divide P as all three factors are included in the set!!

So C

[ajith]

Is p divisible by 168?

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

Could someone please explain an approach to answer this DS question without substituting numbers?

Thank you


P.S. I am not adding the answer choices since they are same for all the DS questions.

Any number which has factors 4,3 and 7 will be divisible by 14 and 12

84 is smallest of such numbers and it is not divisible by 168

Hence E

[gmatmachoman]

@Ajith

If the question would have been : Is P divisible by 84??

Hope Both statements together will wrk rite??

[eaakbari]

Stem
168 = 2^3 * 7 *3

Hence p will have to have all of the following factors to be divisible by 168

Statement one
14 = 2 * 7
Hence p is div by 2 and 7
But insuff

Statemnent two
2^2 * 3
Hnce p is div by 2^2 and 3
Insuff

Combining
we can say p is div by 2^2 and 3 and 7
But we need another factor of 2 to be div by 168

Hence insuff

Answer E

[ajith]

@Ajith

If the question would have been : Is P divisible by 84??

Hope Both statements together will wrk rite??

Yes it would have worked!

84 is the LCM of 12 and 14!

[anoopprasad]

168 = 14 * 12
So if p is divisible by 14 and 12 it is divisible by 188

Ans: C

[ajith]

168 = 14 * 12
So if p is divisible by 14 and 12 it is divisible by 188

Ans: C

what about 84?

or 252

[thephoenix]

ans is E
clearly s1 and 2 are not suff
lcm of 12 and 14 is 84
combining bth minimum posssible no is 84 which is not div by 168 and rest all are
hence no conclusion and therefore insuff