Data suffeciency Questions Manhattan gmat Ch.10

[golu23]

Guys i'm stuck with these problems need help.

Solve Data Sufficiency Problems #7-14:
7.' Is p divisible by 168?
(1) p is divisible by 14
(2) p is divisible by 12

8. Is pq divisible by 168?
(1) p is divisible by 14
(2) q is divisible by 12

9. Is the sum of integers a and b divisible by 7?
(l)'a is not divisible by 7.
(2) b is not divisible by 7.

10. Is the sum of integers a and b divisible by 7?
(1) a is not divisible by 7.
(2) a - b is divisible by 7.

11. What is the greatest common factor of x and y?
(1) x and yare both divisible by 4.
(2)x- y=4

12. Is x divisible by 120?
(1) x is divisible by 12.
(2) x is divisible by 30.

13. ' Isx divisible by8?
(1) x is divisible by 24.
(2) x is not divisible by 16.

Need some strategy/simple method to solve these kind of questions .

[bblast]

You should try using factoring the expressions :

7. Is p divisible by 168?
(1) p is divisible by 14
(2) p is divisible by 12

looking at the problem statement we realize that 168 is a multiple of 24.
if we factor it we get 168=7*24.
24 can be further written as 12*2 ->that can be written as (2^2*3)*2 = 2^3*3

thus 168 = 7* 2^3*3

now to divide out this entire length of primes we need the same primes in the denominator.



look at the statements

1>p/14 = I, thus we have 2*7 |2>p/12 = I, we got 2^2*3
i dont have any info about the rest factors | but we are still missing a 2 and a 7.

roping in statement 1 we get a 7. But overall we are still missing a 2.

note that we need to take LCM while considering both statements together. So the 2 in statement 1 is already counted while taking the 2-2's from statement 2. Dont make the mistake of adding the number of repetitive 2's and 3's from both the statements.

hence answer is E.

try applyin this to all the problems at hand.