Data Sufficiency

I have a conceptual issue on questions like these, can someone please suggest a good approach ?

If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105?

(1) x is a multiple of 9

(2) y is a multiple of 25

Thanks in advance
-Ricky

rickyishere wrote:I have a conceptual issue on questions like these, can someone please suggest a good approach ?

If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105?

(1) x is a multiple of 9

(2) y is a multiple of 25

Thanks in advance
-Ricky

always break down numbers and variables by primes.

x = 2*3 (because x is divisible by 6 so X must have all the prime factors of 6)
y = 2*7 (because y is divisible by 14 so y must have all the prime factors of 14)
105 = 5*3*7

we want to know whether xy = (105) (some other number) or another example would be 6 = 3x2

we already know that xy have the following prime factors:
x*y = 2*3*2*7

to check whether a number is a multiple of another number, it must have all the prime factors of that other number.

so

Statement (1)

x = 3*3, we already know x = 2*3
x could be have 7 and 5 and cannot have 7 and 5. Insufficient.

Statement (2)

y= 5*5
for 105 we need 5*3*7. We already know, y=2*7, x = 2*3

x*y = 5*5*2*7*2*3

Sufficient.

Thus, B is the answer.

The question tells us;

Known factors of;

x = 2 * 3, ...

y = 2 * 7, ...

105=2*5*7

The question rephrased is;

is 5 a factor of x or y.

1) This simply tells us that x has 3^2 as a factor. This does not tell us there is a 5 so it does not answer the question. Insufficient.

2) This tells us y has 5^2 as a factor. This allows us to conclude that xy has 5 as a factor and that xy is a multiple of 105. Sufficient.

B is and answer.

Can you please confirm that OA?

Hope this helps.

Thanks,

Jared

Gurpinder wrote:

rickyishere wrote:I have a conceptual issue on questions like these, can someone please suggest a good approach ?

If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105?

(1) x is a multiple of 9

(2) y is a multiple of 25

Thanks in advance
-Ricky

always break down numbers and variables by primes.

x = 2*3 (because x is divisible by 6 so X must have all the prime factors of 6)
y = 2*7 (because y is divisible by 14 so y must have all the prime factors of 14)
105 = 5*3*7

we want to know whether xy = (105) (some other number) or another example would be 6 = 3x2

we already know that xy have the following prime factors:
x*y = 2*3*2*7

to check whether a number is a multiple of another number, it must have all the prime factors of that other number.

so

Statement (1)

x = 3*3, we already know x = 2*3
x could be have 7 and 5 and cannot have 7 and 5. Insufficient.

Statement (2)

y= 5*5
for 105 we need 5*3*7. We already know, y=2*7, x = 2*3

x*y = 5*5*2*7*2*3

Sufficient.

Thus, B is the answer.

I am sorry but i don't understand it, can you explain the highlighted part again?

sk818020 wrote:The question tells us;

Known factors of;

x = 2 * 3, ...

y = 2 * 7, ...

105=2*5*7

The question rephrased is;

is 5 a factor of x or y.

1) This simply tells us that x has 3^2 as a factor. This does not tell us there is a 5 so it does not answer the question. Insufficient.

2) This tells us y has 5^2 as a factor. This allows us to conclude that xy has 5 as a factor and that xy is a multiple of 105. Sufficient.

B is and answer.

Can you please confirm that OA?

Hope this helps.

Thanks,

Jared

Jared,

The OA is B and you are correct. I like your approach, if I am understanding correctly this how we can solve problems like these :

a) split the first integer in prime factors ,

b) split the second integer in prime factors

c) split see what the prime factors of the product of first and second integer

d) find all prime factors which are not in a or b but present in c

The correct option would be the one which has prime factors as in d).

Agree?

Thank
-Ricky

rickyishere wrote:

sk818020 wrote:The question tells us;

Known factors of;

x = 2 * 3, ...

y = 2 * 7, ...

105=2*5*7

The question rephrased is;

is 5 a factor of x or y.

1) This simply tells us that x has 3^2 as a factor. This does not tell us there is a 5 so it does not answer the question. Insufficient.

2) This tells us y has 5^2 as a factor. This allows us to conclude that xy has 5 as a factor and that xy is a multiple of 105. Sufficient.

B is and answer.

Can you please confirm that OA?

Hope this helps.

Thanks,

Jared

Jared,

The OA is B and you are correct. I like your approach, if I am understanding correctly this how we can solve problems like these :

a) split the first integer in prime factors ,

b) split the second integer in prime factors

c) split see what the prime factors of the product of first and second integer

d) find all prime factors which are not in a or b but present in c

The correct option would be the one which has prime factors as in d).

Agree?

Thank
-Ricky

Yeah, I think the rule I stick to is if you ever see a question where they actually give you values instead of variables and they ask you about divisibility the first thing you wanna do is break all the values down into the primes because you are going to need to know it. You're absolutely correct that my strategy is that on these types of problems your going to be looking for a missing prime. If its there sufficient. If not, its not sufficient.

Thanks,

Jared