Statement 1:

m = 2a, p = 2b where a and b both are co-prime

(m, p) could be (4, 6), (4, 10)

Remainder should be 2 or more, as both are multiple of 2

Sufficient

Statement 2:
30 = 2*3*5
(m, p) could be (3, 10), (3,5) ,(5,6), (6,15)

Remainder can be 1, 2, 3 or even more

Insufficient

Answer: A

akhp77 wrote:Statement 1:

m = 2a, p = 2b where a and b both are different prime nos

(m, p) could be (4, 6), (4, 10)

Remainder should be 2 or more, as both are multiple of 2

Sufficient

Statement 2:
30 = 2*3*5
(m, p) could be (3, 10), (3,5) ,(5,6), (6,15)

Remainder can be 1, 2, 3 or even more

Insufficient

Answer: A

hi akhp77
i really like you solution
but only one question, how did you come that a=2m, and p=2b where both a and b are both prime numbers
to me only one m must be prime
for example 14=2*7 and 16=2*8
or i am missing something?

You are right, a and b need not be different prime numbers but rather two different integers greater than 1.


Here's a nice rule to keep in mind.: If a and b are two positive integers that have a common factor of c, the remainder when a is divided by b must be a multiple of c.

For example, when a multiple of 18 is divided by 30, the remainder must be a multiple of 6 (i.e. 0,6,12,18 or 24) , since GCF(18,30) = 6.

Similarly, when a multiple of 155 is divided by 210, the remainder must be a multiple of 5 (i.e. 0 , 5 , 10 ,..., 205) since GCF (155,210) = 5.

Question: If x is a positive multiple of 38, and r is the remainder when x is divided by 54, how many possible values of r are greater than 46?

clock60 wrote:

akhp77 wrote:Statement 1:

m = 2a, p = 2b where a and b both are different prime nos

(m, p) could be (4, 6), (4, 10)

Remainder should be 2 or more, as both are multiple of 2

Sufficient

Statement 2:
30 = 2*3*5
(m, p) could be (3, 10), (3,5) ,(5,6), (6,15)

Remainder can be 1, 2, 3 or even more

Insufficient

Answer: A

hi akhp77
i really like you solution
but only one question, how did you come that a=2m, and p=2b where both a and b are both prime numbers
to me only one m must be prime
for example 14=2*7 and 16=2*8
or i am missing something?

You are right.
I have edited that,

kevincanspain wrote:
Question: If x is a positive multiple of 38, and r is the remainder when x is divided by 54, how many possible values of r are greater than 46?

[spoiler]
3? 48,50,52[/spoiler]

Right!