If x and y are positive integers, what is the remainder of

Question

If x and y are positive integers, what is the remainder of xy/4 ?
1. The remainder of x/4 is 3 
2. The remainder of y/4 is 2

abhijit_sen · Answer

Statement 1:
Tells us about X but does not tells us anything about Y so cannot answer the question.

Statement 2:
Tells us about Y but does not tells us anything about X so cannot answer the question.

Combining both the statements:
XY/4 will have a reminder of 2*3/4 = 2

So both statements together can answer the question. (C)

marcodonzelli · Answer

i followed this steps:

1. tells us that x can be 3,7,11....alone insuff
2. " " y can be 2,6,10,14....alone insuff

combining: i.e. 7*6=42 which has a remainder of 2.

how do you find it?

pmenon · Answer

I get C.

stat 1 says that x/4 has remainder 3. thats fine, so x can be 7, 11, etc. but stat 1 doesnt say anything about y.

stat 2 is the reverse. we know about x, but not about y. insuff.

together, we know that x=7,11,15... and y=6,10,14...

combining any of the two values, youll see that the product always has a remainder of 2. try it out.

neelesh · Answer

From 1 ->  x = 4k_1 + 3  == INSUFFICIENT

From 2 ->  x = 4m_1 + 2  == INSUFFICIENT

From 1 & 2

(4k_1 + 3)(4m_1 + 2) = (4j_1 + remainder)

->  4(4k_1m_1 + 2k_1 + 3m_1) + 6 = (4j_1+ remainder)

->  4*(4k_1m_1 + 2 + 3m_1 + 1) + 2 = (4j_1+ remainder)

Hence remainder should be 2.

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