ds:remainder

Question

guys

What is the remainder when the positive integer x is divided by 8?

1. when x is divided by 12, the remainder is 5.
2. when x is divided by 18, the remainder is 7.

is it C or E ?

cheers

scthakur · Answer

It will be E.

From stmt1: x = 12a + 5 for a = 0,1,2,3,4,......
From stmt2: x = 18b + 7 for b = 0,1,2,3,......

Combining two, 12a + 5 = 18b + 7, or 12a = 18b + 2 or, 6a = 9b + 1
or, a = (9b+1)/(2*3)

Thus, in order for a to be an integer, 9b+1 should have 2 and 3 as its factors. But, that will never be possible as if any number n has a set of factors, these will not be the factors of (n+1). Accordingly, 9b has 3 as the factor, hence 9b+1 will not have 3 as the factor and accordingly, a will not be an integer.

Hence, even after combining stmt1 and stmt2, we will not get a common number.. Hence, insufficient.

amitdgr · Answer

Thanks scthakur .... I really never know this property .......... +1!

GMAT TIGER · Answer

Seem the question is wrong (or misleading) because any integer, x, when divided by 12 has reminder 5 cannot have reminder 7 when the same integer is divided by 18. the reminder could be 5 or 11 or 17. none can be reminder when x is divided by 18.

so this is a flawed question.

so this is a flawed question.

amitdgr · Answer

Can you explain a bit more

I seem to get the point but only partially .....

GMAT TIGER · Answer

I meant to say X cannot have 2 values. As per the statements 1 and 2, x has 2 values and thats, as per GMAT standard, is substandard.

You do not get such questions in real test.

scthakur · Answer

GT, what you say is right only when x is common between stmt1 and stmt2. But, if x is not common between stmt1 and stmt2, then what you say may not be true.

GMAT TIGER · Answer

I said this only in the context of this question. But if x is not common between stmt1 and stmt2, then what I said is also true cuz I have not said anything when the scenerio changes. :wink:

scthakur · Answer

Well, even in the context of this question, 
stmt1 gives x = 5,17, 29, .....
stmt2 gives x = 7, 25, 43, ......

and the question is independently giving values of x in statement 1 and in statement 2. Why should the two statements provide a common value (if this is what you meant)?

ds:remainder

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