What is the larger number: a or b? (a) a/b has remainder of

Question

What is the larger number: a or b?

(a) a/b has remainder of 7

(b) b/a has remainder of 8

am1974 · Answer

The answer should be E?

(1) a/b has remainder of 7

a = 15, b = 8 => a> b
a = -15, b = -8 => a < b, so not suffecient

(2) Similarly 2 is not suffecient.

Together: a = 15, b = 8, so a/b has the remainder 7 and b/a has th remainder 8; In this case a> b

But if a = -15, b = -8 then also a/b has the remainder 7 and b/a has the remainder 8, but in this case a < b

So answer is E. Guys, please respond what you think.

Thanks

am1974 · Answer

Hello,

Can anybody confirm the above answer?

Thanks

pawargmat · Answer

OG's defintion of remainder is as follows "If x and y are postive integers, there exist unique integers q and r , called the quotient and remainder, respectively, such that y=xq+r and 0<=r b.Similarly, if b/a has a remainder, b has to be >a.

stolyar · Answer

So:

(1) a>b
(2) b>a

To be D, the sets should not be mutually exclusive; they should be the same. I think that the question is malformulated and has no correct answer.

pawargmat · Answer

Stoylar.. I want to confirm that 'both the sets should be mutually exclusive' is a requirement in DS question. I am assuming that you mean both options should yield the same answer. Please confirm.

stolyar · Answer

If it is D, then (1) and (2) must have the same answer or conclusion.

wonder_gmat · Answer

I vote for  C .

I don't see how you could not have a remainder when you devide the smaller number by larger number, as pawargmat stated.

Example:
8 mod 9 = 8

jjomalls:
Where did you get this problem from? Because I'd be interested to see what their answer is and an explanation supporting it.

pawargmat · Answer

8mod9 cannot have a remainder of 8, as per OG's defintion (as for me I would have thought 8 is the remainder ...before seeing this definition of course)

if we try to write 8mod9 in y=xq+r form, 9=xq+8, xq has to be 0 implying that x should be 0 in which case, x would not be positive which will violate the definition.

wonder_gmat · Answer

Yes the definition is correct but x doesn't have to be zero. All x can be is 1 and q can be zero. Because the definition basically says there is a multiplier of x such that the y is  at least as  much as the product of q and x.

So for example:

8 mod 9 --> x = 9, y = 8, q = 0, r = ?

r = y - qx
 = 8 - (0)(9)
 = 8

In this case 9 goes into 8 zero times. Thus the multiplier q equals 0.

example 2:

9 mod 8 --> x = 8, y = 9, q = 1, r = ?

r = y - qx
 = 9 - (1)(8)
 = 9 - 8
 = 1

gmatblast · Answer

Can anybody confirm this? I am getting E.

Thanks

gmatblast · Answer

kpadma, anand,

what do you think on this? Please explain your reasoning.

Thanks

hallelujah1234 · Answer

(1) a = 7 (mod b)
 or bm = -7 (mod a)

(2) b = 8 (mod a)
 

Combining (1) and (2) gives:

8m = -7 (mod a)


Answer is E

What is the larger number: a or b? (a) a/b has remainder of

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