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jjomalls
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What is the larger number: a or b? (a) a/b has remainder of 20 Oct 2003, 15:23
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What is the larger number: a or b?

(a) a/b has remainder of 7

(b) b/a has remainder of 8



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What is the larger number: a or b? (a) a/b has remainder of 20 Oct 2003, 18:03
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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.

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am1974
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What is the larger number: a or b? (a) a/b has remainder of 02 Nov 2003, 19:41
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Hello,

Can anybody confirm the above answer?

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What is the larger number: a or b? (a) a/b has remainder of 03 Nov 2003, 06:02
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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<x."

Therefore I think, remainder is not defined for -ve numbers. And since x is positive, smaller number divided by a larger number cannot have a remainder.

So, I think the answer is D. If a/b has a remainder a has to be > b.Similarly, if b/a has a remainder, b has to be >a.
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What is the larger number: a or b? (a) a/b has remainder of 03 Nov 2003, 06:17
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pawargmat
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<x."

Therefore I think, remainder is not defined for -ve numbers. And since x is positive, smaller number divided by a larger number cannot have a remainder.

So, I think the answer is D. If a/b has a remainder a has to be > b. Similarly, if b/a has a remainder, b has to be >a.


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.
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What is the larger number: a or b? (a) a/b has remainder of 03 Nov 2003, 06:58
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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.
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What is the larger number: a or b? (a) a/b has remainder of 03 Nov 2003, 07:09
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If it is D, then (1) and (2) must have the same answer or conclusion.
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What is the larger number: a or b? (a) a/b has remainder of 03 Nov 2003, 09:53
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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.
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pawargmat
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What is the larger number: a or b? (a) a/b has remainder of 03 Nov 2003, 10:19
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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.
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What is the larger number: a or b? (a) a/b has remainder of 03 Nov 2003, 11:31
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pawargmat
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.


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
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What is the larger number: a or b? (a) a/b has remainder of 17 Mar 2004, 12:20
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Can anybody confirm this? I am getting E.

Thanks
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What is the larger number: a or b? (a) a/b has remainder of 21 Mar 2004, 11:33
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kpadma, anand,

what do you think on this? Please explain your reasoning.

Thanks
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What is the larger number: a or b? (a) a/b has remainder of 21 Mar 2004, 14:18
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jjomalls
What is the larger number: a or b?

(a) a/b has remainder of 7

(b) b/a has remainder of 8


(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



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