In an integer division operation, the divisor is x, the quotient is y,

Question

In an integer division operation, the divisor is x, the quotient is y, the dividend is z, and remainder is r. Is x > y?

(1) z = 151

(2) r = 11

Kudos for a correct  solution .

Harley1980 · Accepted Answer

We can write this task in such way:
 z = x*y + r

1) we know only  z  and this is insufficient.
2) we know only  r  and this is insufficient

1+2)  151 = x*y + 11  
This is looks like insufficient, but we know that  x  and  y  should be integer and remainder should be less than divisor:  x>11 .
And from this information we can infer that  x*y = 151-11 = 140  
and as  x  should be more than 11, the least possible number is 14 and  y  should be equal to 10
So  x > y  and answer is C

Lucky2783 · Answer

z=xy+r

(1) z = 151
 Insufficient. 
(2) r = 11
 Insufficient.

x*y= 140 
x>11
so minimum 'x' is 14 and maximum 'y' is '10' .

Answer C .

Celestial09 · Answer

Hi,
IMO it should be C. that is after combining both statements.
 St 1) just be talking about z-151 nothing comes out.
151/2 or 151/150. so remainder being same still x and y cant be quantified.

st 2) r = 11. 
still nothing comes out

combining both:
 find the number which when divides 151 leaves remainder of 11 
x should be 14 and y be 10.

Though while solving I assigned x as 140 / 28 too.. which leaves remainder of 11 when divided by 151
hence C
Regards
Celestial

Kudos if its a correct solution

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Quick hypothetical situations should prove statement 1 to be insufficient. If x is 151, then you'd be dividing the same thing by itself and y would be 1 with no remainder, and x would be much larger than y. But you could flip that and make x = 1, in which you'd just be dividing 151 by 1 and the quotient (y) would be 151, much larger than x.

Recognizing the algebra of division can be quite helpful here, too. Since Quotient = Dividend * Divisor + Remainder, just knowing statement 1 tells you that 151 = xy + r, and clearly that's not enough information to solve.

Statement 2 is also insufficient. Keep in mind here that, without knowing statement 1, you essentially just have an undefined problem with a remainder of 11. Algebraically that's:

z = xy + 11

And clearly not enough information to solve.

But taken together, the information is sufficient. Why, if it still leaves two variables?

151 = xy + 11, so:

140 = xy

The other crucial element of this being a division problem is that the divisor can't be less than the remainder! If you're dividing 151 by, say, 7, you'd never have 11 left over. Even though 7 * 20 = 140, you wouldn't stop there and say that the remainder is 11, because 11 can still divide one more time by 7 (making it 21, remainder 4). So since 140 = xy AND x > 11, there's no way for an integer y to be greater than x. Therefore the two statements together are sufficient.

y4nkee · Answer

Typo:
Should be
Dividend=Divisor*Quotient + Remainder

Shrey9 · Answer

Bunuel  , can you help me out with my confusion here, i read that Y is the quotient, and X is the divisor..
Why x has to be greater than y ? as We can also divide 140 by 7 i.e X and in that case quotient i.e Y would be 20.
Please correct me if i am missing out on some information, but it's causing me a lot of confusion here.
How's X > Y here ?

Bunuel · Answer

If  x  and  y  are  positive integers , there exist unique integers  q  and  r , called the  quotient  and  remainder , respectively, such that  y =divisor*quotient+remainder= xq + r  and  0\leq{r}<x .

For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since  15 = 6*2 + 3 .

Notice that  0\leq{r}<x  means that remainder is a non-negative integer and always less than divisor.

It's easier to understand if you consider a simple example: when you divide by 3, the remainder could only be 0, 1, or 2.

For more on this please check the links below:

6. Remainders 
     Theory   
 REMAINDERS 
 Remainders: Tips and hints 
 Divisibility and Remainders on the GMAT 
 Remainders on the GMAT 
 A Remainders Shortcut for the GMAT 
 All About Negative Remainders on the GMAT 
 A Tricky Question on Negative Remainders 
 Compilation of tips and tricks to deal with remainders 
 Cyclicity and the remainders on the GMAT 
 GMAT Question Patterns: Remainders 
     Questions   
 Units digits, exponents, remainders problems  
 DS Questions 
 PS Questions

rodri102 · Answer

How come x can't equal 70 and y equal 2? The remainder would be 11 is this case as well.

rye · Answer

But isn't this true that z is a prime number i.e. 151, therefore x has to be greater than y? Thus making A sufficient?

Same with B: any number has x > y until it is a perfect square , in which case it is equal. By telling remainder 11, the question clearly tells that the number is not a perfect square, thus making condition 2 also sufficient?

Thus D is correct?

bumpbot · Answer

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In an integer division operation, the divisor is x, the quotient is y,

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