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# What is the value of integer z?

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Math Expert
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What is the value of integer z?  [#permalink]

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09 Feb 2015, 06:30
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65% (hard)

Question Stats:

48% (01:18) correct 52% (01:16) wrong based on 451 sessions

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What is the value of integer z?

(1) z is the remainder when positive integer y is divided by positive integer (y - 1)
(2) y is not a prime number

Kudos for a correct solution.

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Re: What is the value of integer z?  [#permalink]

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09 Feb 2015, 08:12
2
2
Bunuel wrote:
What is the value of integer z?

(1) z is the remainder when positive integer y is divided by positive integer (y - 1)
(2) y is not a prime number

Kudos for a correct solution.

statement 1: y is at least one. if y=2 then (y-1) is a factor of y and reminder z is zero. If y=13 then (y-1) is not a factor of y and reminder z is one.

statement 2: clearly not sufficient

1+2) we can eliminate the case in which y=2. z will always be one.

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Re: What is the value of integer z?  [#permalink]

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09 Feb 2015, 08:49
2
Bunuel wrote:
What is the value of integer z?

(1) z is the remainder when positive integer y is divided by positive integer (y - 1)
(2) y is not a prime number

Kudos for a correct solution.

(1) z is the remainder when positive integer y is divided by positive integer (y - 1)
y could be 8. In this case the remainder would be 1
y could also be 2. Here the remainder is 0.
Insufficient.

(2) y is not a prime number
Nothing is indicated about integer z.
Insufficient.

Combined, the remainder will always be 1 as the denominator will always 1 less than the numerator.
Sufficient.

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Re: What is the value of integer z?  [#permalink]

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09 Feb 2015, 09:18
1
Here we go :

St1:

y = 2
y-1 = 1

Remainder z = 0

y = 3
y-1 = 2

Remainder z =1 (z is an integer)

Clearly not sufficient

St2: y is not a prime number

Not sufficient

Combining St1 and St2

We can rule out the case where y = 2

Hence Z will always be 1.

Option C is correct
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Re: What is the value of integer z?  [#permalink]

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12 Feb 2015, 14:17
Bunuel wrote:
What is the value of integer z?

(1) z is the remainder when positive integer y is divided by positive integer (y - 1)
(2) y is not a prime number

Kudos for a correct solution.

z = ?

(1) z is the remainder when positive integer y is divided by positive integer (y - 1)

Consecutive positive integers y and (y-1) are always co-primes and if y is divided by (y-1) then the remainder will always be 1
y = (y - 1) * 1 + 1

we can try out a few numbers
y = 2 , (y-1) = 1, remainder = 1
y = 5 , (y-1) = 4, remainder = 1
y = 10, (y-1) = 9, remainder = 1
y = 2561, (y-1) = 2560, remainder = 1

Hence z = 1
So Stmt (1) is sufficient.

(2) y is not a prime number
This gives no information about z
Hence Stmt (2) is insufficient

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Re: What is the value of integer z?  [#permalink]

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12 Feb 2015, 22:23
Hi prasun9,

You should double check your work. You were using a math theory that actually does NOT fit every example that you listed.

Here's the error:

What's the remainder when 2 is divided by 1? (hint: it's NOT 1). Knowing this, how would your answer change?

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Re: What is the value of integer z?  [#permalink]

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Updated on: 12 Feb 2015, 23:54
Bunuel wrote:
What is the value of integer z?

(1) z is the remainder when positive integer y is divided by positive integer (y - 1)
(2) y is not a prime number

Kudos for a correct solution.

Option C

1. z = y/y-1

From this the z can take values of 1 & 0

2. The reason they gave "y is not a prime" is to remove the answer of z=0

coz when y =2 , y-1 = 1 and z =R(2/1) = 0

So when you combine 1 & 2 you get z = 1 as the only answer.

Originally posted by aj13783 on 12 Feb 2015, 23:33.
Last edited by aj13783 on 12 Feb 2015, 23:54, edited 1 time in total.
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Re: What is the value of integer z?  [#permalink]

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12 Feb 2015, 23:47
1
What is the value of integer z?

(1) z is the remainder when positive integer y is divided by positive integer (y - 1)
(2) y is not a prime number

Statement 1 - (y)/(y-1) = (y-1+1)/(y-1) = Rem (1) or (0)
so Z = 0 for y=2, otherwise Z=1
Not Sufficient.

Statement 2 - Not sufficient.

(1)+(2) = Y is not 2. So Z will be 1.
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Re: What is the value of integer z?  [#permalink]

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13 Feb 2015, 04:19
1
This is an value DS question, where you got an unique value for z.
1). Statement 1 is insufficient.
Suppose say y=40 then y-1 is 39. And remainder is 1.
If y=16 then y-1 is 15 and again remainder is 1.
But if we take y=2 then y-1 is 1. And the remainder is zero because all the numbers are divisible by 1.
2). Statement 2 is insufficient.
Together sufficient,
Statement 2 tells that 2 is not possible. Because its a prime number.
So obviously when you divide any number by its predecessor . the quotient is 1 and remainder 1.
So z is 1.
Together sufficient.
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Re: What is the value of integer z?  [#permalink]

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16 Feb 2015, 05:17
Bunuel wrote:
What is the value of integer z?

(1) z is the remainder when positive integer y is divided by positive integer (y - 1)
(2) y is not a prime number

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

Solution: C.

This question is a classic “Why Are You Here?” question. Statement 1 may look sufficient if you pick numbers (8 and 7; 15 and 14; 5 and 4 ? the remainder is always 1). But what about 2 and 1? There’s no remainder there, so z would equal 0. Statement 2 tells us that (y - 1) cannot be 1, because y cannot be 2. This takes away that one flaw with statement 1, and means that both statements together are sufficient.
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Re: What is the value of integer z?  [#permalink]

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16 Feb 2015, 22:44
AT first glance stmt A seems sufficient bUt thats how GMAT tricks us isn't it? if y=2 then y-1=1 and remainder z=0 in this case..but if y= any positive number other than 2 then remainder would be 1.. hence not sufficient. Using statement 2 we have y is not prime so it cant not be equal to 2 definately hence solved. Hence C is the answer. hope the explanation helps.
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Re: What is the value of integer z?  [#permalink]

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15 May 2015, 10:22
why can't y be 1, as its not a prime???Thus 1/0---inconclusive. or 9/8,10/9--remainder 1..Thus E
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Re: What is the value of integer z?  [#permalink]

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15 May 2015, 10:26
hak15 wrote:
why can't y be 1, as its not a prime???Thus 1/0---inconclusive. or 9/8,10/9--remainder 1..Thus E

y cannot be 1 because in this case y-1=0 and division be 0 is not allowed.
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Re: What is the value of integer z?  [#permalink]

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15 May 2015, 10:41
Bunuel wrote:
hak15 wrote:
why can't y be 1, as its not a prime???Thus 1/0---inconclusive. or 9/8,10/9--remainder 1..Thus E

y cannot be 1 because in this case y-1=0 and division be 0 is not allowed.

Despite that , Isn't there possibility of distinct answer, leading us to E
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Re: What is the value of integer z?  [#permalink]

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15 May 2015, 10:45
1
hak15 wrote:
Bunuel wrote:
hak15 wrote:
why can't y be 1, as its not a prime???Thus 1/0---inconclusive. or 9/8,10/9--remainder 1..Thus E

y cannot be 1 because in this case y-1=0 and division be 0 is not allowed.

Despite that , Isn't there possibility of distinct answer, leading us to E

No.

(1) says that z is the remainder when positive integer y is divided by positive integer (y - 1). If y=1, no integer can be the remainder when y=1 is divided by y-1=0 because division by 0 is NOT allowed.
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What is the value of integer z?  [#permalink]

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23 Jan 2019, 23:16
Bunuel wrote:
What is the value of integer z?

(1) z is the remainder when positive integer y is divided by positive integer (y - 1)
(2) y is not a prime number

Kudos for a correct solution.

Hi

Can anyone clarify why are we not considering negative remainders?
For example:
3=2*1+1
or
3=2*2-1
Hence even if we combine the two statements we get 2 remainders: +1/-1.

IMO ans should then be E.

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Re: What is the value of integer z?  [#permalink]

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23 Jan 2019, 23:25
nitesh50 wrote:
Bunuel wrote:
What is the value of integer z?

(1) z is the remainder when positive integer y is divided by positive integer (y - 1)
(2) y is not a prime number

Kudos for a correct solution.

Hi

Can anyone clarify why are we not considering negative remainders?
For example:
3=2*1+1
or
3=2*2-1
Hence even if we combine the two statements we get 2 remainders: +1/-1.

IMO ans should then be E.

VeritasPrepBrian
gmatbusters
Bunuel
chetan2u

Here is how Official Guide defines remainder:

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 $$0\leq{r}<x$$.

As you can see, a remainder according to the GMAT is always positive or 0.
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Re: What is the value of integer z?  [#permalink]

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23 Jan 2019, 23:28
Bunuel wrote:
What is the value of integer z?

(1) z is the remainder when positive integer y is divided by positive integer (y - 1)
(2) y is not a prime number

Kudos for a correct solution.

Statement 1

z is the remainder when positive integer y is divided by positive integer (y - 1)

here when y= 2, remainder of 2/1 will be 0
when y = 3, remainder of 3/2 will be 1
when y =4, remainder of 4/3 will be 1

2 are getting two values of z, not sufficient

Statement 2, not sufficient

Combination will remove the case when y was 2

C
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Re: What is the value of integer z?  [#permalink]

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23 Jan 2019, 23:54
nitesh50 wrote:
Bunuel wrote:
What is the value of integer z?

(1) z is the remainder when positive integer y is divided by positive integer (y - 1)
(2) y is not a prime number

Kudos for a correct solution.

Hi

Can anyone clarify why are we not considering negative remainders?
For example:
3=2*1+1
or
3=2*2-1
Hence even if we combine the two statements we get 2 remainders: +1/-1.

IMO ans should then be E.

VeritasPrepBrian
gmatbusters
Bunuel
chetan2u

Hi..

As Bunuel has explained, remainder can never be negative and will always be integer, so remainder is an integer equal to or greater than 0.

Having said this, even negative number will give you positive remainder.
Although not tested on GMAT, but if you were to find the remainder when -11 is divided by 3, the answer will be 1..
-11 = -3*3-2 is OK as equation but not for remainder..
It will be -11 = -3*4+1, so remainder is 1
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Re: What is the value of integer z?  [#permalink]

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24 Jan 2019, 05:45
nitesh50 wrote:
Bunuel wrote:
What is the value of integer z?

(1) z is the remainder when positive integer y is divided by positive integer (y - 1)
(2) y is not a prime number

Kudos for a correct solution.

Hi

Can anyone clarify why are we not considering negative remainders?
For example:
3=2*1+1
or
3=2*2-1
Hence even if we combine the two statements we get 2 remainders: +1/-1.

IMO ans should then be E.

VeritasPrepBrian
gmatbusters
Bunuel
chetan2u

"Remainder" by definition is what "remains". So after you evenly divide out the groups, what remains is the remainder.

The concept of "negative remainders" is theoretical. It helps us solve some kind of questions easily as discussed here: https://www.veritasprep.com/blog/2014/0 ... -the-gmat/

When GMAT talks about remainders, it is just talking about 0 or positive remainders.
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Re: What is the value of integer z?   [#permalink] 24 Jan 2019, 05:45
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