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What is the value of integer z?

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

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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

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[Reveal] Spoiler: OA

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

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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.

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

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New post 09 Feb 2015, 08:49
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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.

Answer: C

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

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New post 09 Feb 2015, 09:18
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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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New post 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

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

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New post 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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New post 12 Feb 2015, 23:33
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.

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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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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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.
This doesn’t anything about z.
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.
So the answer is C.
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Re: What is the value of integer z? [#permalink]

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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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New post 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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New post 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
@Bunuel@VeritasPrepKarishma Please clarify

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

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

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New post 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
@Bunuel@VeritasPrepKarishma Please clarify


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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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
@Bunuel@VeritasPrepKarishma Please clarify


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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Re: What is the value of integer z?   [#permalink] 21 Sep 2017, 03:48
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