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What is the value of integer z?

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Bunuel
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What is the value of integer z? [#permalink] What is the value of integer z?   20 Sep 2012, 10:00
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A
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C
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E

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Veritas Prep 10 Year Anniversary Promo Question #7


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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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Re: What is the value of integer z? [#permalink] What is the value of integer z?   20 Sep 2012, 10:01
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AbhiJ

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Answer is 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. This is why statement 2 is so important. Alone, it’s useless...so why is it there? 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. But of more strategic importance, statement 2 should alert you to that problem with statement 1. Most test-takers miss that flaw when looking at statement 1 alone, but astute test-takers will reconsider once statement 2 is presented.
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Re: What is the value of integer z? [#permalink] What is the value of integer z?   20 Sep 2012, 10:03
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
Answer is C
1 insufficient as remainder can be 1, 2
2) insufficient
3) both sufficient
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Re: What is the value of integer z? [#permalink] What is the value of integer z?   20 Sep 2012, 10:04
My answer is C.
(1) if y = 1 or 2 => can't determine z
(2) nothing to determine z

(1) + (2): y > 3 & y : (y-1) always has reminder 1
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Re: What is the value of integer z? [#permalink] What is the value of integer z?   20 Sep 2012, 10:04
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Stmt 1 is not sufficient as r=1 when y= 3,4,5 and r=0 when y = 2
Stmt 2 is not suff
Combine Answer C
as y=!2 hence r is always = 1
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Re: What is the value of integer z? [#permalink] What is the value of integer z?   20 Sep 2012, 10:04
Answer A.

It leaves remainder 1.
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Re: What is the value of integer z? [#permalink] What is the value of integer z?   Updated on: 20 Sep 2012, 10:46
Option C.
Since y-1 is positive.. y has to be atleast 2. now for any y>2, y/y-1 will give 1 as remainder but for Y=2 remainder is 0.
however y is not prime.. so can not be 2. hence we know remainder will be 1 from above.

Originally posted by Manjulika on 20 Sep 2012, 10:05.
Last edited by Manjulika on 20 Sep 2012, 10:46, edited 1 time in total.
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Re: What is the value of integer z? [#permalink] What is the value of integer z?   20 Sep 2012, 10:05
Bunuel wrote:

Veritas Prep 10 Year Anniversary Promo Question #7


One quant and one verbal question will be posted each day starting on Monday Sept 17th at 10 AM PST/1 PM EST and the first person to correctly answer the question and show how they arrived at the answer will win a free Veritas Prep GMAT course ($1,650 value). Winners will be selected and notified by a GMAT Club moderator. For more questions and details please check here: veritas-prep-10-year-anniversary-giveaway-138806.html

To participate, please make sure you provide the correct answer (A,B,C,D,E) and explanation that clearly shows how you arrived at it.
Winners will be announced the following day at 10 AM Pacific/1 PM Eastern Time.


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


Ans: A

Z = 1

y-1 and y are two consecutive numbers. When divided it will give remainder 1
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Re: What is the value of integer z? [#permalink] What is the value of integer z?   20 Sep 2012, 10:06
A is sufficient as remainder will always be one when we divide two consecutive integers with the higher one as numerator.

B. doesn't lead us to any solution as what is z is not mentioned.
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Re: What is the value of integer z? [#permalink] What is the value of integer z?   20 Sep 2012, 10:07
Ans is C
Statement1:
for ex y=2
2/1 then remainder =0
if y=3
3/2 then remainder=1
Not sufficient
Statement2: y can be 1,4,6 ---Not sufficent
By combining both
y cannot be 2,so in all cases remainder will be 1
Hence sufficient
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Re: What is the value of integer z? [#permalink] What is the value of integer z?   20 Sep 2012, 10:08
Bunuel wrote:

Veritas Prep 10 Year Anniversary Promo Question #7


One quant and one verbal question will be posted each day starting on Monday Sept 17th at 10 AM PST/1 PM EST and the first person to correctly answer the question and show how they arrived at the answer will win a free Veritas Prep GMAT course ($1,650 value). Winners will be selected and notified by a GMAT Club moderator. For more questions and details please check here: veritas-prep-10-year-anniversary-giveaway-138806.html

To participate, please make sure you provide the correct answer (A,B,C,D,E) and explanation that clearly shows how you arrived at it.
Winners will be announced the following day at 10 AM Pacific/1 PM Eastern Time.


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



(E)
(1) INSUFF because values will be diffrent if y is even or odd so z will vary
(2) insufficient to answer the given question
together also, not possible to figure out z
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Re: What is the value of integer z? [#permalink] What is the value of integer z?   20 Sep 2012, 10:09
Manjulika wrote:
Option A.
Since y-1 is positive.. y has to be atleast 2. now for any y>=2, y/y-1 will give 1 as remainder

I had to click submit button atleast 3 times to post.. some problem with quick reply option?
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Re: What is the value of integer z? [#permalink] What is the value of integer z?   Updated on: 20 Sep 2012, 10:31
What is the value of integer ?

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

(2) is not a prime number

the answer is E
y and y-1 is consequetive integers
so y divided by y-1 results remainder of 1 which is unknown
INSUFFICIENT
2 is clearly INSUFFICIENT
together is also INSUFFICIENT to say the value of z because when y is 1 y-1 will be 0 which cannot be the case and 1 is not a prime

Originally posted by SobirovaZulxumor on 20 Sep 2012, 10:12.
Last edited by SobirovaZulxumor on 20 Sep 2012, 10:31, edited 2 times in total.
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Re: What is the value of integer z? [#permalink] What is the value of integer z?   20 Sep 2012, 10:15
My Ans IS E-

Statement 1-z is the remainder when positive integer y is divided by positive integer (y - 1)- not sufficient the nos can vary
Statement 2- By itself also not sufficient to find Z
Together also not sufficient.
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Re: What is the value of integer z? [#permalink] What is the value of integer z?   20 Sep 2012, 10:17
Answer is A

(1)y/(y-1)=1+1/(y-1); since z is integer so (y-1) must be 1 or -1. But y-1>0. Then,(y-1) must be 1 => z=1=>(1)Sufficient
(2)y is not prime number is not Sufficient.
So A
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Re: What is the value of integer z? [#permalink] What is the value of integer z?   20 Sep 2012, 10:32
What is the value of integer ?

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

(2) is not a prime number
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Statement 1 is sufficient - Y is a positive number so 1, 2,3,......... and Y-1 is also a Positive number, therefore minimum value of Y can be either 2, 3, 4, etc.
... and remainder always be 1, So value of Z is 1
statement 2- Y is not a prime number, Since it is a positive number so it will again the number can be 4, 6 , 8, 9, 10 etc. and Y-1 will always result in 1 less than the number itself... So Remainder will be 1

And Answer is D, both are sufficient
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Re: What is the value of integer z? [#permalink] What is the value of integer z?   20 Sep 2012, 10:37
How can (A)??

(i) what will happen if y=1 ; y/(y-1) = 1/(1-1) = infinity
Z=infinity

(ii) no sufficient data

together also, not possible to find out z
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Re: What is the value of integer z? [#permalink] What is the value of integer z?   20 Sep 2012, 10:38
fameatop 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
Answer is C
1 insufficient as remainder can be 1, 2
2) insufficient
3) both sufficient



How remainder can be 2 in statement1...Obviously not possible
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Re: What is the value of integer z? [#permalink] What is the value of integer z?   20 Sep 2012, 10:44
gamelord wrote:
My answer is C.
(1) if y = 1 or 2 => can't determine z
(2) nothing to determine z

(1) + (2): y > 3 & y : (y-1) always has reminder 1



If y=1,then y-1=0, which cannot be a postive integer
Hence u contradicted the st1
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Re: What is the value of integer z? [#permalink] What is the value of integer z?   20 Sep 2012, 10:49
Numbers of the form (y,y-1) are called coprimes because they have only 1 common factor and that is 1. The only scenario when y divided by y-1 will give a remainder 0 is when y is 2 but since statement says that, y cannot be a prime number. So both the statements together are sufficient to answer the question.
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Re: What is the value of integer z? [#permalink]
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