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What is the value of integer z? 20 Sep 2012, 10:00
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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: https://gmatclub.com/forum/veritas-prep ... 38806.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
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What is the value of integer z? 20 Sep 2012, 10:52
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So the first statement is sufficient because y has to be greater than zero because even though zero is an integer, its neither positive or negative. When y=1 the remainder is 1 and when y=2 the remainder is 1. So the first statement is sufficient.

The second is not sufficient because y not being prime does not help us. So the second is insufficient.

If we put both of them together y has too many choices y could be 1,4,6,8,9,12,14,15
So the correct answer is A.
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What is the value of integer z? 20 Sep 2012, 10:55
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y-1 is a positive number, so value of y can not be 1, otherwise y-1 will be zero.......and that contradicts the statement
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What is the value of integer z? 20 Sep 2012, 10:57
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I choose option C:

Statement 1:
Since it is given that (Y -1) is positive integer, Y cannot be 1 or lesser than 1. Y >= 2

for Y = 2, Z = 0 as 2/1 => quotient 2 remainder 0
for Y >= 2 z = 1

Z=0, Z=1 insufficient.

Statement 2:
Statement does not say anything about Z.

insufficient.

Statement 1 & 2:
from 1
we have two scenario: if y = 2 than z = 0; if y >=2 z = 1
from 2
y not equal to 2

so y >2 and in this scenario z = 1.

Answer choice C.

OA please?
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What is the value of integer z? 20 Sep 2012, 11:07
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Ans C.
statmnt 1: insufficient when y=2; however y cant be equal to 1 as y-1= 0 NOT a positive integer.
statmnt 2: Insuff.
combining together 1 & 2 we get z=1
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What is the value of integer z? 20 Sep 2012, 11:18
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Answer is E

1)z is the remainder when positive integer y is divided by positive integer y-1
let y=2
so y = 1(2) + z or reminder 0
let y = 1
however if y = 1 then the denominator becomes 0 and thus Undefined or z need not be equal to 0
so INSUFFICIENT eliminate A,D

2)y is not a prime number

Says nothing about C


Insufficent eliminate B

Now both together again will give you the possiblity of Y having 1 or 4 or a grater non prime number
however any number greater than 1 gives reminder as 1 and the number 1 alone gives a undefined value
so both together also fails
eliminate C

so the Ans is E
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What is the value of integer z? 20 Sep 2012, 13:36
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Bunuel

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
Show more
----------------------------------------------------------------------------------------------------

The answer is A as y and z are two consec numbers and has to be 2 and 1. There are no two number which will give an integer as reminder when divided.
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What is the value of integer z? 20 Sep 2012, 21:34
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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- is not sufficient because there is no relation between Y an Z here.

Hence Answer will be A, Sorry for the previous answer....I just missed the the 2nd point.
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What is the value of integer z? 21 Sep 2012, 00:39
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A is the answer as the statement 1 says. y and y-1 both are positive, if y is divided by y-1 then remainder is always 1. so z=1.
statement 2 is insufficient
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What is the value of integer z? 21 Sep 2012, 02:42
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Ans - A

Remainder theorem-

when y /y-1
remainder = f(1)

f(y) = y
substituting the value of y =1

Therefore answer will always be 1.
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What is the value of integer z? Updated on: 21 Sep 2012, 04:15
Originally posted by bijoydinanath on 21 Sep 2012, 03:35.
Last edited by bijoydinanath on 21 Sep 2012, 04:15, edited 1 time in total.
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Answer: C

According to statement 1, y could be 2 or 4, which gives us different values of z; not sufficient
(2) No relation between z and y

1+2:

y should be greater than 3; therefore, y and y-1 will always have the remainder of 1.

Answer C
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What is the value of integer z? 21 Sep 2012, 03:44
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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[/quote]

Lets take easier statement first.

Statement 2 just tells us that Y is not 2, 3, 5, or any other odd prime but it doesn't tell us anything about Z.

Stmt 1: Lets take Y to be 1, 2 or 3, Y-1 will be 0, 1 or 2. Y could be 0 also however since statement explicitly mentions that Y is positive integer and 0 is non negative integer, Y can not be 0.

1/0- Division by 0 is undefined in GMAT
2/1= 0 remainder
3/2= 1 remainder

Thus we have multiple answers, hence not sufficient.

Together: We know that Y is not prime, hence Y = 2 is ruled out and any other integer more then 2 divided by Int-1 will give a remainder of 1. Hence together sufficient. Answer is C.
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What is the value of integer z? 21 Sep 2012, 03:57
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Answer A:

Since z is the remainder when positive integer y is divided by positive integer (y - 1), which is 1 short of y, therefore, z =1
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What is the value of integer z? 21 Sep 2012, 04:16
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rajareena
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
Show more

Lets take easier statement first.

Statement 2 just tells us that Y is not 2, 3, 5, or any other odd prime but it doesn't tell us anything about Z.

Stmt 1: Lets take Y to be 1, 2 or 3, Y-1 will be 0, 1 or 2. Y could be 0 also however since statement explicitly mentions that Y is positive integer and 0 is non negative integer, Y can not be 0.

1/0- Division by 0 is undefined in GMAT
2/1= 0 remainder
3/2= 1 remainder

Thus we have multiple answers, hence not sufficient.

Together: We know that Y is not prime, hence Y = 2 is ruled out and any other integer more then 2 divided by Int-1 will give a remainder of 1. Hence together sufficient. Answer is C.[/quote]

Looking at statement 1 -

any number can be represented in the form of divisor and remainder as below:

A = K(y-1) +z .............for all the values of K
at k=1
A=y-1 +Z....................A=y hence z=1

As A=y K can never be more than 1
at y=1
1 =1-1+z...............z=1
2=2-1+z...............z=1
3=3-1+z...............z=1

Hence statement 1 is sufficient.
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What is the value of integer z? 21 Sep 2012, 08:48
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We have a winner!



Winner:

AbhiJ

Official Explanation:

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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What is the value of integer z? 21 Sep 2012, 09:51
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Thanks a Bunch to Veritas Prep for being so generous , awarding prizes day after day.

Bb and Bunnel, you guys are doing some awesome work which makes this site a personalized experience - a GMAT-Club in true sense of the word.
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What is the value of integer z? 17 Jun 2017, 02:02
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The most important thing in this problem is avoid to overlook that Y and Y-1 are consecutive non negative integer.
The division of 2 consecutive number is always 1 except in 1 case (2,1) - (1,0) non considered - therefore:
1 - Not suff. solution are 0 and 1
2 - Clearly Not suff.

1&2 Suff and Z=1
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What is the value of integer z? 19 Aug 2023, 21:49
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