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

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Difficulty:   75% (hard)

Question Stats: 42% (01:23) correct 58% (01:23) wrong based on 239 sessions

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What is the value of integer z?

(1) z represents the remainder when positive integer x is divided by positive integer (x – 1)
(2) x is not a prime number

Kudos for a correct solution.

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

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Statement (1) z represents the remainder when positive integer x is divided by positive integer (x – 1)
E.g: Remainder (2/1) = 0 = z
Remainder (3/2) = 1 = z
Remainder (4/3) = 1 = z
Different values of z (0,1) and hence NOT sufficient.

Statement (2) x is not a prime number
NOT sufficient.

Statement (1) + Statement (2)
By saying that x is not a prime number, we have got rid of one ouster Remainder (2/1) =0.
And for the rest of the numbers:
Remainder (3/2) = 1 = z
Remainder (4/3) = 1 = z
...so on.

Therefore, z is always 1. Sufficient

Originally posted by Patronus on 07 Jul 2015, 03:09.
Last edited by Patronus on 07 Jul 2015, 04:34, edited 1 time in total.
##### General Discussion
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What is the value of integer z?  [#permalink]

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Bunuel wrote:
What is the value of integer z?

(1) z represents the remainder when positive integer x is divided by positive integer (x – 1)
(2) x is not a prime number

Kudos for a correct solution.

Given, Z is an integer and Z=?

Statement 2 is def not sufficient as z and x have no given connection

Per statement 1: x= p(x-1)+z

if x=2, z=0
x=3, z=1
etc
Thus we have 2 values for z = 0,1 and this statement is thus not sufficient.

Combining 1 and 2

We have been given that x is NOT a prime number. This removes x=2,z=0 case and thus the only remainder value we can get when we divide x by x-1 such that x is not a prime number is 1 as x and x-1 are co-prime numbers. Thus, z=1 and C is the correct answer.
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What is the value of integer z?  [#permalink]

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Bunuel wrote:
What is the value of integer z?

(1) z represents the remainder when positive integer x is divided by positive integer (x – 1)
(2) x is not a prime number

Kudos for a correct solution.

Question : Integer z = ?

Statement 1: z represents the remainder when positive integer x is divided by positive integer (x – 1)

@x = 2 then z = 0
@x = Greater than 2 then z = 1
NOT SUFFICIENT

Statement 2: x is not a prime number

NOT SUFFICIENT

Combining the two statements
x can't be Prime and for every other value of x the remainder when x divided bu (x-1) will be 1 hence
z=1
SUFFICIENT

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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 represents the remainder when positive integer x is divided by positive integer (x – 1)
(2) x is not a prime number

Kudos for a correct solution.

Statement 1:
When positive integer x is divided by positive integer (x – 1) reminder Will always be equal to 1 Except for the case when X = 2 in that case reminder will be equal to 0

Take Example

Remainder (2/1) = 0
Remainder (100/99) = 1
Remainder (98/97) = 1

[ Or we can say

Two consecutive number always have one common factor that is 1 ]

Since we dont know if X = 2 or greater than 2, We will not be able to Tell if Z = 0 or Z = 1

Insufficient.

Statement 2 :
X is not a prime number. What about Z nothing is mentioned about Z --- Insufficient.

Combining Statement 1 and 2 We get
X is not equal to 2 (Since 2 is prime number)

Hence Z = 1 ( As per the explanation given in statement 1 analysis)

Hence Option 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 represents the remainder when positive integer x is divided by positive integer (x – 1)
(2) x is not a prime number

Kudos for a correct solution.

STATEMENT 1: There are 2 possible answers: z=0 and z=1. Example #1: x=2, then x-1=1, so x/(x-1)=2/1. There is no remainder here. Example #2, x=3 (or any other greater integer), then x-1=2, so x/(x-1)=3/2. The remainder is 1 here. Hence, statement 1 is NOT SUFFICIENT.

STATEMENT 2: We don't know the relationship between x and z. Hence, statement 2 is NOT SUFFICIENT.

STATEMENTS 1+2: From Statement 1 we know that there are 2 possible answers, z=0 and z=1. z will equal zero only when x=2. Statement 2 tells us that x is not a prime number, so x cannot be 2. In all other cases, z=1. So Statements 1+2 are SUFFICIENT.

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

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Top Contributor
Bunuel wrote:
What is the value of integer z?

(1) z represents the remainder when positive integer x is divided by positive integer (x – 1)
(2) x is not a prime number

Kudos for a correct solution.

Target question: What is the value of integer z?

Statement 1: z represents the remainder when positive integer x is divided by positive integer (x – 1)
In almost all cases, we will get a remainder of 1 when we divide x by (x-1).
For example, 6 divided by 5 equals 1 with remainder 1 (in other words z = 1)
9 divided by 8 equals 1 with remainder 1 (in other words z = 1)
22 divided by 21 equals 1 with remainder 1 (in other words z = 1)
.
.
.
and so on.,

The only time we don't get a remainder of 1 is when x = 2
If x = 2, then x divided by (x-1) becomes 2 divided by 1, in which case the remainder is 0 (in other words z = 0)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x is not a prime number
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
From statement 1, we learned that the remainder will always be 1 AS LONG as x does not equal 2
Statement 2 tells us that x does not equal 2
If x does not equal 2, then dividing x by (x-1) will always leave remainder 1
In other words, z must equal 1
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
_________________ Re: What is the value of integer z?   [#permalink] 05 Aug 2018, 08:44
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