What is the value of integer z?

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
No info about how knowing about x not being prime number gives any info about z.
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

Answer (C)

#1
2/1 = 2, remainder 0
4/3 = 1, remainder 1
same goes for every other value higher than that, i.e 5/4, 6/5 etc.
insufficient

#2
no info about z, lol, insufficient

#1 +#2
2 = prime so we remove the 2/1 equation from our available options thus leaving the only possible remainder as 1
sufficient

C

1) When any positive integer x divided by positive integer (x - 1) remainder will always be 1 Except case than x = 2; 2/1 = 2 and remainder is 0
2) x not equal prime - insufficient

1 + 2) x not equal 2 so case 2/1 impossible and remainder always be 1

Answer is C
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(1) z is the remainder when positive integer x is divided by positive integer (x – 1)
X=2, X-1=1 remainder 0
X=3, X-1=2 remainder 1
Insufficient.
(2) x is not a prime number
no relation between x and Z can be established.

Together :
X is not 2 (and other primes)
X=-4 , X-1=-5 remainder 4not possible as X is positive as per statement A.

Answer : C

I also got C for this one also,

Stmt 1 - z is the remainder when x is divided by x-1. Test the cases
if x = 2, then z would be 0 ( 2/2-1 = 2 r 0)
If x = 5, then z would be 1 (5/ 5-4 = 1 r 1)
Therefore, stmt 1 is insufficient

Stmt 2 - Does not discuss z

Together, that means x is not 2 and any other integer would give a reminder of 1, therefore z=1



As an aide, one tip/trick I find out on DS is that when a statement like statement 2 here gives you a "random" bit of information, it most likely has on impact on the other statement.

What is the value of integer z?

(1) z is the remainder when positive integer x is divided by positive integer (x – 1)
x = 1(x – 1) + 1. However, IF x-1 =1 or x = 2, the remainder is 0. In the other cases, the remainder is 1.
=> Insufficient
(2) x is not a prime number

No mention about x => INSUFFICIENT

(1) and (2): x cannot be 2 because 2 is prime number. The others, both prime and non-prime integer, always have the remainder of 1 => Conclusion: The remainder is 1 with all x, which is not prime integer => Sufficient

Choose C

Trying not to look at others answers before attempting this one for myself, my answer is (a)

I plugged in values, to visualize this.

Statement 1: x/(x-1) = Quotient + Z
lets say :
x=4.... 4/3 = 1 remainder 1...
x=5.... 5/4= 1 remainder 1
x=20 20/19 = 1 remaiber 1 <--- this is the case for all values

Statement 2: Kniwing that X isn't prime doesn't really give us anything

VERITAS PREP OFFICIAL SOLUTION:

Now look at statement 1. There’s a lot to unpack – the concept of remainder, the definitions of “positive integer x and positive integer (x – 1)”, the fact that x then can’t be 1 (or x-1 would be 0 and therefore prohibited), the fact that the two values being divided are consecutive integers. So it’s not surprising that, on their way to the trap answer selected by nearly 60% of respondents in the Veritas Prep Question Bank, many feel the glory when they unravel the variables and processes and think:

“Ah, ok. 5/4 would work and that’s 1 remainder 1. 10/9 would work and that’s 1 remainder 1. 100 divided by 99 would work and that’s 1 remainder 1. I get it…remainder is always 1.”

After all that work, statement 2 is as much a formality as a 2 run lead with no baserunners in the 9th inning. Piece of cake. So people start to hear that crowd chanting their name a-la “De-rek-Jeeeet-er”, they pat themselves on the back for the accomplishment, and they pick A. Without ever seeing the opportunity that statement 2 really should provide them:

“Wait…that’s not the script I want – it shouldn’t be that easy.”

Those who know the GMAT well – those Jeterian scholars who have honed their craft through practice and determination to go with the natural talent – look at statement 2 and think “why does this matter? Why would the author write such a mundanely-irrelevant statement? The question is about z and the statement is about x? Come on…”

And in doing so, they’ll ask “Why would a prime number matter? And what kind of prime numbers might change things?” And when you’re talking prime numbers, just like when you’re talking Yankee lore, you have to bring up Number 2. 2 is the only even prime number and it’s the lowest prime number. If you see the definition “prime” and you don’t consider 2, you’re probably making a mistake. So statement 2 here should be your clue to test x = 2 and realize:

2/1 = 2 with no remainder. Based on statement 1 alone the answer is almost always “remainder 1″ but this one exception allows for a remainder of 0, proving that statement 1 is not sufficient. You need statement 2 to rule it out, making the answer C (for captain?).

The real takeaway here?

Even if you think you’ve “won” after statement 1, if statement 2 looks so much like a mere formality that it’s almost anti-climactic there’s a good chance it’s there as a clue. Ask yourself why statement 2 might matter – sometimes it will and sometimes it won’t, but it’s always worth checking in these cases – and you may find that the real “glory” you’re after requires you to take a step back from that “win” you thought you had earlier on.
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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

No information about z so
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

Answer: Option C

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
No information about z
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

Answer: C

Cheers,
Brent

If x/x-1 in any case will yield 1 as a remainder, except when x=2, then the second statement is true. Because it eliminates 2 as a prime number and other numbers divided by a number one less than itself will give 1 as a remainder. So, why the answer is C not B here? What do I miss?

I think you are using info from (1) when evaluating (2). When evaluating statements individually you should use only info in that statement and the stem.
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(1) x - 1 is a positive integer. This implies x is at least 2.
If x = 2, then z = 0
If x = 3, then z = 1

Insufficient.

(2) x not prime

Obviously insufficient on its own lol

(1 & 2)

Sufficient! For x > 2, it is always the case that z = 1

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