If xyz = 1001, is x odd? (1) y is odd (2) z is odd

Solution: If we consider all x,y and z as integers,then this question is illogical as we wouldn't need either of the statements.
1001 = 7*11*13
Statement1 : From this we know y is an integer.
Let y=11, if z=13, then x=7.Yes. If z=6.5,then x=14.No. Insufficient

Statement2 : From this we know z is an integer.
Let z=13,if y = 11 then x=7.Yes. If y=5.5,then x=14.No. Insufficient

Combined: So, y and z are integers which has to be odd. So x is also a odd integer.Sufficient.

Option C

The question states about even or odd. I believe that gives the benefit of doubt to assume the numbers in question as integers.
The question does not ask about rational or integer.
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Statement 1:
Doesn't provide any information about x or z.
INSUFFICIENT

Statement 2:
Doesn't provide any information about x and y
INSUFFICIENT

Combining 1 & 2:
Doesn't provide any information about x,y or z being integer or not.
if, x=1001/5 y=5/1001 and z=1001 will give product 1001.
Also if x=7 y=13 and z=11, their product will be 1001.
We cannot say that x is odd in 1st case since,a fraction cannot be even or odd.
In 2nd case x is odd.
We do not know for sure weather x is odd or not.
INSUFFICIENT

Answer:- E

I believe the correct answer is E. The question never mentions whether x is integer or not.
If x=\(\frac{1001}{3}\),y=1, and z=3, their product is 1001, but x isn't an integer. On the other hand if x=1001,y=1, and z=1, x is an integer.

we do not know whether x, y, and z are strictly integers.

1001 = 11*7*13
with y = 7/2, z = 13/2, and x = 11*2*2, we still get the same product for xyz. hence, to conclude that x is odd, we need to know that the product yz is odd. hence, (C)

I see people assuming that should never be assumed in DS questions.

In this question, nowhere is it mentioned that x,y,z MUST be integers. In order to have an unambiguous yes or no for this question, the correct statement must tell you that x=integer. If this is not true, then you will get a "NO" for all values of x but if x= integer , then again you get a YES or NO depending on the actual value of the integer. This here should have made you mark E for this question. No need for fancy calculations.

For calculation minded people, look below, I am only taking the case when x=integer.

Per statement 1, y=odd, lets assume y=1

Given, xyz=1001---> 2 scenarios

Scenario 1: y=1,z=1001/2 and x=2, answer to is x=odd is NO

Scenario 2: y=1,z=1001/3 and x=3, answer to is x=odd is YES

Thus you get 2 different answers and hence not sufficient.

Per statement 2, You proceed in exactly the same way as in statement 2 but now with z=odd, lets assume z=1

Given, xyz=1001---> 2 scenarios

Scenario 1: z=1,y=1001/2 and x=2, answer to is x=odd is NO

Scenario 2: z=1,y=1001/3 and x=3, answer to is x=odd is YES

Thus you get 2 different answers and hence not sufficient.

Even after combining, you see that y=z=1001 and x=1/1001 satisfies both the statements and gives a "no" while for all other cases you do get x=odd integer. Thus you still get 2 different answers and hence E is the correct answer.
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VERITAS PREP OFFICIAL SOLUTION:

Now, before we reveal the answer choices and choice-by-choice statistics from Question Bank users, let’s point this out: this question ranks as one of the top 30 most difficult questions in the bank, with only 15% of all respondents answering correctly (and, as you’ll see, a sample size of over 200 users). And consider this: in GMAT multiple choice questions a random guess has a probability of 20% of being correct. Question Bank users – those who care enough about their GMAT progress that they are actively seeking out additional practice questions – are worse than a random guess at this question. Which should go to show you the power of the trap being laid here. Let’s go to the statistics, taken straight from the GMAT Question Bank:



Note the answers – almost no one thought that either of statement 1 or 2 (but not both) was sufficient, which is good evidence that just about everyone in the question bank “tried” on this question. And the most popular answer choices were just about split between C and D. In either case, people employed the number property that Odd*Odd*Odd = Odd – without considering that x could be a noninteger. Consider this possibility:

y = 1001, z = 1001, and x = 1/1001.

The statements hold, but x is not odd in this case.

What’s even worse is the procedure that those who spent more time on this might have used. It’s possible to factor out 1001 into 7 * 11 * 13, but that’s a time-consuming process. So for those who investigated that much further, they may well have gotten this question wrong in over two minutes, costing them not just one correct answer but some valuable time en route to another.

What can you learn from this? A few things:

1. Don’t be overly impressed by seeing opportunities to employ rules that you have memorized. It’s quite easy to get lulled into a wrong answer because the question “rewarded” you for knowing something that you had on a flash card, but keep in mind that this is a reasoning test that will force you to think often. When an answer seems too good to be true, investigate further.
2. It’s “Page One,” but be absolutely certain not to make assumptions on Data Sufficiency questions. Force yourself to consider numbers with different properties – negatives, nonintegers, and 0 in particular.
3. Don’t assume that, just because a question looks easy, it’s easy. This question is in no way one of the top 30 “most intimidating” questions in the question bank, but it ranks as one of the 30 most frequently missed.

At Veritas Prep, we’re big fans of the strategy “Think Like the Testmaker” — meaning, learn how the authors of the GMAT employ devices to trap you. While it’s likely one of the first traps you learn about, the assumption that we all make about integers or positive numbers frequently lends itself to trap answers. As you can see from these statistics, many elite test-takers missed this question because of that assumption. And as you’ll see in future posts (and, although we hope not, probably in your own future mistakes) these types of mistakes happen to just about everyone and make for some of the statistically-most-difficult questions on the GMAT. Be careful about assumptions — and don’t just take our word for, it, but rather listen to almost 85% of your GMAT competitors who had to learn this one the hard way.


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(1) y is odd

Let y = 1, x = 1/3 & z =3003..........xyz = 1001...........Answer is NO

Let y = 1, x = 1 & z =1001.......... xyz = 1001...........Answer is Yes

Insufficient

(2) z is odd

Let z = 1, x = 1/3 & y =3003..........xyz = 1001...........Answer is NO

Let z = 1, x = 1 & y =1001.......... xyz = 1001...........Answer is Yes

Insufficient

Combine 1 & 2

Same examples above yield no clear answer

Insufficient

Answer: E

Answer should be E.

These questions are very tricky, need to watch out if anything mentioned in question as integer.

Statement 1: y is odd
x = 1, y = 1001, z =1 OR x = 1/2, y = 1001, z = 2 -> InSuff
Statement 2: z is odd, same as above -> InSuff

(1)+(2) => x = 1, y = 1001, z = 1 OR x = 1/7, y = 7007, z = 1 -> InSuff -> Answer (E)

Hi, they havent asked if x is an odd integer. they've only asked if X is odd. so how does it matter if X is a fraction?