If p, q and r are integers, is pq + r even? NP Ch2 Q16

[starburst83]

Hi,

Apologies if this has been answered before, but if it has, I cannot find the answer in this forum.

To start, statement (2) states: "q + r is odd". The solution for statement (2) states that "The variables q and r must either both be odd or both be even..."

If "q + r is odd", then must not one be odd and the other even?

After all, O + E = O (and E + O = O).

However, if "q and r must either both be odd or both be even", then either case would result in an even: O + O = E and E + E = E

So how can we evaluate statement (2) if we state that they "must either both be odd or both be even"?

Secondly, shouldn't there be a comma after the first "q" in the question stem? Given that it is the second-to-last item in the list (right before "and"), which is greater than three items long, and that the GMAT prefers serial commas, and that this is a GMAT book? :)

And that is all for now.

Thanks for you time.

SB

[esledge]

In the future, please post the full text of the question even if your question is only about part of it. For completeness, here it is :-)

If p, q, and r are integers, is pq + r even?

(1) p + r is even.
(2) q + r is odd.

To start, statement (2) states: "q + r is odd". The solution for statement (2) states that "The variables q and r must either both be odd or both be even..."

If "q + r is odd", then must not one be odd and the other even?

After all, O + E = O (and E + O = O).

However, if "q and r must either both be odd or both be even", then either case would result in an even: O + O = E and E + E = E

So how can we evaluate statement (2) if we state that they "must either both be odd or both be even"?

That is definitely an error. The chart for (2) is correct, as it lists every scenario such that EITHER q or r is even, but not both of them. Thanks for bringing this to our attention. We'll be sure to fix the text to match the chart before the next printing.

Secondly, shouldn't there be a comma after the first "q" in the question stem? Given that it is the second-to-last item in the list (right before "and"), which is greater than three items long, and that the GMAT prefers serial commas, and that this is a GMAT book? :)

Indeed :-) We'll get that comma in there, too.

[starburst83]

Thanks for the reply.

I'll be sure to include the complete question next time. :)

[esledge]

No worries. Thanks again for the good catch.