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

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If p, q, and r are integers, is pq + r even?  [#permalink]

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New post 10 Mar 2011, 13:18
4
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A
B
C
D
E

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Question Stats:

60% (01:47) correct 40% (01:28) wrong based on 193 sessions

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

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

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Re: If p, q, and r are integers, is pq + r even?  [#permalink]

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New post 10 Mar 2011, 13:52
GMATD11 wrote:
1) If p,q and r are integers, is pq+r even?

1) p+r is even
2) q+r is add

M getting D

OA is different. Pls confirm if answer is not D


We want to know if pq+r is even

Statement 1) says p+r is even implying that p and r are either both odd or both even. When they are both even, then irrespective of q being even or odd, pq+r will be even. When they are both odd, depending on q, pq+r can be odd or even. So, insufficient

Statement 2) says q+r is odd, implying at least one of q or r is odd and the other one is even. When r is odd and q is even, pq+r is odd. When q is odd and r is even, pq+r is even or odd depending on value of p, so insufficient.

Combining the two, when p and r are even and hence q is odd, pq+r is even

when p and r are odd and hence q is even, pq+r is odd, so again insufficient

Answer E
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Re: If p, q, and r are integers, is pq + r even?  [#permalink]

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New post 10 Mar 2011, 20:15
1) Insufficient
p + r = even
p = even r = even. The answer is YES
p = odd r = odd q = even. The answer is NO

2) Insufficient
q + r = odd
q = odd r = even p = even. The answer is YES
q = odd r = even p = odd. The answer is NO

combine 1) and 2) Insufficient
p + r = even
q + r = odd
let r = even, p = even, q=odd. The answer is YES
let r = odd, p = odd, q= even. The answer is NO

Hence E.

GMATD11 wrote:
1) If p,q and r are integers, is pq+r even?

1) p+r is even
2) q+r is add

M getting D

OA is different. Pls confirm if answer is not D
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Re: If p, q, and r are integers, is pq + r even?  [#permalink]

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New post 10 Mar 2011, 20:22
For pq+r to be even, pq = even and r = even OR pq = odd and r = odd.

From (1)
p + r is even so p is even and r is even or p is odd and r is odd

but no info about q, if q is even and p and r are odd, then pq+r is odd, otherwise even



From (2) , q + r is odd, so q is even and r is odd OR q is odd and r is even

So if p is even, then pq -> even + r (odd) = odd or even + r (even) = even

Not sufficient

Combining both (1) and (2), if p and r ar even, pq + r is even

if p and r are odd then, pq + r is odd (as q is even then)

Hence we don't have definitive answer,and the answer is E.
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If p, q, and r are integers, is pq + r even?  [#permalink]

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New post Updated on: 26 Jun 2018, 06:18
1
If p, q, and r are integers, is pq + r even?

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

Manhattan tells me I should make the table which works fine. I tried doing it without the table and that worked too. However, without the table I was less convinced and more confused because in your head it gets jumbled up. So is there another foolproof way of doing these? Or do I have to stick with the Manhattan table?

Originally posted by karmapatell on 07 Apr 2013, 03:26.
Last edited by Bunuel on 26 Jun 2018, 06:18, edited 2 times in total.
Formatted.
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Re: A proper organised way to solve this type of questions?  [#permalink]

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New post 07 Apr 2013, 03:46
1
karmapatell wrote:
If p, q, and r are integers, is pq + r even?

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

Manhattan tells me I should make the table which works fine. I tried doing it without the table and that worked too. However, without the table I was less convinced and more confused because in your head it gets jumbled up. So is there another foolproof way of doing these? Or do I have to stick with the Manhattan table?


The Manhattan table works fine, another method is using real numbers .

(1) p + r is even. \(3+1 = even\), so is \(3q+1\) even? depends on q : not Sufficient
(2) q + r is odd. \(2+1=odd\), so is \(p2+1\) even? depends on p : not Sufficient

(1)+(2) p + r is even AND q + r is odd
Example 1: \(3+1=even\)--\(2+1 = odd\)
\(2*3+1=odd\)
Example 2:\(2+2=even\)--\(3+2=odd\)
\(2*3+2=even\)
Not Sufficient
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Re: A proper organised way to solve this type of questions?  [#permalink]

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New post 08 Apr 2013, 05:13
karmapatell wrote:
If p, q, and r are integers, is pq + r even?

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

Manhattan tells me I should make the table which works fine. I tried doing it without the table and that worked too. However, without the table I was less convinced and more confused because in your head it gets jumbled up. So is there another foolproof way of doing these? Or do I have to stick with the Manhattan table?


From F.S 1, assume p=r=0, thus, we get a YES for the question stem. Now assume p=1, r=1,q = 2 we get a NO. Insufficient.

From F.S 2, assume q=0,r=1, we get a NO for the question stem.Now assume r=2,q=1 ,p=2, we get a YES. Insufficient.

Taking both together, we have p=0,r=0,q=1, and a YES. Again taking, r=1,p=1,q=0, a NO. Insufficient.

What might help you in selecting good numbers is the fact that from the F.S 1,either both p,r are even or both are odd. Similarly, from F.S 2, q and r are odd/even or even/odd.

E.
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Re: If p, q, and r are integers, is pq + r even?  [#permalink]

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New post 06 Jan 2014, 09:44
karmapatell wrote:
If p, q, and r are integers, is pq + r even?

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

Manhattan tells me I should make the table which works fine. I tried doing it without the table and that worked too. However, without the table I was less convinced and more confused because in your head it gets jumbled up. So is there another foolproof way of doing these? Or do I have to stick with the Manhattan table?


Odds and Evens, ok

Statement 1

Clearly Insufficient

Statement 2

Same here

Statements 1 and 2 combined

p+r = even
q+r = odd

p-q = odd

Then p must be even and q odd or the other way around

If p is even then pq will be even and 'r' will be even = All even= Answer is YES
if q is even then pq will again be even and 'r' will be odd= All odd = Answer is NO

Hence E is your best choice

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Re: If p, q, and r are integers, is pq + r even?  [#permalink]

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New post 30 Jun 2018, 05:38
chetan2u niks18 pushpitkc pikolo2510 VeritasPrepKarishma

I was not able to combine statements correctly after individually assessing them.

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


Quote:
(1) p + r is even.

This means either p or r is even or BOTH are even.
Since we can not have a definite ans about p,
first term (ie p*q) can be even or odd. Since
we can not definitely know that r is even or odd, final sum
of p*q and r can be either even or odd

Quote:
(2) q + r is odd.

This means either q or r is odd.
Hence first term (ie p*q) can be even or odd. Since
we can not definitely know that r is even or odd, final sum
of p*q and r can be either even or odd

How do we analyze after combing both statements and decide between C/E
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Re: If p, q, and r are integers, is pq + r even?  [#permalink]

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New post 30 Jun 2018, 05:48
1
adkikani wrote:
chetan2u niks18 pushpitkc pikolo2510 VeritasPrepKarishma

I was not able to combine statements correctly after individually assessing them.

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


Quote:
(1) p + r is even.

This means either p or r is even or BOTH are even.----EITHER BOTH ARE ODD OR BOTH ARE EVEN
Since we can not have a definite ans about p,
first term (ie p*q) can be even or odd. Since
we can not definitely know that r is even or odd, final sum
of p*q and r can be either even or odd

Quote:
(2) q + r is odd.

This means either q or r is odd.
Hence first term (ie p*q) can be even or odd. Since
we can not definitely know that r is even or odd, final sum
of p*q and r can be either even or odd

How do we analyze after combing both statements and decide between C/E


1) P+R IS EVEN
both P and R is even or both odd..
2) q+r is odd
one is odd and other is even, so q is opposite of r

combined..
pq+r
A) let both p and r be even then q will be opposite of r so odd
pq+r = E*O+E=E+E=Even
B) let both p and r be ODD then q will be opposite of r so even
pq+r = E*O+O=E+O=Odd

so both E and O possible
insuff
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Re: If p, q, and r are integers, is pq + r even?  [#permalink]

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New post 30 Jun 2018, 05:53
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Hey Arpit,

Make a table of P , Q and R

when you combine, the possibilities are

P-Q-R
1) E-O-E
2) O-E-O

Now check them for pq+r. I think making a quick table will help you clear the confusions

answer will be E
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Re: If p, q, and r are integers, is pq + r even?  [#permalink]

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New post 30 Jun 2018, 06:17
(1) insufficient
Ex+e result is even
Ox+o result is odd if x is even, even if x is odd
Insufficient

(2) insufficient
Xe+o odd if x is even, odd if x is odd
Xo+e even if x is even, odd if x is odd

(1) and (2) are insufficient
Eo+e even
Oe+o odd
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Re: If p, q, and r are integers, is pq + r even? &nbs [#permalink] 30 Jun 2018, 06:17
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