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If p, q, and r are integers, is pq + r even? [#permalink]
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10 Mar 2011, 13:18
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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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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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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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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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Updated on: 26 Jun 2018, 06:18
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.
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Re: A proper organised way to solve this type of questions? [#permalink]
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07 Apr 2013, 03:46
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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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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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 pq = 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 Cheers! J



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Re: If p, q, and r are integers, is pq + r even? [#permalink]
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30 Jun 2018, 05:38
chetan2u niks18 pushpitkc pikolo2510 VeritasPrepKarishmaI 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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30 Jun 2018, 05:48
adkikani wrote: chetan2u niks18 pushpitkc pikolo2510 VeritasPrepKarishmaI 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 EVENSince 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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30 Jun 2018, 05:53
Hey Arpit, Make a table of P , Q and R when you combine, the possibilities are PQR 1) EOE 2) OEO 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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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




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