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DS - number properties [#permalink]
 08 Apr 2011, 23:23
Question Stats:
78% (01:43) correct
21% (00:59) wrong based on 0 sessions
guys does your answer match the OA?
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Re: DS - number properties [#permalink]
08 Apr 2011, 23:44
Is pqr even?
or
Is one of the integers p,q or r even?
1) Sufficient
p-1 is odd and r+1 is odd. Hence p is even and r is even.
2) Sufficient
p is even and r is odd or vice-versa. In any case it is sufficient.
Hence D.
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Re: DS - number properties [#permalink]
08 Apr 2011, 23:45
St 1: Since (p-1)(r+1) is Odd, it means both (p-1) and (r+1) are odd, which also means that both p and r are even (since they are integers).
A product of 3 integers would be even if atleast one of them is even. Hence pqr is even. Sufficient.
St 2: (q-r)^2 is odd.
This suggests that the difference between q and r is also odd (since square of odd integer is odd). Since the difference is odd, one of them has to be an Even integer. E.g. 6-3 = 3. Both cannot be odd or both cannot be even. E.g. 9-3=6 and 8-4=4.
Again, a product of 3 integers would be even if atleast one of them is even. Hence pqr is even. Sufficient.
Answer - D
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Re: DS - number properties [#permalink]
09 Apr 2011, 00:19
indeed the question is if the product is even. my contention is what if r= 0? in that case,
1. (p-1)*1 = odd this p is even .. but pqr =0
2. (q-0)^2 = odd ..i.e. q = odd and pqr = 0
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Re: DS - number properties [#permalink]
09 Apr 2011, 00:54
@vibhav, 0 is considered even, so nothing is violated in that case too.
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Re: DS - number properties [#permalink]
09 Apr 2011, 01:22
wow i didn't know that! thanks subhash!
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Re: DS - number properties [#permalink]
09 Apr 2011, 01:39
vibhav wrote: guys does your answer match the OA? Also discussed here: m03-74401.htmlThis question can be answered using the rules of Even/Odd: Multiplication rule: Even * Any Integer = EvenEven * Odd = EvenEven * Even = EvenOdd * Odd = OddAddition rule: Even \pm Odd = OddOdd \pm Even = OddOdd \pm Odd = EvenEven \pm Even = EvenAnd these rules are valid for all +ve, 0, -ve, odd/even numbers. By the way, 0 is an even number. Q: Is p*q*r = even? OR Is any of p, q, r is even. Because, if one of p,q,r is even, the product will be even. 1. (p-1)(r+1) = odd We know Odd*Odd=Odd Implies: (p-1) = odd Even - odd =odd Even-1=odd p=even p*q*r=even*q*r=even Sufficient. 2. (q-r)^2 = odd (q-r)*(q-r)=odd odd*odd = odd Implies: (q-r) = odd Even - odd = odd Odd - Even = odd Either q or r is even. p*q*r = even Sufficient. Ans: "D"
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Re: DS - number properties [#permalink]
10 Apr 2011, 13:34
1. Sufficient.
p-1 is odd => p is even
r+1 is odd => r is even
pqr is even
2. Sufficient.
when r is odd , q is even .
when r is even , q is odd
either ways pqr product is even. enough to answer the question.
Answer is D.
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Re: DS - number properties [#permalink]
10 Apr 2011, 14:58
D as 1. as explained above. Sufficient 2. Sufficient as (q-r)(q-r) is odd that is q <> r; q - r is not even => exactly one of them is even and the other is odd. so pqr is even = due to that even
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Re: DS - number properties [#permalink]
10 Apr 2011, 21:47
Just read Manhattan's number properties workbook.
So lemme try to explain this for my own sake:
1. Sufficient
Only odd x odd can equal an odd number. Hence, P and R are both even. Any number multiplied by an even number is even. As such, PQR is even.
2. Sufficient
Just like #1, odd x odd is the only way to get odd. As such, Q - R must be odd. Either Q or R are even/odd or odd/even. Either way, one of the numbers in the set is even, so the product of PQR must be even.
Booyah! I would never have been able to figure that out without MGMAT!
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Re: DS - number properties [#permalink]
11 Apr 2011, 01:10
hi all, i am of diff opinion. I am sure its C both statements are required to answer. 1 gives info of only p & r, while 2 gives info of q. We need to know the product value of p,q & r. so both statements are essentially needed.
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Re: DS - number properties [#permalink]
11 Apr 2011, 06:49
vibhav wrote: guys does your answer match the OA? Is pqr even? This is asking if either p, q or r is even. If one is even, then Yes! 1) (p-1)(r+1) is odd RULE ====================== ODD x EVEN results to EVEN ODD x ODD results to ODD ====================== Using that rule, (p-1) is ODD and (r+1) is ODD. This means p (the number after p-1) is EVEN. We can stop there and realize that pxqxr is EVEN. Sufficient! 2) (q-r)(q-r) ois ODD This means q-r is ODD. RULE ======================== ODD +/- ODD = EVEN EVEN +- ODD = ODD ======================== From the rule, one of q and r is EVEN. Then, it's SUFFICIENT to say that pxqxr is EVEN. Hence D.
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Re: DS - number properties [#permalink]
11 Apr 2011, 06:51
sdas wrote: hi all, i am of diff opinion. I am sure its C both statements are required to answer. 1 gives info of only p & r, while 2 gives info of q. We need to know the product value of p,q & r. so both statements are essentially needed. To choose (C) means that statement 1 nor statement 2 is sufficient. But in the sample above, Statement 1 and 2 can both answer the question without the need of each other.
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Re: DS - number properties [#permalink]
11 Apr 2011, 06:52
aznboi986 wrote: Just read Manhattan's number properties workbook.
So lemme try to explain this for my own sake:
1. Sufficient
Only odd x odd can equal an odd number. Hence, P and R are both even. Any number multiplied by an even number is even. As such, PQR is even.
2. Sufficient
Just like #1, odd x odd is the only way to get odd. As such, Q - R must be odd. Either Q or R are even/odd or odd/even. Either way, one of the numbers in the set is even, so the product of PQR must be even.
Booyah! I would never have been able to figure that out without MGMAT! I do agree. MGMAT is really good in breaking these things down into easier to comprehend pieces. 
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Re: DS - number properties [#permalink]
11 Apr 2011, 19:04
vibhav wrote: indeed the question is if the product is even. my contention is what if r= 0? in that case,
1. (p-1)*1 = odd this p is even .. but pqr =0
2. (q-0)^2 = odd ..i.e. q = odd and pqr = 0 This is actually a pertinent point, I think. Question might need to be reworded to "positive integers" or "non-zero integers" instead of just "integers". Zero is neither even nor odd (as a helpful forummer once pointed to to me).
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Re: DS - number properties [#permalink]
11 Apr 2011, 23:32
oster wrote: vibhav wrote: indeed the question is if the product is even. my contention is what if r= 0? in that case,
1. (p-1)*1 = odd this p is even .. but pqr =0
2. (q-0)^2 = odd ..i.e. q = odd and pqr = 0 This is actually a pertinent point, I think. Question might need to be reworded to "positive integers" or "non-zero integers" instead of just "integers". Zero is neither even nor odd (as a helpful forummer once pointed to to me). "0" is definitely EVEN. "0" is neither POSITIVE nor NEGATIVE.
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Re: DS - number properties [#permalink]
14 Apr 2011, 18:30
oster wrote: Zero is neither even nor odd (as a helpful forummer once pointed to to me). In some exams, even numbers refer to positive even numbers only (e.g. in CAT for IIMs - if you don't know which exam I am talking about, just ignore it) but as far as GMAT is concerned, an even number is the one which is divisible by 2. Hence 0, -4 and 68 are all even numbers. (This is also the more widely accepted definition, I think) My guess is someone might have told you that '1 is neither prime nor composite.' (which is true)
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Re: DS - number properties [#permalink]
16 Apr 2011, 11:10
Very Truly said O is definitely even number & 1 is not a prime no. as pointed by karishma
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Re: DS - number properties
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16 Apr 2011, 11:10
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