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# DS - number properties

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08 Apr 2011, 22:23
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:41) correct 38% (00:45) wrong based on 24 sessions

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[Reveal] Spoiler: OA

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Re: DS - number properties [#permalink]

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08 Apr 2011, 22:44
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]

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08 Apr 2011, 22:45
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.

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Re: DS - number properties [#permalink]

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08 Apr 2011, 23:19
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]

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08 Apr 2011, 23:54
@vibhav, 0 is considered even, so nothing is violated in that case too.
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Re: DS - number properties [#permalink]

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09 Apr 2011, 00:22
wow i didn't know that! thanks subhash!
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Re: DS - number properties [#permalink]

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09 Apr 2011, 00:39
vibhav wrote:

Also discussed here:
m03-74401.html

This question can be answered using the rules of Even/Odd:

Multiplication rule:
Even * Any Integer = Even
Even * Odd = Even
Even * Even = Even
Odd * Odd = Odd

Even $$\pm$$ Odd = Odd
Odd $$\pm$$ Even = Odd
Odd $$\pm$$ Odd = Even
Even $$\pm$$ Even = Even

And 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]

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10 Apr 2011, 12:34
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.

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Re: DS - number properties [#permalink]

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10 Apr 2011, 13:58
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]

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10 Apr 2011, 20:47
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]

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11 Apr 2011, 00:10
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]

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11 Apr 2011, 05:49
vibhav wrote:

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]

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11 Apr 2011, 05:51
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]

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11 Apr 2011, 05:52
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]

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11 Apr 2011, 18:04
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]

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11 Apr 2011, 22:32
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]

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14 Apr 2011, 17:30
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]

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16 Apr 2011, 10:10
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   [#permalink] 16 Apr 2011, 10:10
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