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# How many of integers P, Q, and R are zeroes? (1) PQR=0 (2)

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Senior Manager
Joined: 30 Aug 2003
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How many of integers P, Q, and R are zeroes? (1) PQR=0 (2) [#permalink]  06 Feb 2004, 15:25
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How many of integers P, Q, and R are zeroes?

(1) PQR=0
(2) P+Q+R=0
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shubhangi

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Joined: 03 Jul 2003
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Kudos [?]: 22 [0], given: 0

Good One!

Ans: E

1) N = 1,2 or 3
2) N = 0 , 1, 3
Senior Manager
Joined: 23 Aug 2003
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Location: In the middle of nowhere
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Kudos [?]: 12 [0], given: 0

1) Of PQR ...Insufficient
each of them can be zero..or all three can be zero...other combinations...

2) P+Q+R ...Insufficient...
(-2)+1+1.....1+0+(-1)....

Vivek.
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"Start By Doing What Is Necessary ,Then What Is Possible & Suddenly You Will Realise That You Are Doing The Impossible"

Senior Manager
Joined: 30 Aug 2003
Posts: 325
Location: dallas , tx
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Kudos [?]: 9 [0], given: 0

could some one explain ...how do u solve statement 2.. ??..are you guys assuming negetive value also..becoz if all are postive integers then there has tobe 3 zeros..
pls explain..
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shubhangi

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Location: Singapore
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Kudos [?]: 0 [0], given: 0

If no condition on integers is specified,, u should try both -ve and +ve integers.
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Joined: 30 Oct 2003
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Location: NewJersey USA
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Kudos [?]: 41 [0], given: 0

Let me explain
1) Atleast one of P, Q and R is zero. We cannot determine how many are zeroes here. It could be 1 or 2 or 3 zeroes.
2) Sum of three numbers is zero
Here it is possible that P = -(Q+R) or Q = -(P+R) and none of them might be zero.
All can be zeroes. So this condition is insufficient. Here either none are zeroes or one is zero or three are zeroes

Combine both
P = -(Q+R) here R might be zero which will satisfy A) then P = -Q which will satisfy B). So one zero will satisfy A and B
If All numbers are zero then also Both A) and B are satisfied.
So We cannot tell if there is one zer or three zeroes.

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