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04 Jul 2018, 23:34
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
44% (02:07) correct
56%
(01:47)
wrong
based on 52
sessions
History
Date
Time
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Not Attempted Yet
If P and Q are non-zero integers, is the equation Py + Qx = 7, exactly the same equation as 9x - 6y = 21 ?
(1) P + Q = 1
(2) P*Q = -6
(1) P + Q = 1
(2) P*Q = -6
04 Jul 2018, 23:44
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amanvermagmat
Two equations are equal if and only if all of their coefficients are equal.
We'll look for statements that give us this information, a Logical approach.
Rewriting our equations so they both equal 7 gives:
Py + Qx = 7
3x - 2y = 7
So our equations are equal when P = -2 and Q = 3.
(1) One equation, two variables --> infinite solutions.
Insufficient.
(2) One equation, two variables --> infinite solutions.
Insufficient
Combined:
Two equations, two variables usually gives one unique solution but in this case both of our equations are symmetrical.
So, while we can find the right numbers (they happen to be 3 and -2), we don't know which is P and which is Q.
Insufficient
(E) is our answer.
05 Jul 2018, 05:02
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amanvermagmat
Given, Py + Qx = 7----------(a)
& 9x - 6y = 21 Or, 3x + -(2)y =7 ---(b)
Equating x & y co-efficient in (a) and (b) we have P=-2 & Q=3
So, when P=-2 and Q=3, both the equations become same.
Re-phrased Question stem:- Is P=-2 ,Q=3 ?
Statement-2
P + Q = 1
When P=-2 & Q=3, our answer to question stem is Yes, but there are 'n' number of combinations for which P+Q=1.
Hence, insufficient.
Statement-2
P*Q=-6
When P=-2 & Q=3, our answer to question stem is Yes, but there are 'n' number of combinations for which P*Q=-6.
Hence, insufficient.
(1)+(2), we have
\((P-Q)^2=(P+Q)^2-4*PQ\)
we know the value of P+Q & PQ from st1 & st2 respectively, therefore, we can calculate P-Q & subsequently, value of P & Q can be determined.
So, (\(P-Q)^2=1^2-4*(-6)=1+24=25\)
So, P-Q=5 Or, P-Q=-5
P-Q=5 & P+Q=1. yields P=3, Q=-2...In this case answer to question is No.
P-Q=-5 & P+Q=1. yields P=-2, Q=3...In this case answer to question is Yes.
So, insufficient.
Ans (E)
