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# DS quadratic question where stat 1 and 2 only give one common root

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Intern
Joined: 05 Mar 2017
Posts: 4
DS quadratic question where stat 1 and 2 only give one common root [#permalink]

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07 Apr 2017, 13:08
Hi guys,

I have a question to the fundamentals of DS questions.

I know that both DS statements are true and non-contradictory. Thus, I was quite baffled to do a DS question where statement one gives me two quadratic roots: -23, 23, but statement two gives me the quadratic roots: -23, -17.

Could someone explain how this is possible? In my mind, the statements are contradictory then, since only one root is common between the two statements.

The question was from Veritas Prep CAT#2 with Question ID: 07578 (not sure if I'm allowed to post the question here due to copyright).

Thanks!
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Manager
Joined: 17 May 2015
Posts: 232
Re: DS quadratic question where stat 1 and 2 only give one common root [#permalink]

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07 Apr 2017, 21:24
1
starryskyes wrote:
Hi guys,

I have a question to the fundamentals of DS questions.

I know that both DS statements are true and non-contradictory. Thus, I was quite baffled to do a DS question where statement one gives me two quadratic roots: -23, 23, but statement two gives me the quadratic roots: -23, -17.

Could someone explain how this is possible? In my mind, the statements are contradictory then, since only one root is common between the two statements.

The question was from Veritas Prep CAT#2 with Question ID: 07578 (not sure if I'm allowed to post the question here due to copyright).

Thanks!

Hi starryskyes,

Whatever you have explained above is perfectly fine in a DS question. In such cases, answer would be C.

Let me give you one example from Quant Review(official question).

Is $$y = 6$$

(1) $$y^{2} = 36$$
(2) $$y^{2} - 7y + 6 = 0$$

From st.(1) we have two roots. y = 6 or -6 . Hence, not sufficient.

From st.(2) we get (y-6)(y-1) = 0 => y = 6 or 1. NOT Sufficeint.

Now by combining (1) and (2), we have a unique answer y = 6. Hence, Sufficient. Answer (C)

Hope it helps.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India
Re: DS quadratic question where stat 1 and 2 only give one common root [#permalink]

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09 Apr 2017, 23:40
1
starryskyes wrote:
Hi guys,

I have a question to the fundamentals of DS questions.

I know that both DS statements are true and non-contradictory. Thus, I was quite baffled to do a DS question where statement one gives me two quadratic roots: -23, 23, but statement two gives me the quadratic roots: -23, -17.

Could someone explain how this is possible? In my mind, the statements are contradictory then, since only one root is common between the two statements.

The question was from Veritas Prep CAT#2 with Question ID: 07578 (not sure if I'm allowed to post the question here due to copyright).

Thanks!

You are right - both DS statements are true and non-contradictory. The point is that in this question too, the two statements are true and non contradictory. Let me explain.

Let's simplify:

Question stem: What is x?

Stmnt 1: x is either 23 or -23.
Stmnt 2: x is either -23 or -17.

Now you know that both statements are true. So the value of x has to be one of 23 and -23. It also has to be one of -23 and -17. So the only value that x can take is -23. That will keep both statements true.
In that case, x will be one of 23 and -23 (it is -23) and x will also be one of -23 and -17 (it is -23).

The statements are not contradictory. Using both, we realise that the only value x can take is -23.

I hope this sorts out your doubt!
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Re: DS quadratic question where stat 1 and 2 only give one common root   [#permalink] 09 Apr 2017, 23:40
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