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Intercept at the point (2,0)

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Source: — Data Sufficiency |
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by MartyMurray » Mon Feb 22, 2016 3:25 am
didieravoaka wrote:Does the equation y = (x - p)(x - q) intercept the x-axis at (2, 0)?

(1) pq = -8

(2) -2 - p = q
The question can be translated to the following. Is 0 = (2 - p)(2 - q)?

Statement 1:

Try various factors of -8.

p = 1 q = -8 (2 - p)(2 - q) = (1)(6) = 6 No.

p = -4 q = 2 (2 - p)(2 - q) = (2)(0) = 0 Yes.

Insufficient.

Statement 2:

Try various numbers.

Already tried p = -4 q = 2 Yes.

Try p = 1000 q = -1002 (2 - p)(2 - q) will be a huge negative number. No.

Insufficient.

Combined the statements can be used to determine the possible values of p and q. Do you need to do the math given that you have two variables and two distinct equations? Maybe not, but sometimes even with 2 equations you can get multiple possible values for the variables.

Substitute Statement 2 into Statement 1 to get p(-2 - p) = -8.

2p + p² = 8 p² + 2p - 8 = 0 (p + 4)(p - 2) = 0

So if -2 - p = q, then either p = 2 and q = -4 or p = -4 and q = 2.

Either way 0 = (2 - p)(2 - q).

Sufficient.

The correct answer is C.
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by GMATGuruNY » Mon Feb 22, 2016 4:13 am
Does the equation y = (x - p)(x - q) intercept the x-axis at the point (2,0)?

(1) pq = -8

(2) -2 - p = q
Since (2, 0) implies that x=2 and y=0, substitute x=2 and y=0 into y = (x - p)(x - q):
0 = (2-p)(2-q).
The resulting equation will be valid if p=2 or q=2.

Question stem, rephrased:
Does p=2 or q=2?

Statement 1: pq = -8
It's possible that p=2 and q=-4, in which case the answer to the question stem is YES.
It's possible that p=1 and q=-8, in which case the answer to the question stem is NO.
Since the answer is YES in the first case but NO in the second case, INSUFFICIENT.

Statement 2: p+q = -2
It's possible that p=2 and q=-4, in which case the answer to the question stem is YES.
It's possible that p=1 and q=-3, in which case the answer to the question stem is NO.
Since the answer is YES in the first case but NO in the second case, INSUFFICIENT.

Statements combined:
Test factor pairs of -8.
In a viable pair, the sum of the two factors will be -2.
Factor pairs of -8:
1, -8
2, -4
4, -2
8, -1.

Only the red pair is viable, implying two cases:
p=2, q=-4
p=-4, q=2.
In each case, the answer to the question stem is YES.
SUFFICIENT.

The correct answer is C.
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