If y = |x - 2| + |x - 3|, is y = 1?
1) 2 < x < 3
2) x > 2
OA: A
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A little help with this one, please?
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GMATGuruNY
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|a-b| = the DISTANCE between a and b.fambrini wrote:If y = |x - 2| + |x - 3|, is y = 1?
1) 2 < x < 3
2) x > 2
OA: A
Thus:
|x-2| = the distance between x and 2.
|x-3| = the distance between x and 3.
y = the SUM of these two distances.
Question stem rephrased:
Is the sum of the two distances equal to 1?
The distance between 2 and 3 is 1.
Thus, if x is BETWEEN these two endpoints, then the sum of the two distances will be EQUAL TO 1:
2 <--- |x-2| ---> x <---|x-3|---> 3.
As indicated by the blue portion, |x-2| + |x-3| = the distance between 2 and 3 = 1.
By extension, if x is BEYOND either endpoint -- if x is to the left of 2 or to the right of 3 -- then the sum of the two distances will be GREATER THAN 1.
Thus:
y=1 if x is between 2 and 3.
y>1 if x if x<2 or x>3.
Statement 1: 2<x<3
Since x is between 2 and 3, y=1.
SUFFICIENT.
Statement 2: x>2
If x=2.5, then x is between 2 and 3, with the result that y=1.
If x=4, then x is NOT between 2 and 3, with the result that y>1.
INSUFFICIENT.
The correct answer is A.
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Hi fambrini,
GMAT questions are built around patterns (math rules, formulas, grammar, logic, etc.), so even if you don't initially spot a pattern, you can often do some 'brute force' work to prove that a pattern is there.
We're told that Y = |X - 2| + |X - 3|. We're asked if Y = 1. This is a YES/NO question and this question can be solved by TESTing VALUES.
1) 2 < X < 3
Let's TEST the most obvious value we can think of...
IF... X = 2.5
|2.5 - 2| + |2.5 - 3| = .5 + .5 = 1 and the answer to the question is YES
Next, let's choose a different value in that range...
IF... X = 2.4
|2.4 - 2| + |2.4 - 3| = .4 + .6 = 1 and the answer to the question is YES
That's interesting! Two different values of X produced the exact same answer. Let's try one more...
IF... X = 2.99
|2.99 - 2| + |2.99 - 3| = .99 + .1 = 1 and the answer to the question is YES
It certainly appears that the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT
2) X > 2
With this Fact, we can use ANY of our prior examples from Fact 1:
IF... X = 2.5
|2.5 - 2| + |2.5 - 3| = .5 + .5 = 1 and the answer to the question is YES
But what if we TEST a value that is greater than 3?
IF... X = 4
|4 - 2| + |4 - 3| = 2 + 1 = 3 and the answer to the question is NO.
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
GMAT questions are built around patterns (math rules, formulas, grammar, logic, etc.), so even if you don't initially spot a pattern, you can often do some 'brute force' work to prove that a pattern is there.
We're told that Y = |X - 2| + |X - 3|. We're asked if Y = 1. This is a YES/NO question and this question can be solved by TESTing VALUES.
1) 2 < X < 3
Let's TEST the most obvious value we can think of...
IF... X = 2.5
|2.5 - 2| + |2.5 - 3| = .5 + .5 = 1 and the answer to the question is YES
Next, let's choose a different value in that range...
IF... X = 2.4
|2.4 - 2| + |2.4 - 3| = .4 + .6 = 1 and the answer to the question is YES
That's interesting! Two different values of X produced the exact same answer. Let's try one more...
IF... X = 2.99
|2.99 - 2| + |2.99 - 3| = .99 + .1 = 1 and the answer to the question is YES
It certainly appears that the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT
2) X > 2
With this Fact, we can use ANY of our prior examples from Fact 1:
IF... X = 2.5
|2.5 - 2| + |2.5 - 3| = .5 + .5 = 1 and the answer to the question is YES
But what if we TEST a value that is greater than 3?
IF... X = 4
|4 - 2| + |4 - 3| = 2 + 1 = 3 and the answer to the question is NO.
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
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Jay@ManhattanReview
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Let us take statement 1. Assume that x = 2, we get y = |2 - 2| + |2 - 3| = 1. Now assume that x = 3, we get y = |3 - 2| + |3 - 3| = 1. We see that value of y remains constant = 1 for a linear equation (y = |x - 2| + |x - 3|) whether x = 2 or x = 3, thus it would also render the same value of y = 1, if 2 < x < 3. Statement 1 is sufficient.fambrini wrote:If y = |x - 2| + |x - 3|, is y = 1?
1) 2 < x < 3
2) x > 2
OA: A
Statement 2 is not sufficient as for 2 < x < 3, we get y = 1, but y > 1 for x > 3. Say x = 4, then y = 3. Not sufficient.
Hope this helps!
-Jay
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