If y is not equal to 1, is x = 1?
1. x2 + y2 = 1
2. y = 1 - x
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If y is not equal to 1, is x = 1?
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800_or_bust
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(1) Not sufficient. x could be zero, and y=-1. Or x could be +/-1, in which case y=0. Or x^2 = y^2 = 1/2. Etc...prata wrote:If y is not equal to 1, is x = 1?
1. x2 + y2 = 1
2. y = 1 - x
(2) Not sufficient. y could be any value, except 1. Thus x can be any value except 0.
(1) & (2) combined: This is sufficient. Combining the two statements:
x^2 + (1-x)^2 = 1
Then x^2 + (1 - 2x + x^2) = 1
2x^2 - 2x = 0
x(2x - 2) = 0. So x = 0 or x = 1, but x cannot equal 0 from (2) above. Hence, x = 1 and y = 0.
Answer is C.
Last edited by 800_or_bust on Mon Jun 27, 2016 9:53 am, edited 3 times in total.
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Hi prata,
This DS question can be solved by TESTing VALUES.
We're told that Y CANNOT be 1. We're asked if X = 1. This is a YES/NO question.
1) X^2 + Y^2 = 1
IF....
X = 1
Y = 0
Then the answer to the question is YES.
IF....
X = -1
Y = 0
Then the answer to the question is NO.
Fact 1 is INSUFFICIENT
2) Y = 1 - X
Here, you might find it helpful to rewrite the equation as...
X + Y = 1
IF....
X = 1
Y = 0
Then the answer to the question is YES.
IF....
X = -1
Y = 2
Then the answer to the question is NO.
Fact 2 is INSUFFICIENT
Combined, we know...
X^2 + Y^2 = 1
X + Y = 1
The only pair of values that will 'fit' both equations at the same time are 0 and 1. Since we're told that the Y CANNOT be 1, then it must be the 0. By extension, the X MUST be 1 and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
This DS question can be solved by TESTing VALUES.
We're told that Y CANNOT be 1. We're asked if X = 1. This is a YES/NO question.
1) X^2 + Y^2 = 1
IF....
X = 1
Y = 0
Then the answer to the question is YES.
IF....
X = -1
Y = 0
Then the answer to the question is NO.
Fact 1 is INSUFFICIENT
2) Y = 1 - X
Here, you might find it helpful to rewrite the equation as...
X + Y = 1
IF....
X = 1
Y = 0
Then the answer to the question is YES.
IF....
X = -1
Y = 2
Then the answer to the question is NO.
Fact 2 is INSUFFICIENT
Combined, we know...
X^2 + Y^2 = 1
X + Y = 1
The only pair of values that will 'fit' both equations at the same time are 0 and 1. Since we're told that the Y CANNOT be 1, then it must be the 0. By extension, the X MUST be 1 and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
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There's a nice discussion here with some other approaches: https://www.beatthegmat.com/if-y-is-not- ... 76846.html
Cheers,
Brent
Cheers,
Brent
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DavidG@VeritasPrep
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Not safe at all! (Though, obviously, integers would be easier to use, so you'd likely start with those values.) If the question doesn't specify that you're talking about integers, and it's not a word problem involving entities that would logically take integer values (you wouldn't worry about 1/3 of a cat) you cannot assume that the variables can only assume integer values.prata wrote:Would it be safe to assume that while solving inequalities only integers have to be considered while testing values of x and y?
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Hi prata,
On Test Day, on most of the questions that you can solve by TESTing VALUES, sticking with positive integers will be enough for you to get to the correct answer. However, certain questions will 'hinge' on the idea that the variables could be negative, or 0 or a non-integer (and you'll almost certainly face some of these issues in Data Sufficiency). To score at the higher levels in the Quant section, you have to be flexible enough in your thinking to realize that there are OTHER options besides positive integers.
GMAT assassins aren't born, they're made,
Rich
On Test Day, on most of the questions that you can solve by TESTing VALUES, sticking with positive integers will be enough for you to get to the correct answer. However, certain questions will 'hinge' on the idea that the variables could be negative, or 0 or a non-integer (and you'll almost certainly face some of these issues in Data Sufficiency). To score at the higher levels in the Quant section, you have to be flexible enough in your thinking to realize that there are OTHER options besides positive integers.
GMAT assassins aren't born, they're made,
Rich
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OptimusPrep
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On the GMAT, you would be given everything related to the question.prata wrote:Would it be safe to assume that while solving inequalities only integers have to be considered while testing values of x and y?
If not given, do not limit yourself. Especially in the DS questions, where some of the values might be fractions.
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S1:
x² + y² = 1
If y = 0, then x = 1 or x = -1. If y ≠ 0, then x ≠ 1. NOT SUFFICIENT
S2:
y = 1 - x
If y = 0, then x = 1. If y ≠ 0, then x ≠ 1. NOT SUFFICIENT
S1 + S2
x² + y² = 1
x² + (1 - x)² = 1
x² + 1 - 2x + x² = 1
2x² - 2x = 0
x * (x - 1) = 0
So x = 0 or x = 1. But if x = 0, then y = 1, and we were told in the stem that y ≠1. So we must have x = 1, and we're set!
x² + y² = 1
If y = 0, then x = 1 or x = -1. If y ≠ 0, then x ≠ 1. NOT SUFFICIENT
S2:
y = 1 - x
If y = 0, then x = 1. If y ≠ 0, then x ≠ 1. NOT SUFFICIENT
S1 + S2
x² + y² = 1
x² + (1 - x)² = 1
x² + 1 - 2x + x² = 1
2x² - 2x = 0
x * (x - 1) = 0
So x = 0 or x = 1. But if x = 0, then y = 1, and we were told in the stem that y ≠1. So we must have x = 1, and we're set!
