235. Are x and y both positive?
a. 2x - 2y = 1
b. x�y > 1
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Are x and y both positive? a. 2x - 2y = 1 b. x�y > 1
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Brent@GMATPrepNow
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Target question: Are x and y both positive?varun289 wrote:235. Are x and y both positive?
a. 2x - 2y = 1
b. x�y > 1
Statement 1: 2x - 2y = 1
There are several pairs of numbers that satisfy this condition. Here are two:
Case a: x = 1 and y = 0.5, in which case x and y are both positive
Case b: x = -0.5 and y = -1, in which case x and y are not both positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x/y > 1
This tells us that x/y is positive. This means that either x and y are both positive or x and y are both negative. Here are two possible cases:
Case a: x = 4 and y = 2, in which case x and y are both positive
Case b: x = -4 and y = -2, in which case x and y are not both positive
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2
Statement 1 tells us that 2x - 2y = 1.
Divide both sides by 2 to get: x - y = 1/2
Solve for x to get x = y + 1/2
Now take the statement 2 inequality (x/y > 1) and replace x with y + 1/2 to get:
(y + 1/2)/y > 1
Rewrite as: y/y + (1/2)/y > 1
Simplify: 1 + 1/(2y) > 1
Subtract 1 from both sides: 1/(2y) > 0
If 1/(2y) is positive, then y must be positive.
Statement 2 tells us that either x and y are both positive or x and y are both negative.
Now that we know that y is positive, it must be the case that x and y are both positive
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
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puneetkhurana2000
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gmat_for_life
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Hello Experts,
I have a small doubt regarding this question. On combining the 2 statements, we get x-y=1/2 and x>y.
- If we consider x as 1/2, y will be equal to 0. This would also satisfy x>y. Because 0 is neither positive nor negative, X and Y are NOT both positive.
- If we consider x as 2, y will be equal to 3/2. this would also satisfy x>y. Both x and y are positive in this case.
Based on the above analysis, I reached at E as the answer. Could you please let me know what's wrong with my analysis?
Regards,
Amit
I have a small doubt regarding this question. On combining the 2 statements, we get x-y=1/2 and x>y.
- If we consider x as 1/2, y will be equal to 0. This would also satisfy x>y. Because 0 is neither positive nor negative, X and Y are NOT both positive.
- If we consider x as 2, y will be equal to 3/2. this would also satisfy x>y. Both x and y are positive in this case.
Based on the above analysis, I reached at E as the answer. Could you please let me know what's wrong with my analysis?
Regards,
Amit
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Brent@GMATPrepNow
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We cannot conclude that x>ygmat_for_life wrote:Hello Experts,
I have a small doubt regarding this question. On combining the 2 statements, we get x-y=1/2 and x>y.
- If we consider x as 1/2, y will be equal to 0. This would also satisfy x>y. Because 0 is neither positive nor negative, X and Y are NOT both positive.
- If we consider x as 2, y will be equal to 3/2. this would also satisfy x>y. Both x and y are positive in this case.
Based on the above analysis, I reached at E as the answer. Could you please let me know what's wrong with my analysis?
Regards,
Amit
All we are told is that x�y > 1
I think you took x�y > 1 and multiplied both sides by y to get x > y, but this is incorrect.
We can't do this because we don't know whether y is positive or negative.
IF y is positive, then we do in fact get x > y
IF y is negative, then we get x < y
For more on this, watch the following free video: https://www.gmatprepnow.com/module/gmat ... /video/979
Cheers,
Brent
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Matt@VeritasPrep
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You can't have y = 0, or you'd invalidate S2 (which must be true, since it's given as a statement). If y = 0, then x/y is indeterminate, not > 1, but we're told in S2 that x/y > 1.gmat_for_life wrote:Hello Experts,
I have a small doubt regarding this question. On combining the 2 statements, we get x-y=1/2 and x>y.
- If we consider x as 1/2, y will be equal to 0. This would also satisfy x>y. Because 0 is neither positive nor negative, X and Y are NOT both positive.
- If we consider x as 2, y will be equal to 3/2. this would also satisfy x>y. Both x and y are positive in this case.
Based on the above analysis, I reached at E as the answer. Could you please let me know what's wrong with my analysis?
Regards,
Amit
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gmat_for_life
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Thank you Matt and Brent!
I have now understood why '0' is not a valid value for y.
Thanks again,
Amit
I have now understood why '0' is not a valid value for y.
Thanks again,
Amit
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Matt@VeritasPrep
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No prob!gmat_for_life wrote:Thank you Matt and Brent!
I have now understood why '0' is not a valid value for y.
Thanks again,
Amit
It's easy to forget about division by 0. This can be a problem in other algebra questions too, like
9x = x²
We *want* to divide both sides by x, and conclude that x = 9, but we've forgotten that x COULD be 0! If so, we've just divided by 0 and broken the equation, so we have to consider x = 0 before dividing by a variable.
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toby001
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Hi Brent,Brent@GMATPrepNow wrote:Target question: Are x and y both positive?varun289 wrote:235. Are x and y both positive?
a. 2x - 2y = 1
b. x�y > 1
Statement 1: 2x - 2y = 1
There are several pairs of numbers that satisfy this condition. Here are two:
Case a: x = 1 and y = 0.5, in which case x and y are both positive
Case b: x = -0.5 and y = -1, in which case x and y are not both positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x/y > 1
This tells us that x/y is positive. This means that either x and y are both positive or x and y are both negative. Here are two possible cases:
Case a: x = 4 and y = 2, in which case x and y are both positive
Case b: x = -4 and y = -2, in which case x and y are not both positive
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2
Statement 1 tells us that 2x - 2y = 1.
Divide both sides by 2 to get: x - y = 1/2
Solve for x to get x = y + 1/2
Now take the statement 2 inequality (x/y > 1) and replace x with y + 1/2 to get:
(y + 1/2)/y > 1
Rewrite as: y/y + (1/2)/y > 1
Simplify: 1 + 1/(2y) > 1
Subtract 1 from both sides: 1/(2y) > 0
If 1/(2y) is positive, then y must be positive.
Statement 2 tells us that either x and y are both positive or x and y are both negative.
Now that we know that y is positive, it must be the case that x and y are both positive
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
When we combine both statements and solve for X in terms of Y, we can only divide by Y because we know it's non-zero from statement 2, correct?
Thanks!
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Brent@GMATPrepNow
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That's correct.toby001 wrote:Hi Brent,Brent@GMATPrepNow wrote:Target question: Are x and y both positive?varun289 wrote:235. Are x and y both positive?
a. 2x - 2y = 1
b. x�y > 1
Statement 1: 2x - 2y = 1
There are several pairs of numbers that satisfy this condition. Here are two:
Case a: x = 1 and y = 0.5, in which case x and y are both positive
Case b: x = -0.5 and y = -1, in which case x and y are not both positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x/y > 1
This tells us that x/y is positive. This means that either x and y are both positive or x and y are both negative. Here are two possible cases:
Case a: x = 4 and y = 2, in which case x and y are both positive
Case b: x = -4 and y = -2, in which case x and y are not both positive
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2
Statement 1 tells us that 2x - 2y = 1.
Divide both sides by 2 to get: x - y = 1/2
Solve for x to get x = y + 1/2
Now take the statement 2 inequality (x/y > 1) and replace x with y + 1/2 to get:
(y + 1/2)/y > 1
Rewrite as: y/y + (1/2)/y > 1
Simplify: 1 + 1/(2y) > 1
Subtract 1 from both sides: 1/(2y) > 0
If 1/(2y) is positive, then y must be positive.
Statement 2 tells us that either x and y are both positive or x and y are both negative.
Now that we know that y is positive, it must be the case that x and y are both positive
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
When we combine both statements and solve for X in terms of Y, we can only divide by Y because we know it's non-zero from statement 2, correct?
Thanks!
We know that y/y = 1, because statement 2 (x�y > 1) essentially tells us that y does not equal zero.
Cheers,
Brent
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Jeff@TargetTestPrep
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We are not provided any given information in the question stem, so we can immediately move to the analysis of the two statements.varun289 wrote:235. Are x and y both positive?
a. 2x - 2y = 1
b. x�y > 1
Statement One Alone:
2x - 2y = 1
The first thing we should do here is simplify statement one.
2(x - y) = 1
x - y = ½
x = y + ½
We see that x is ½ more than y. However, they may or may not be positive. For example, if y = 1, then x = 1.5 and both are positive. On the other hand, if y = 0, then x = 0.5 and they are not both positive. (Recall that 0 is not positive.)
Thus, statement one alone is insufficient.
Statement Two Alone:
x/y > 1
Statement two does not provide enough information to determine whether x and y are either both positive or both negative. For example, if x = 2 and y = 1, then both are positive. However, if x = -2 and y = -1, then both of them are not positive. Thus, statement two alone is insufficient.
Statements One and Two Together:
It's important to be cognizant of situations in which we are provided an inequality and an equation with the same two variables. In these situations, we can substitute the equation into the inequality. Doing so will allow us to simplify the inequality. Recall that in statement one, we have x = ½ + y. Now we can substitute ½ + y for x in the inequality x/y > 1. Thus, we have:
(½ + y)/y > 1
½/y + y/y > 1
½/y + 1 > 1
½/y > 0
Because ½/y is greater than zero, y MUST also be greater than zero. Lastly, because we know that x = ½ + y, it follows that x also MUST be greater than zero. Thus, both x and y are positive.
Answer: C
Jeffrey Miller
Head of GMAT Instruction
[email protected]
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gmatstudent2017
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Hi Brent,
I picked numbers to solve this problem and had a similar approach to you.
(1): I simplified the equation to get x-y = 1/2 and then picked numbers to satisfy the equation.
a. 2.5 - 2 = 1/2 --> yes both x and y are positive
b. -0.5 - -1 = 1/2 --> no both x and y are not positive
Since X and Y can be positive or negative, this statement is insufficient.
(2): x/y > 0 --> Insufficient because x and y are the same sign so they can both be positive or negative.
(1) & (2): From (1) we have x - y = 1/2 and from (2) we have x/y = positive. I picked numbers to satisfy both of these equations
a. -2.5 - -3 = 1/2 and in this case -2.5/-3 = positive so the answer is no x and y are not positive
b. 2.5 -2 = 1/2 and 2.5/2 = positive so the answer is yes x and y are both positive
Since there are still two possible answers, this statement is also insufficient so I picked E.
Can you please explain where I went wrong? I noticed our approaches were similar until you solved statement 1 in terms of X. Why can we not leave that equation as x-y = 1/2? Is the reason I got E because I didn't solve that equation in terms of X? Thank you in advance!
I picked numbers to solve this problem and had a similar approach to you.
(1): I simplified the equation to get x-y = 1/2 and then picked numbers to satisfy the equation.
a. 2.5 - 2 = 1/2 --> yes both x and y are positive
b. -0.5 - -1 = 1/2 --> no both x and y are not positive
Since X and Y can be positive or negative, this statement is insufficient.
(2): x/y > 0 --> Insufficient because x and y are the same sign so they can both be positive or negative.
(1) & (2): From (1) we have x - y = 1/2 and from (2) we have x/y = positive. I picked numbers to satisfy both of these equations
a. -2.5 - -3 = 1/2 and in this case -2.5/-3 = positive so the answer is no x and y are not positive
b. 2.5 -2 = 1/2 and 2.5/2 = positive so the answer is yes x and y are both positive
Since there are still two possible answers, this statement is also insufficient so I picked E.
Can you please explain where I went wrong? I noticed our approaches were similar until you solved statement 1 in terms of X. Why can we not leave that equation as x-y = 1/2? Is the reason I got E because I didn't solve that equation in terms of X? Thank you in advance!
Brent@GMATPrepNow wrote:Target question: Are x and y both positive?varun289 wrote:235. Are x and y both positive?
a. 2x - 2y = 1
b. x�y > 1
Statement 1: 2x - 2y = 1
There are several pairs of numbers that satisfy this condition. Here are two:
Case a: x = 1 and y = 0.5, in which case x and y are both positive
Case b: x = -0.5 and y = -1, in which case x and y are not both positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x/y > 1
This tells us that x/y is positive. This means that either x and y are both positive or x and y are both negative. Here are two possible cases:
Case a: x = 4 and y = 2, in which case x and y are both positive
Case b: x = -4 and y = -2, in which case x and y are not both positive
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2
Statement 1 tells us that 2x - 2y = 1.
Divide both sides by 2 to get: x - y = 1/2
Solve for x to get x = y + 1/2
Now take the statement 2 inequality (x/y > 1) and replace x with y + 1/2 to get:
(y + 1/2)/y > 1
Rewrite as: y/y + (1/2)/y > 1
Simplify: 1 + 1/(2y) > 1
Subtract 1 from both sides: 1/(2y) > 0
If 1/(2y) is positive, then y must be positive.
Statement 2 tells us that either x and y are both positive or x and y are both negative.
Now that we know that y is positive, it must be the case that x and y are both positive
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
