Math Gurus: can you please check what is wrong with my approach.
Statement 2: if x=y+a
then y=x-a
That makes the original statement: Does (x + a)^2 = (x-a)^2? for any value of x and a, can it be true?
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the original question may ask whether a=0 or not? It may also ask given x=-7,a=2 is y=5? (or x=7,a=-2, y=-5, even we can apply modes here ... restatements could be various)Does (x + a)^2 = y^2?
(1) x = y - a
(2) x = y + a
with statement (1) we cannot answer if a=0 or not; also not clear if 7=! -5+2 neither -7=! 5-2 This is Not Sufficient and the answer cannot be A.
statement (2) does not provide any useful information either, as we don't know if a=0 or not; neither we know if -7=! 5+2 nor 7=! -5-2 Not Sufficient.
combined st(1&2): y-a=y+a must be Sufficient, as we know for sure that a=0 and then can answer the question as Yes, (x + a)^2 = y^2
p.s. I am surprised throughout the year NR's post could not find the right click for this question, even experts gave this two tries
the terrible mistake of most posters here including Fabio's was using original statement from question (x + a)^2 = y^2 for plugging in statement (1) and statement (2) expressions.
when we rewrite statement (1) from x+a=y into (x+a)^2=y^2 we should not forget that this is an arbitrary way of squaring both sides, we don't know the signs of (x+a) and y
the same rule of thumb is noticed for many prior solutions concerning statement (2)
zooki wrote:Math Gurus: can you please check what is wrong with my approach.
Statement 2: if x=y+a
then y=x-a
That makes the original statement: Does (x + a)^2 = (x-a)^2? for any value of x and a, can it be true?
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Don't noe if this approach is good but i picked numbers for this problem where x=2,a=3 so (x+a)^2=y^2
which is (2^2+2(6)+3^2)=25, so y= 5,so seeing the statements only statement (A) satisfies the condition where x= 5-3, which gives us 2 so it is sufficient whereas statement 2 gives us x= 5+3, which is insufficient.
Plz correct me if this approach is correct !!
which is (2^2+2(6)+3^2)=25, so y= 5,so seeing the statements only statement (A) satisfies the condition where x= 5-3, which gives us 2 so it is sufficient whereas statement 2 gives us x= 5+3, which is insufficient.
Plz correct me if this approach is correct !!
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Target question: Does (x + a)^2 = y^2?Night reader wrote:Does (x + a)^2 = y^2?
(1) x = y - a
(2) x = y + a
Statement 1: x = y - a
Rearrange to get: x + a = y
If two values are equal, then their squares must also be equal.
That is, (x + a)^2 must equal y^2
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: x = y + a
There are several sets of numbers that meet this condition. Here are two:
Case a: x=1, y=1, a=0, in which case (x + a)^2 equals y^2
Case b: x=2, y=1, a=1, in which case (x + a)^2 does not equal y^2
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
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This approach does not work. You are assuming that the information in the target question is correct and then determining whether each statement confirms this.coolanubhav2002 wrote:Don't noe if this approach is good but i picked numbers for this problem where x=2,a=3 so (x+a)^2=y^2
which is (2^2+2(6)+3^2)=25, so y= 5,so seeing the statements only statement (A) satisfies the condition where x= 5-3, which gives us 2 so it is sufficient whereas statement 2 gives us x= 5+3, which is insufficient.
Plz correct me if this approach is correct !!
Also keep in mind that, if x=2 and y=3, then y can equal either 5 or -5. So, statement A may or may not work in your approach.
If you're interested in learning more about how to tackle DS questions, we have a free set of videos that cover everything you need to know: https://www.gmatprepnow.com/module/gmat-data-sufficiency
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Good question.zooki wrote:Math Gurus: can you please check what is wrong with my approach.
Statement 2: if x=y+a
then y=x-a
That makes the original statement: Does (x + a)^2 = (x-a)^2? for any value of x and a, can it be true?
I like how you have used the statement 2 information to rephrase the target question as "Does (x + a)^2 = (x-a)^2?"
(x + a)^2 will equal (x-a)^2 when a=0.
(x + a)^2 will not equal (x-a)^2 when a does not equal 0.
Since (x + a)^2 may or may not equal (x-a)^2, statement 2 is not sufficient to answer the rephrased target question.
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Direct substitutionNight reader wrote:Does (x + a)^2 = y^2?
(1) x = y - a
(2) x = y + a
(1) (y - a + a)^2 = (y)^2 = y^2
SUFFICIENT
(2) (y + a + a)^2 = (y + 2a) = y^2
INSUFFICIENT because we don't know what "a" is
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Does (x + a)^2 = y^2?
(1) x = y - a
(2) x = y + a
(1) (y-a+a)^2 =y^2 Sufficient
(2) (y+a+a)^2 = (y+2a)^2 Not sufficient
Ans: A
(1) x = y - a
(2) x = y + a
(1) (y-a+a)^2 =y^2 Sufficient
(2) (y+a+a)^2 = (y+2a)^2 Not sufficient
Ans: A
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