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Speicific question about quant comparison q -- algebra
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13 May 2020, 13:03
13 May 2020, 13:03
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Question Stats:
100% (00:49) correct
0% (00:00) wrong based on 1 sessions
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Hello, can someone help me understand the method used in the below solution to this problem? Also if I wanted to learn more about the concepts involved in the math in this question -- what would I search for? Is this just general algebra or is there a more specific subcategory
Also, specifically, First, square the given equation x2=y2+1 --> why are you doing this? This would not be my first thought... is this just because the quantity answer choices include x^4? And that there are no numbers involved in this question, that there are only variables?
to most efficiently evaluate the quantities finding that x4=y4+2y2+1.
Now, it is possible to evaluate both quantities in terms of the single variable of y.
x2=y2+1 and xy≠0
Quantity A
x4
Quantity B
y4+1
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
hide explanation
If presented clear algebraic information in a Quantitative Comparison, look to solve algebraically.
First, square the given equation x2=y2+1
to most efficiently evaluate the quantities finding that x4=y4+2y2+1.
Now, it is possible to evaluate both quantities in terms of the single variable of y.
Quantity A is x4 which can be replaced when evaluating the quantities by the equivalent value of y4+2y2+1.
Next, subtract y4 and 1 from each quantity to simplify the comparison to 2y2 in Quantity A and 0 in Quantity B.
Any value squared, except 0, will be positive.
The problem posits that xy≠0
, so Quantity A will always be greater > 0.
The correct answerA
Also, specifically, First, square the given equation x2=y2+1 --> why are you doing this? This would not be my first thought... is this just because the quantity answer choices include x^4? And that there are no numbers involved in this question, that there are only variables?
to most efficiently evaluate the quantities finding that x4=y4+2y2+1.
Now, it is possible to evaluate both quantities in terms of the single variable of y.
x2=y2+1 and xy≠0
Quantity A
x4
Quantity B
y4+1
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
hide explanation
If presented clear algebraic information in a Quantitative Comparison, look to solve algebraically.
First, square the given equation x2=y2+1
to most efficiently evaluate the quantities finding that x4=y4+2y2+1.
Now, it is possible to evaluate both quantities in terms of the single variable of y.
Quantity A is x4 which can be replaced when evaluating the quantities by the equivalent value of y4+2y2+1.
Next, subtract y4 and 1 from each quantity to simplify the comparison to 2y2 in Quantity A and 0 in Quantity B.
Any value squared, except 0, will be positive.
The problem posits that xy≠0
, so Quantity A will always be greater > 0.
The correct answerA
Re: Speicific question about quant comparison q -- algebra
[#permalink]
13 May 2020, 23:10
13 May 2020, 23:10
1
This problem is to test basic mathematics skill. It asks whether you know how to expand (a+b)^2 (squared), which gives us, a^2+2ab+b^2.
The question states that x^2=y^2+1 and that xy≠0 which means x and y have some value (positive or negative) and are not 0.
To calculate for option A, we need to square x^2, because x^2^2 = x^4, its just like (a^m)^n = a^mn (where you multiply m and n).
So the RHS (right hand side) will become (y^2+1)^2 = y^4 +2y^2 +1.
Now option B is only y^4+1, and does not have 2y^2, since it is stated that xy≠0, y cannot be 0, and thus, option A will be always greater than option B.
Thus option A is the answer.
This is a problem of basic mathematics and would recommend to have a look at this webiste: https://www.toppr.com/guides/maths-formulas/algebra-formula/
The question states that x^2=y^2+1 and that xy≠0 which means x and y have some value (positive or negative) and are not 0.
To calculate for option A, we need to square x^2, because x^2^2 = x^4, its just like (a^m)^n = a^mn (where you multiply m and n).
So the RHS (right hand side) will become (y^2+1)^2 = y^4 +2y^2 +1.
Now option B is only y^4+1, and does not have 2y^2, since it is stated that xy≠0, y cannot be 0, and thus, option A will be always greater than option B.
Thus option A is the answer.
This is a problem of basic mathematics and would recommend to have a look at this webiste: https://www.toppr.com/guides/maths-formulas/algebra-formula/
Re: Speicific question about quant comparison q -- algebra
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15 May 2020, 11:14
15 May 2020, 11:14
Expert Reply
I did not understand it the way it is formatted 
