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# If the difference between two numbers is 4, then which of th

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If the difference between two numbers is 4, then which of th [#permalink]  08 Apr 2018, 10:20
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Question Stats:

16% (02:31) correct 83% (01:22) wrong based on 36 sessions
If the difference between two numbers is 4, then which of the following would be sufficient to determine the value of each of the numbers?
Indicate all possible values.

A. The sum of the numbers is 4.
B. The difference between the squares of the numbers is 16.
C. The square of the difference between the numbers is 16.
D. The sum of the squares of the numbers is greater than 8.
E. Twice the greater number is 8.
F. The smaller of the two numbers is less than 8.
G. The product of the two numbers is 0, and neither of the numbers is negative.

Drill 1
Question: 8
Page: 508
[Reveal] Spoiler: OA

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Sandy
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Re: If the difference between two numbers is 4, then which of th [#permalink]  18 Apr 2018, 15:33
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Explanation

Translate the question and answer choices into algebra.

You are given that $$x - y = 4$$.
Choice (A) tells you that $$x + y = 4$$, and you can solve these equations simultaneously by stacking them and adding to get 2x = 8, x = 4 and y = 0.
Choice (A) is sufficient and correct.

Choice (B) tells you that $$x^2 - y^2 = 16$$, and can be factored: $$x^2 - y^2 = (x + y)(x - y) = 16$$. You are given that $$(x - y) = 4$$, so (x + y) must also equal 4 and for that to happen, x = 4 and y = 0.
Choice (B) is also sufficient and correct.

Choice (C) states $$(x - y)^2 = 16$$. This is simply the result of squaring what you were already given and you have no way to determine what the values of x
and y are, making this choice incorrect.

Choices (D) and (F) are inequalities, which means there will be multiple numbers that can work with the criteria given; eliminate both choices.

Choice (E) tells you that the greater number is 4. Since x - y = 4, that now means the smaller number must be 0, making choice (E) sufficient.

Finally, choice (G) states xy = 0, so at least one of the numbers must be 0. Since you were also given x – y = 4 and that neither number is negative, this means the other number must be 4. Choice (G) is sufficient and correct.
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Re: If the difference between two numbers is 4, then which of th [#permalink]  27 Jun 2018, 12:10
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Re: If the difference between two numbers is 4, then which of th [#permalink]  27 Jun 2018, 12:46
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The OA is correc A,E,G.

However, is the explanation incorrect. B is not a choice
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Re: If the difference between two numbers is 4, then which of th [#permalink]  09 Jul 2018, 20:06
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sandy wrote:
Explanation

Translate the question and answer choices into algebra.

You are given that $$x - y = 4$$.
Choice (A) tells you that $$x + y = 4$$, and you can solve these equations simultaneously by stacking them and adding to get 2x = 8, x = 4 and y = 0.
Choice (A) is sufficient and correct.

Choice (B) tells you that $$x^2 - y^2 = 16$$, and can be factored: $$x^2 - y^2 = (x + y)(x - y) = 16$$. You are given that $$(x - y) = 4$$, so (x + y) must also equal 4 and for that to happen, x = 4 and y = 0.
Choice (B) is also sufficient and correct.

Choice (C) states $$(x - y)^2 = 16$$. This is simply the result of squaring what you were already given and you have no way to determine what the values of x
and y are, making this choice incorrect.

Choices (D) and (F) are inequalities, which means there will be multiple numbers that can work with the criteria given; eliminate both choices.

Choice (E) tells you that the greater number is 4. Since x - y = 4, that now means the smaller number must be 0, making choice (E) sufficient.

Finally, choice (G) states xy = 0, so at least one of the numbers must be 0. Since you were also given x – y = 4 and that neither number is negative, this means the other number must be 4. Choice (G) is sufficient and correct.

In choice B, there are TWO possible cases: $$x^2 - y^2 = 16$$ or $$y^2 - x^2 = 16$$ -> NOT SUFFICIENT.
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Re: If the difference between two numbers is 4, then which of th [#permalink]  12 Jun 2019, 23:57
leanhdung wrote:
sandy wrote:
Explanation

Translate the question and answer choices into algebra.

You are given that $$x - y = 4$$.
Choice (A) tells you that $$x + y = 4$$, and you can solve these equations simultaneously by stacking them and adding to get 2x = 8, x = 4 and y = 0.
Choice (A) is sufficient and correct.

Choice (B) tells you that $$x^2 - y^2 = 16$$, and can be factored: $$x^2 - y^2 = (x + y)(x - y) = 16$$. You are given that $$(x - y) = 4$$, so (x + y) must also equal 4 and for that to happen, x = 4 and y = 0.
Choice (B) is also sufficient and correct.

Choice (C) states $$(x - y)^2 = 16$$. This is simply the result of squaring what you were already given and you have no way to determine what the values of x
and y are, making this choice incorrect.
-------------------------------------------------

Choices (D) and (F) are inequalities, which means there will be multiple numbers that can work with the criteria given; eliminate both choices.

Choice (E) tells you that the greater number is 4. Since x - y = 4, that now means the smaller number must be 0, making choice (E) sufficient.

Finally, choice (G) states xy = 0, so at least one of the numbers must be 0. Since you were also given x – y = 4 and that neither number is negative, this means the other number must be 4. Choice (G) is sufficient and correct.

In choice B, there are TWO possible cases: $$x^2 - y^2 = 16$$ or $$y^2 - x^2 = 16$$ -> NOT SUFFICIENT.

------------
terrific !
yes, we fell victim to the mathematical stereotype of x first y later !
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Re: If the difference between two numbers is 4, then which of th [#permalink]  12 Apr 2020, 22:51
sandy wrote:
Explanation

Translate the question and answer choices into algebra.

You are given that $$x - y = 4$$.
Choice (A) tells you that $$x + y = 4$$, and you can solve these equations simultaneously by stacking them and adding to get 2x = 8, x = 4 and y = 0.
Choice (A) is sufficient and correct.

Choice (B) tells you that $$x^2 - y^2 = 16$$, and can be factored: $$x^2 - y^2 = (x + y)(x - y) = 16$$. You are given that $$(x - y) = 4$$, so (x + y) must also equal 4 and for that to happen, x = 4 and y = 0.
Choice (B) is also sufficient and correct.

Choice (C) states $$(x - y)^2 = 16$$. This is simply the result of squaring what you were already given and you have no way to determine what the values of x
and y are, making this choice incorrect.

Choices (D) and (F) are inequalities, which means there will be multiple numbers that can work with the criteria given; eliminate both choices.

Choice (E) tells you that the greater number is 4. Since x - y = 4, that now means the smaller number must be 0, making choice (E) sufficient.

Finally, choice (G) states xy = 0, so at least one of the numbers must be 0. Since you were also given x – y = 4 and that neither number is negative, this means the other number must be 4. Choice (G) is sufficient and correct.

As the question stated that we have to Indicate all possible values not values which must be true,,,, so why we don't pick the option,C,D
C. The square of the difference between the numbers is 16. (if X=0, Y=4 ,,,,difference between x n y is -4 so -4^2=16
D.The sum of the squares of the numbers is greater than 8. (if X=0, Y=4 ,,,,Sum of 0^2+4^2=16 which is greater than 16

kindly guide me where I'm taking these concepts in wrong way
Re: If the difference between two numbers is 4, then which of th   [#permalink] 12 Apr 2020, 22:51
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