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505-555 (Easy)|   Algebra|      
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Bunuel
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If x and y are positive integers, and x – 2y = 5, which of the followi 28 Dec 2020, 10:00
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82% (01:49) correct 18% (02:37) wrong based on 198 sessions

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If x and y are positive integers, and \(x – 2y = 5\), which of the following could be the value of \(x^2 – 4y^2\)?

(A) –3
(B) 0
(C) 14
(D) 45
(E) 51
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D
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If x and y are positive integers, and x – 2y = 5, which of the followi 28 Dec 2020, 10:31
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x – 2y = 5
x= 5+2y

Value of x^2 - y^2 = (5+2y)^2 + 2y
= 25+20y

Since y is positive, the least value of 25+20y is when y=1
25+20=45; Option D
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If x and y are positive integers, and x – 2y = 5, which of the followi 28 Dec 2020, 10:45
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Bunuel
If x and y are positive integers, and \(x – 2y = 5\), which of the following could be the value of \(x^2 – 4y^2\)?

(A) –3
(B) 0
(C) 14
(D) 45
(E) 51
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\(x = 5 + 2y\)

Let \(y = 1\), so \(x = 7\)

Thus, \(x^2 – 4y^2 = 7^2 - 4*1^2 = 45\), Answer must be (D)
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If x and y are positive integers, and x – 2y = 5, which of the followi 28 Dec 2020, 10:49
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Bunuel
If x and y are positive integers, and \(x – 2y = 5\), which of the following could be the value of \(x^2 – 4y^2\)?

(A) –3
(B) 0
(C) 14
(D) 45
(E) 51
Show more
\(x^2 – 4y^2 = (x-2y)*(x+2y)\)
\(x^2 – 4y^2 = 5*(x+2y)\)

So, we need to have a multiple of 5 as answer.
Only B and D satisfy the condition.

Since (x+2y) ≠ 0 as x and y are positive integers, B is eliminated,

Answer D.
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If x and y are positive integers, and x – 2y = 5, which of the followi 28 Dec 2020, 11:11
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If x and y are positive integers, and x–2y=5, which of the following could be the value of x^2–4y^2?

given, x^2–4y^2= (x–2y)*(x+2y)= 5*(x+2y), where x and y are positive integers.

(A) –3-> not possible.
(B) 0-> not possible
(C) 14-> not possible.
(D) 45-> Only multiple of 5.
(E) 51-> not possible.

So, I think D. :)
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If x and y are positive integers, and x – 2y = 5, which of the followi 29 Dec 2020, 12:55
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Bunuel
If x and y are positive integers, and \(x – 2y = 5\), which of the following could be the value of \(x^2 – 4y^2\)?

(A) –3
(B) 0
(C) 14
(D) 45
(E) 51
Show more

\(x – 2y = 5\)

\(x=5+2y\) [For every positive value of y and x the result of \(x^2 – 4y^2\) will be the same. Let y=1 for making calculation easy]

\(x=5+2*1=7; \ so, \ x=7, y=1\)

Now, putting the value at \(x^2 – 4y^2\)

=\(7^2 – 4*1^2[/m\\
\\
[m]=49-4=45\)

The answer is \(D.\)
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If x and y are positive integers, and x – 2y = 5, which of the followi 08 Nov 2025, 03:22
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