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# If x and y are positive integers such that x^2 - y^2 = 23. What is the

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Joined: 31 Jan 2018
Posts: 9
If x and y are positive integers such that x^2 - y^2 = 23. What is the  [#permalink]

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03 Feb 2018, 21:18
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45% (medium)

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62% (01:31) correct 38% (01:14) wrong based on 71 sessions

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If x and y are positive integers such that x^2 - y^2 = 23. What is the value of y?

A. 10
B. 11
C. 12
D. 23
E. Cannot be determined
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: If x and y are positive integers such that x^2 - y^2 = 23. What is the  [#permalink]

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03 Feb 2018, 21:59
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ggpapas wrote:
If x and y are positive integers such that $$x^2$$ - $$y^2$$ = 23

What is the value of y?

A.10
B.11
C.12
D.23
E. Cannot be determined

$$x^2-y^2=23....(x-y)(x+y)=23$$
But 23 is prime, so 23=1*23..
Since both x and y are POSITIVE..
x+y=23
x-y=1....
Solve this x=12 and y=11
B
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Re: If x and y are positive integers such that x^2 - y^2 = 23. What is the  [#permalink]

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03 Feb 2018, 22:13
ggpapas wrote:
If x and y are positive integers such that $$x^2$$ - $$y^2$$ = 23

What is the value of y?

A.10
B.11
C.12
D.23
E. Cannot be determined

$$x^2$$ - $$y^2$$ = $$23$$

Or, $$(x + y)(x - y) = 23$$

Or, $$(12 + 11)(12 - 11) = 23$$

So,Answer Y must be (B) 11
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If x and y are positive integers such that x^2 - y^2 = 23. What is the  [#permalink]

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04 Feb 2018, 13:40
ggpapas wrote:
If x and y are positive integers such that x^2 - y^2 = 23. What is the value of y?

A. 10
B. 11
C. 12
D. 23
E. Cannot be determined

Although using the difference of squares identity is probably more efficient, you can also use answer choices.

Simply square the integers given.*

A) 10. $$10^2 = 100$$
B) 11. $$11^2 = 121$$ (121 - 100) = 21
C) 12. $$12^2 = 144$$ (144 - 121) = 23
That's a match.

The numbers must be
x = 12, y = 11, because
$$(144 - 121) = (12^2 - 11^2) = 23$$

y = 11

*23 is positive. LHS is (positive) - (positive).
x must be greater than y. Hence there is no need to worry about squaring any integer less than 10 (Answer A).

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Joined: 27 Dec 2016
Posts: 292
Re: If x and y are positive integers such that x^2 - y^2 = 23. What is the  [#permalink]

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05 Feb 2018, 18:43

X^2-11^2 = 23
X^2-121 = 23
X^2 = 144
X= 12

Re: If x and y are positive integers such that x^2 - y^2 = 23. What is the   [#permalink] 05 Feb 2018, 18:43
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