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If x^2<81 and y^2<25, what is the largest prime number that can be equ

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If x^2<81 and y^2<25, what is the largest prime number that can be equ  [#permalink]

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New post Updated on: 14 Jul 2018, 01:41
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If x^2<81 and y^2<25, what is the largest prime number that can be equal to x-2y?

A) 3
B) 7
C) 11
D) 13
E) 17

Originally posted by selim on 13 Jul 2018, 15:24.
Last edited by Bunuel on 14 Jul 2018, 01:41, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If x^2<81 and y^2<25, what is the largest prime number that can be equ  [#permalink]

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New post 13 Jul 2018, 15:45
I overlooked that the numbers do not have to be intergers, therefore the following would work:

x= 8.9 , y = -4.9

x-2y = 8.9 - (-9.8) = 18.7

Hence choice E is the biggest prime
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Re: If x^2<81 and y^2<25, what is the largest prime number that can be equ  [#permalink]

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New post 13 Jul 2018, 19:00
My approach is the following:

We need the greatest prime number, so we have to maximize x-2y, how? y has to be negative

So then:

\(x^{2}<9^{2}\) ---> x = 9
\(y^{2}<(-5)^{2}\) ---> y = -5

Limit = 9 + 10 = 19 prime but we can't take it, we need a prime less than 19

If we take one digit less we have that:

\(x^{2}=8^{2}\) ---> x = 8
\(y^{2}=(-4)^{2}\) ---> y = -4

So then 8 + 8 =16 not prime

There are two numbers between 16 and 19 --> 17 (prime) and 18 (not prime)

Answer E
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Re: If x^2<81 and y^2<25, what is the largest prime number that can be equ  [#permalink]

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New post 13 Jul 2018, 20:15
1
selim wrote:
If \(x^2\) < 81 and \(y^2\) < 25 what is the largest prime number that can be equal to x-2y ?

A) 3
B) 7
C) 11
D) 13
E) 17


Algebraic approach -

\(x^2<81 => -9<x<9\) --------(1)

\(y^2<5=> -5<y<5\), multiply this equation by \(-2\) to get

\(-10<-2y<10\) -----(2). Add equation (1) & (2) to get

\(-19<x-2y<19\). In this range the Largest Prime Number is \(17\).

Option E
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Re: If x^2<81 and y^2<25, what is the largest prime number that can be equ  [#permalink]

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New post 13 Jul 2018, 20:17
1
selim wrote:
If \(x^2\) < 81 and \(y^2\) < 25 what is the largest prime number that can be equal to x-2y ?

A) 3
B) 7
C) 11
D) 13
E) 17



\(x^2<81.......|x|<9.........x>-9...and...x<9\)
\(y^2<25.......|y|<5.........y>-5.... and.... y<5\).....

the MAX value of x-2y is when x is positive and y is negative
so just LESS than 9-2*(-5)=9+10=19 so <19
therefore x-2y can take ANY value <19...
17 is the closest prime number to 19, hence answer 17


E
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Re: If x^2<81 and y^2<25, what is the largest prime number that can be equ  [#permalink]

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New post 14 Jul 2018, 01:42
1
selim wrote:
If x^2<81 and y^2<25, what is the largest prime number that can be equal to x-2y?

A) 3
B) 7
C) 11
D) 13
E) 17


This is my own question and below is official solution:



10. If x^2<81 and y^2<25, what is the largest prime number that can be equal to x-2y?
A. 7
B. 11
C. 13
D. 17
E. 19

Notice that we are not told that \(x\) and \(y\) are integers.

\(x^2<81\) means that \(-9<x<9\) and \(y^2<25\) means that \(-5<y<5\). Now, since the largest value of \(x\) is almost 9 and the largest value of \(-2y\) is almost 10 (for example if \(y=-4.9\)), then the largest value of \(x-2y\) is almost 9+10=19, so the actual value is less than 19, which means that the largest prime that can be equal to \(x-2y\) is 17. For example: \(x=8\) and \(y=-4.5\).

Answer: D.
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Re: If x^2<81 and y^2<25, what is the largest prime number that can be equ &nbs [#permalink] 14 Jul 2018, 01:42
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