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# M03-06

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:19
2
13
00:00

Difficulty:

55% (hard)

Question Stats:

53% (01:07) correct 47% (01:04) wrong based on 277 sessions

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If $$x^2 \lt 81$$ and $$y^2 \lt 25$$, what is the largest prime number that can be equal to $$x-2y$$?

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

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16 Sep 2014, 00:19
3
6
Official Solution:

If $$x^2 \lt 81$$ and $$y^2 \lt 25$$, what is the largest prime number that can be equal to $$x-2y$$?

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

Notice that we are not told that $$x$$ and $$y$$ are integers.

$$x^2 \lt 81$$ means that $$-9 \lt x \lt 9$$ and $$y^2 \lt 25$$ means that $$-5 \lt y \lt 5$$. 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 $$y=-4.5$$.

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07 Oct 2014, 03:17
19
4
I solved this (slightly) more algebraically in the sense that: -9 < x < 9 and -5<y<5 so multiplying the inequality of y by -2 we get

10 > -2y > -10, flipping the inequality for x around the same way we get 9 > x > -9 now adding them we obtain

19 > x - 2y > -19, and we see that the biggest prime number in this range is 17
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11 Jul 2015, 00:58
Hello,

While attempting this question I was almost lost before I realized (while testing answer choices) that if X=5 any Y=4 then largest prime is 17.

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Vikas
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16 Sep 2015, 20:35
It is not told anywhere in the question that we have to find any approximate value. Since, it is asking for prime number directly, x and y should be integers!! Because of this thought, I took x and y as integers and got the wrong answer.
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Joined: 11 Oct 2013
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08 Dec 2015, 05:16
Great question. Revolves around the fact that the question has not explicitly mentioned if x and y are integers. So if you presume them as integers, you'll mark the wrong answer!
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Joined: 24 Jun 2013
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28 Jan 2018, 04:30
imperfectdark wrote:
I solved this (slightly) more algebraically in the sense that: -9 < x < 9 and -5<y<5 so multiplying the inequality of y by -2 we get

10 > -2y > -10, flipping the inequality for x around the same way we get 9 > x > -9 now adding them we obtain

19 > x - 2y > -19, and we see that the biggest prime number in this range is 17

why cant we solve as below (i know its wrong coz of the -2 multiplication)
-9<x<9
-10<2y<10

subtract

1<x-2y<-1

is it becoz the -2 in x-2y creates the problem while subtraction or we cannot subtract inequalities with same sign?? pls help
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03 Jun 2018, 21:58
My approach:
Almost all prime numbers are odd. Hence, we need x-2y to be odd. 2y is even, therefore, x must be the largest odd number (which is 7). Since -2y is negative, we need y to be the least negative number (which is 5). 7 - 2(-5) gives us 17
Re: M03-06 &nbs [#permalink] 03 Jun 2018, 21:58
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# M03-06

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