If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is : Problem Solving (PS)

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If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is

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If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is [#permalink]

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25 Dec 2017, 22:39

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If \(10 \leq x \leq 20\) and \(5 \leq y \leq 10\), and xy is a prime number, what is the least possible value of xy?

(A) 2
(B) 11
(C) 53
(D) 77
(E) Not possible

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Re: If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is [#permalink]

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25 Dec 2017, 22:59

Interesting question. I don’t understand how xy can be a prime number as the very fact that the number is formed by multiplying x and y precludes it from being a prime number unless I’m reading the question wrongly.

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Re: If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is [#permalink]

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25 Dec 2017, 23:07

szeth wrote:

Hi..

It is nowhere mentioned x and y are integers..
I was about to add " not possible" as a choice, ill do it now
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If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is [#permalink]

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Updated on: 26 Dec 2017, 01:53

chetan2u , I am new to the forums. How can I retain format of algebraic formulae in my posts? Thanks. BTW- I've read a lot of your posts. You're an awesome teacher and your explanations have helped me learn a lot!

Since \(10 <= x <= 20\) and \(5 <= y <= 10\),

50<=xy<=200.

Now xy is a prime number- no way to get 2, no way to get 11 either. We can get 53 by taking y=5.3 and x=10. So least value of xy is 53. Hence C. Please confirm.

Originally posted by Tranquil Focus on 25 Dec 2017, 23:29.
Last edited by Tranquil Focus on 26 Dec 2017, 01:53, edited 2 times in total.

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Re: If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is [#permalink]

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25 Dec 2017, 23:29

Ah fair enough.

@tranquil focus your method seems to make sense. I do not know how to give kudos via my phone but thanks for solving this

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Re: If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is [#permalink]

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26 Dec 2017, 01:26

Tranquil Focus wrote:

chetan2u , I am new to the forums. How can I retain format of algebraic formulae in my posts?

Writing Mathematical Formulas on the Forum: https://gmatclub.com/forum/rules-for-po ... l#p1096628
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Re: If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is [#permalink]

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28 Dec 2017, 05:45

chetan2u wrote:

If \(10 \leq x \leq 20\) and \(5 \leq y \leq 10\), and xy is a prime number, what is the least possible value of xy?

(A) 2
(B) 11
(C) 53
(D) 77
(E) Not possible

A prime has 2 factors, {1,itself}. The stem doesn't say that x or y are integers.. thus, we can make a prime number multiplying with decimals.

The least possible value for xy = prime, has to be the first prime after the lower range \(5*10=50\), which is \(53=10*5.3\) (10 is x and 5.3 is y).

(C) is the answer.