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

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Joined: 02 Aug 2009
Posts: 7199
If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is  [#permalink]

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25 Dec 2017, 21:39
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42% (01:03) correct 58% (01:04) wrong based on 91 sessions

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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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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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, 21:59
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, 22:07
szeth wrote:
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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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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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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, 00:53
1
1
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, 22:29.
Last edited by Tranquil Focus on 26 Dec 2017, 00:53, edited 2 times in total.
Intern
Joined: 25 Dec 2017
Posts: 6
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, 22:29
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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Joined: 02 Sep 2009
Posts: 52168
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, 00:26
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, 04:45
1
1
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).

Re: If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is &nbs [#permalink] 28 Dec 2017, 04:45
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# If 10 <= x <= 20 and 5 <= y <= 10, and xy is a prime number, which is

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