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chetan2u
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szeth
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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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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Tranquil Focus
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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chetan2u
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.
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chetan2u
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

New Question

Given: \(10 \leq x \leq 20\) and \(5 \leq y \leq 10\), and xy is a prime number.

Asked: What is the least possible value of xy?

\(50 \leq xy \leq 200\)

First prime number \(\geq 50 = 53\)

IMO C
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Please correct me if I am wrong. If the question had stated that both x and y are integers, then 77 would be the correct answer, right?
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chetan2u
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nirushanraj
Please correct me if I am wrong. If the question had stated that both x and y are integers, then 77 would be the correct answer, right?


No, that would not be correct. In that case xy will never be prime.
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