If a, b, and c are positive integers such that 1/a + 1/b = 1

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If a, b, and c are positive integers such that 1/a + 1/b = 1 [#permalink]

18 Nov 2012, 13:06

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If a, b, and c are positive integers such that 1/a + 1/b = 1/c, what is the value of c?

(1) b ≤ 4
(2) ab ≤ 15

[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Nov 2012, 04:01, edited 1 time in total.

Renamed the topic and edited the question.

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Re: Fraction and Inequality [#permalink]

18 Nov 2012, 19:01

monsoon1 wrote:

If a, b, and c are positive integers such that 1/a + 1/b = 1/c, what is the value of c?

(1) b ≤ 4
(2) ab ≤ 15

[Reveal] Spoiler:

OA-> B

given is c= ab/(a+b)
thus, since c is integer, ab/a+b must be an integer.

statement 1: b ≤ 4
No information can be drawn. Not sufficient
statement 2: ab ≤ 15
Only possible value of ab, such that ab/a+b is integer could be when a=2,b=2. Thus, c=1.
Sufficient.

Ans B it is.
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Re: Fraction and Inequality [#permalink]

19 Nov 2012, 17:38

Vips0000 wrote:

monsoon1 wrote:

If a, b, and c are positive integers such that 1/a + 1/b = 1/c, what is the value of c?

(1) b ≤ 4
(2) ab ≤ 15

[Reveal] Spoiler:

OA-> B

How did you find that only these values would satisfy?
Did you test several numbers?

The question also doesn't give us the clue whether the numbers are the same or different.So, we have to test many numbers.right?

Can you please show the steps or any other way to get to the correct answer?

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Re: Fraction and Inequality [#permalink]

19 Nov 2012, 18:01

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monsoon1 wrote:

How did you find that only these values would satisfy?
Did you test several numbers?

The question also doesn't give us the clue whether the numbers are the same or different.So, we have to test many numbers.right?
Can you please show the steps or any other way to get to the correct answer?

You actually dont need to test numbers. It could be purely algebric approach coupled with some logical deductions.

we havec= ab/(a+b)
or c = \frac{1}{(1/a+1/b)}

If you notice this expression and remember that c has to be integer, that would mean Denominator has to be 1 (Since numerator is already 1).
There is only one such possiblity of a and b that could give you 1/a+1/b =1
So you dont need to test any number.

Hope it helps. Lets kudos ;-)

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Re: Fraction and Inequality [#permalink] 19 Nov 2012, 18:01

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If a, b, and c are positive integers such that 1/a + 1/b = 1

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If a, b, and c are positive integers such that 1/a + 1/b = 1

If a, b, and c are positive integers such that 1/a + 1/b = 1

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