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If 7(a – 1) = 17(b – 1), and a and b are both positive

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If 7(a – 1) = 17(b – 1), and a and b are both positive [#permalink] New post 23 May 2017, 01:20
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Question Stats:

33% (00:41) correct 66% (01:46) wrong based on 6 sessions
If 7(a – 1) = 17(b – 1), and a and b are both positive integers the product of which is greater
than 1, then what is the least possible sum of a and b?
A. 2
B. 7
C. 17
D. 24
E. 26

Drill 1
Question: 11
Page: 338-339

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Re: If 7(a – 1) = 17(b – 1), and a and b are both positive [#permalink] New post 04 Jun 2017, 15:01
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Explanation

Because 7 and 17 are prime and have no common factor greater than 1, their least common multiple will be their product: 7 × 17 = 119.

The least possible value for (a – 1), then, is 17, so a = 18; likewise, the least possible value for (b – 1) is 7, so b = 8.

The least possible sum for a and b, therefore, is 18 + 8 = 26.

Be careful if you selected choice A: Although Plugging In a value of 1 for both a and b would yield 0 on both sides of the equation, the
problem specifies that the product of a and b be greater than 1.

Hence option E is correct!
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Re: If 7(a – 1) = 17(b – 1), and a and b are both positive [#permalink] New post 29 May 2018, 09:08
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sandy wrote:
Explanation

Because 7 and 17 are prime and have no common factor greater than 1, their least common multiple will be their product: 7 × 17 = 119.

The least possible value for (a – 1), then, is 17, so a = 18; likewise, the least possible value for (b – 1) is 7, so b = 8.

The least possible sum for a and b, therefore, is 18 + 8 = 26.

Be careful if you selected choice A: Although Plugging In a value of 1 for both a and b would yield 0 on both sides of the equation, the
problem specifies that the product of a and b be greater than 1.

Hence option E is correct!



Can you please explain me the highlighted line.
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Re: If 7(a – 1) = 17(b – 1), and a and b are both positive [#permalink] New post 29 May 2018, 10:33
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We have \(7(a - 1) = 17(b - 1)\).

This can be written as:

\(7(a - 1) = 17(b - 1)\)
\(7 \times 17 = 17 \times 7\). This is the minimum possible value.

So \((a - 1)=17\) and \((b - 1)=7\)

It could also be:

\(7(a - 1) = 17(b - 1)\)
\(7 \times 34 = 17 \times 14\) which is \(7 \times 17 \times 2 = 17 \times 7 \times 2\).

This is \((a - 1)=34\) and \((b - 1)=14\) also possible but not the minimum possible value.
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Re: If 7(a – 1) = 17(b – 1), and a and b are both positive   [#permalink] 29 May 2018, 10:33
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