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If 7(a 1) = 17(b 1), and a and b are both positive
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23 May 2017, 01:20
23 May 2017, 01:20
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Expert Reply
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Question Stats:
29% (02:31) correct
70% (02:28) wrong based on 78 sessions
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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
A. 2
B. 7
C. 17
D. 24
E. 26
Drill 1
Question: 11
Page: 338-339
Question: 11
Page: 338-339
Re: If 7(a 1) = 17(b 1), and a and b are both positive
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04 Jun 2017, 15:01
04 Jun 2017, 15:01
3
Expert Reply
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!
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!
Re: If 7(a 1) = 17(b 1), and a and b are both positive
[#permalink]
29 May 2018, 09:08
29 May 2018, 09:08
1
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!
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.
