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If a and b are integers greater than 1 and a + b = 15, what is the sma

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Carcass
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If a and b are integers greater than 1 and a + b = 15, what is the sma [#permalink] New post   17 Dec 2021, 06:56
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If a and b are integers greater than 1 and a + b = 15, what is the smallest possible value of a - b?

(A) -13
(B) -11
(C) -1
(D) 1
(E) 3
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B
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Re: If a and b are integers greater than 1 and a + b = 15, what is the sma [#permalink] New post   17 Dec 2021, 07:23
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Carcass wrote:
If a and b are integers greater than 1 and a + b = 15, what is the smallest possible value of a - b?

(A) -13
(B) -11
(C) -1
(D) 1
(E) 3


Let's look for a pattern.

If a and b are integers greater than 1 and a + b = 15, then we can list possible values in the form (a, b) and also find the difference a - b:
(2, 13) --> a - b = -11
(3, 12) --> a - b = -9
(4, 11) --> a - b = -7
.
.
.
(10, 5) --> a - b = 5
(11, 4) --> a - b = 7
(12, 3) --> a - b = 9
(13, 2) --> a - b = 11

So, the smallest possible value of a - b is -11

Answer: B
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Re: If a and b are integers greater than 1 and a + b = 15, what is the sma [#permalink] New post   17 Dec 2021, 08:36
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To minimize (a-b), we take maximum value of b and minimum value of a
a + b = 15, possible cases: -
a=2, b=13
a=3, b=12
a=4, b=11
and so on

Only when a=2, b=13, we will obtain minimum value of a-b which is -11
further values of a and b will only yield smaller differences
E.g.: 3-12 = -9, 4-11 = -7, so on which are larger than -11

So answer is B
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gmatclubot
Re: If a and b are integers greater than 1 and a + b = 15, what is the sma [#permalink]
17 Dec 2021, 08:36
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