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If a and b are two positive integers such that

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sandy
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If a and b are two positive integers such that [#permalink] New post   25 Aug 2018, 12:48
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If a and b are two positive integers such that; \(9a \times 5b= 1035\). What is maximum possible value of \(a-b=?\)

Show: :: OA
22
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anudec4
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Re: If a and b are two positive integers such that [#permalink] New post   20 Nov 2018, 01:03
Hi,

Please help with the values of a & b. Is it "a" = 23 & "b"=1?
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bartendingliver
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Re: If a and b are two positive integers such that [#permalink] New post   20 Nov 2018, 02:15
sandy wrote:
If a and b are two positive integers such that; \(9a \times 5b= 1035\). What is maximum possible value of \(a-b=?\)

Show: :: OA
22


it can be both 22 and -22
if a is 23 then, a-b = 22
but if a is 1 then, a-b = -22.

so OA seems not sure, to me.
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chetan2u
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Re: If a and b are two positive integers such that [#permalink] New post   20 Nov 2018, 02:39
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bartendingliver wrote:
sandy wrote:
If a and b are two positive integers such that; \(9a \times 5b= 1035\). What is maximum possible value of \(a-b=?\)

Show: :: OA
22


it can be both 22 and -22
if a is 23 then, a-b = 22
but if a is 1 then, a-b = -22.

so OA seems not sure, to me.


OA is correct. We are looking for MAXIMUM possible...

\(9a \times 5b= 1035\)
Let us get 1035 in standard form .. 1035=1*5*9*23 or 1035=(-23)(-1)(5)(9) But a and b are positive..
Thus, possible values of a and b are 1 and 23 in any order.
we are looking for maximum value of a-b so take the maximum of two values as a, so a=23, and other as b, so b= 1..
23-1=22
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Re: If a and b are two positive integers such that [#permalink] New post   20 Nov 2018, 03:00
Thank you 'bartendingliver' and 'chetan2u'.

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Re: If a and b are two positive integers such that [#permalink] New post   20 Nov 2018, 06:57
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sandy wrote:
If a and b are two positive integers such that; \(9a \times 5b= 1035\). What is maximum possible value of \(a-b=?\)

Show: :: OA
22


GIVEN: (9a)(5b) = 1035
Divide both sides by 9 to get: (a)(5b) = 115
Divide both sides by 5 to get: (a)(b) = 23

Since a and b are positive integers, there are only two possible solutions:
Solution #1: a = 1 and b = 23, in which case a - b = 1 - 23 = -22
Solution #2: a = 23 and b = 1, in which case a - b = 23 - 1 = 22

So, the MAXIMUM value of a - b is 22

Answer: 22

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Re: If a and b are two positive integers such that [#permalink] New post   12 Jul 2023, 05:49
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