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If a and b are positive integers, and x = 2 ⋅ 3 ⋅ 7 ⋅ a, an

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If a and b are positive integers, and x = 2 ⋅ 3 ⋅ 7 ⋅ a, an [#permalink] New post 30 May 2018, 01:41
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Question Stats:

84% (01:12) correct 15% (01:14) wrong based on 13 sessions
If a and b are positive integers, and x = 2 ⋅ 3 ⋅ 7 ⋅ a, and y = 2 ⋅ 2 ⋅ 8 ⋅ b, and the values of both x and y lie between 120 and 130 (not including the two), then a – b =

(A) –2

(B) –1

(C) 0

(D) 1

(E) 2
[Reveal] Spoiler: OA

Last edited by Carcass on 30 May 2018, 15:49, edited 1 time in total.
Edited by Carcass
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Re: If a and b are positive integers, and x = 2 ⋅ 3 ⋅ 7 ⋅ a, an [#permalink] New post 31 May 2018, 07:06
Expert's post
We know that x = 2 ⋅ 3 ⋅ 7 ⋅ a, and y = 2 ⋅ 2 ⋅ 8 ⋅ b

or \(x = 42a\), and \(y = 32b\)

Since x and y are between 120 and 130

\(120< 42a < 130\) \(2.85<a<3.09\)

\(120< 32b < 130\) \(3.75<b<4.06\)

Clearly a =3 b=4 since a and b are integers.

a-b=-1.
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Re: If a and b are positive integers, and x = 2 ⋅ 3 ⋅ 7 ⋅ a, an   [#permalink] 31 May 2018, 07:06
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If a and b are positive integers, and x = 2 ⋅ 3 ⋅ 7 ⋅ a, an

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