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

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Joined: 30 Oct 2017
Posts: 30
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Kudos [?]: 7 [1] , given: 6

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

86% (01:07) correct 13% (01:14) wrong based on 15 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
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1897 [0], given: 397

Re: If a and b are positive integers, and x = 2 ⋅ 3 ⋅ 7 ⋅ a, an [#permalink]  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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