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Math Expert V
Joined: 02 Sep 2009
Posts: 59725
If a and b are positive integers, and x = 2*3*7*a, and y = 2*2*8*b, an  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 68% (01:48) correct 32% (02:00) wrong based on 60 sessions

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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

_________________
Director  P
Joined: 16 Jan 2019
Posts: 507
Location: India
Concentration: General Management
WE: Sales (Other)
Re: If a and b are positive integers, and x = 2*3*7*a, and y = 2*2*8*b, an  [#permalink]

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x is a multiple of 7 between 120 & 130 => x=126
y is a multiple of 8 between 120 & 130 => y=128

From this we can deduce that a=3 & b=4,
a-b=-1 (B)
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
If a and b are positive integers, and x = 2*3*7*a, and y = 2*2*8*b, an  [#permalink]

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Solution

Given:
• a and b are positive integers.
• x = 2 * 3 * 7 * a
• y = 2 * 2 * 8 * b
• Value of both x and y lie between 120 and 130.

To find:
• Value of a - b

Approach and Working:
• x = 2 * 3 * 7 * a = 42 * a
o For a = 1, x = 42
o For a = 2, x = 84
o Similarly, x can be 126, or 168, or 210 and so on.
 Only possible value of x is 126 for a = 3.

• y = 2 * 2 * 8 * b = 32 * b
o y can be 32, or 64, or 96, or 128, or 160, or 192, so on.
 Only possible value of y is 128 for b = 4.

Hence, a - b = 3 - 4 = -1

Hence, the correct answer is option B.

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GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5483
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If a and b are positive integers, and x = 2*3*7*a, and y = 2*2*8*b, an  [#permalink]

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Bunuel wrote:
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

x = 2*3*7*a, and y = 2*2*8*b
a= 3 and b = 4
a-b= -1
IMO B
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8701
Location: United States (CA)
Re: If a and b are positive integers, and x = 2*3*7*a, and y = 2*2*8*b, an  [#permalink]

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Bunuel wrote:
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

2 x 3 x 7 = 42, so a must be 3 since 42 x 3 = 126.

2 x 2 x 8 = 32, so b must be 4 since 32 x 4 = 128.

So a - b = 3 - 4 = -1.

_________________

# Scott Woodbury-Stewart

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If a and b are positive integers, and x = 2*3*7*a, and y = 2*2*8*b, an   [#permalink] 07 Apr 2019, 18:44
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