If a and b are integers such that a > b > 1, which of

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sun Oct 28, 2018 4:04 pm

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If a and b are integers such that a > b > 1, which of the following cannot be a multiple of either a or b?

(A) a - 1
(B) b + 1
(C) b - 1
(D) a + b
(E) ab

OA C

Source: Manhattan Prep

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Source: Beat The GMAT — Problem Solving | Sun Oct 28, 2018 4:04 pm

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by [email protected] » Sun Oct 28, 2018 7:08 pm

Hi All,

We're told that A and B are integers such that A > B > 1. We're asked which of the following CANNOT be a multiple of either A or B. This question can be solved with some basic concept knowledge of the rules behind 'multiples.'

With the exception of "0", multiples are equal to - or greater than - their base number. For example, the multiples of 2 are 0, 2, 4, 6, 8, 10, 12, etc. Here, we're told that A is GREATER than B - and both of those integers are GREATER than 1. Thus, whatever A and B are, a number that is between B and 1 can NEVER be a multiple of either of those 2 variables. Looking at the answer choices, you should be able to immediately spot a value that is LESS than B.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

If a and b are integers such that a > b > 1, which of

by fskilnik@GMATH » Mon Oct 29, 2018 3:07 am

BTGmoderatorDC wrote:If a and b are integers such that a > b > 1, which of the following cannot be a multiple of either a or b?

(A) a - 1
(B) b + 1
(C) b - 1
(D) a + b
(E) ab
Source: Manhattan Prep

$$a > b \ge 2\,\,\,{\rm{ints}}$$
$$?\,\,:\,\,\underline {{\rm{not}}} \,\,{\rm{multiple}}\,\,{\rm{of}}\,\,a,b\,$$
$${\rm{Take}}\,\,\left( {a,b} \right) = \left( {3,2} \right)\,\,\,\,\left\{ \matrix{
\,a - 1\,\,{\rm{is}}\,\,{\rm{a}}\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,b\,\,\,\, \Rightarrow \,\,\,\,\left( A \right)\,\,\,{\rm{out}} \hfill \cr
\,b + 1\,\,{\rm{is}}\,\,{\rm{a}}\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,a\,\,\,\, \Rightarrow \,\,\,\,\left( B \right)\,\,\,{\rm{out}} \hfill \cr
\,ab\,\,{\rm{is}}\,\,{\rm{a}}\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,a,b\,\,\,\, \Rightarrow \,\,\,\,\left( E \right)\,\,\,{\rm{out}} \hfill \cr} \right.$$
$${\rm{Take}}\,\,\left( {a,b} \right) = \left( {4,2} \right)\,\,\,\,\left\{ {\,a + b\,\,{\rm{is}}\,\,{\rm{a}}\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,b\,\,\,\, \Rightarrow \,\,\,\,\left( D \right)\,\,\,{\rm{out}}} \right.$$

Conclusion: the correct answer is (C), by exclusion.

Important: from the fact that b-1 is a POSITIVE integer less than both a and b, we are sure b-1 is not a multiple of any one of them!
(-2 is less than both 1 and 2, and -2 is a multiple of both of them. Be careful not to make wrong conclusions!)

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

If a and b are integers such that a > b > 1, which of

by Brent@GMATPrepNow » Mon Oct 29, 2018 5:40 am

BTGmoderatorDC wrote:If a and b are integers such that a > b > 1, which of the following cannot be a multiple of either a or b?

(A) a - 1
(B) b + 1
(C) b - 1
(D) a + b
(E) ab

Let's make an important observation.
Some positive multiples of 3 are: 3, 6, 9, 12, . . . .
Some positive multiples of 5 are: 5, 10, 15, 20, . . . .
Some positive multiples of 12 are: 12, 24, 36, 48, . . . .

General observation: the positive multiples of k are all greater than or equal to k
So, b-1 cannot be a positive multiples of b (since b-1 is less than b), AND a-1 cannot be a positive multiples of a (since a-1 is less than a)

Since b is LESS THAN a, we know the b-1 is less than b AND b-1 is less than a
As such, b-1 cannot be a multiple of either a or b

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by Scott@TargetTestPrep » Tue Oct 30, 2018 6:11 pm

BTGmoderatorDC wrote:If a and b are integers such that a > b > 1, which of the following cannot be a multiple of either a or b?

(A) a - 1
(B) b + 1
(C) b - 1
(D) a + b
(E) ab

Since b - 1 is less than both a and b, it can't be a multiple of either a or b.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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