If a and b are integers such that a b 1, which of the following ca

Question

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

EgmatQuantExpert · Accepted Answer

Solution 
  Given:  
 • a and b are integers
• a > b > 1

To find:  
 • Which of the given answer choices cannot be a multiple of either ’a’ or ‘b’

Approach and Working:   
 • For a number to be a multiple of ‘a’, it must be greater than ‘a’
• Similarly, for a number to be a multiple of ‘b’, it must be greater than ‘b’
• a > b > 1, and a, b are integers, implies that a and b are positive integers greater than 1.
• a – 1 is less than a, but it can be greater than b. 
 o Thus, it can be a multiple of b 
• b + 1 is always greater than b. 
 o Thus, it can be a multiple of b 
• b – 1 is less than both, a and b. 
 o Thus, it cannot be a multiple of both a and b 
• a + b is greater than both a and b. 
 o Thus, it can be a multiple of both a and b 
• ab is greater than both a and b. 
 o Thus, it can be a multiple of both a and b

Hence, the correct answer is option C

Answer: C

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Free-Session-Algebra-e1533292089856.jpg

souvonik2k · Answer

Suppose a=4; b=3.
4>3>1
Plugging in to the answers:
A) a-1=3--multiple of 3 --eliminate
B) b+1=4--multiple of 4 --eliminate
C) b-1=2--not a multiple -- HOLD
D) a+b=7--not a multiple -- HOLD
E) ab=12--multiple of 3 and 4 --eliminate
Now let us check some other values of a,b
a=6,b=3; a+b=9 --multiple of 3 --eliminate
but b-1=2 --not a multiple - correct answer.
Answer C.

PKN · Answer

Given, a and b are integers & a > b > 1 implies that a and b are positive integers.

Note:- A positive multiple is always greater than or equal to the number it's a multiple of.
So, the answer option which violates our noted reasoning would be the correct answer to the question stem. (keeping in mind that a > b > 1)

Among answer options, b-1 is smaller than both a and b.

Ans. (C)

EMPOWERgmatRichC · Answer

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

fskilnik · Answer

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.

ScottTargetTestPrep · Answer

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

Answer: C

MishalSen1 · Answer

a>b>1

Therefore, b is greater than 1 but less than a

b can take the following values : {2,3,4,5,6,7...........}
a can take the following values : {3,4,5,6,7,8,...........}

from the options:
A. a-1 i.e 3-1 =2 is still a multiple of b (as 2 can be a value taken by b)
B. b+1 i.e 2+1 =3 is still a multiple of a (as 3 can be a value taken by a)
C. b-1 i.e 2-1 =1 this occurs neither in the set of values for b or a therefore this is the answer
D. a+b i.e 2+3 =5 this still a multiple of a (as 5 can be a value taken by a)
E. ab i.e 2*3=6 this is still a multiple of a (as 6 can be a value taken by a)

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions