If 105 divides into n with no remainder, which of the following must

Question

If 105 divides into n with no remainder, which of the following must be a factor of n?

A. 2 
B. 4 
C. 6 
D. 7 
E. 11

BrentGMATPrepNow · Accepted Answer

Another approach is to  pick a value for n  that satisfies the given condition. 
For example, n COULD equal 105

Now check the answer choices
A. 2 is NOT a factor of 105 (ELIMINATE) 
B. 4 is NOT a factor of 105 (ELIMINATE) 
C. 6 is NOT a factor of 105 (ELIMINATE) 
D. 7 IS a factor of 105 (KEEP) 
E. 11 is NOT a factor of 105 (ELIMINATE)

Answer:  D

Cheers,
Brent

Kocket · Answer

If 105 divides into n with no remainder, n must contain one of the factors of 105. 
So prime factorization of 105 gives us 5, 3, 7 
since 7 is the only factor that appears among the answer choices, D is the right answer.

Hope I am right...

OptimusPrepJanielle · Answer

105 divides into n with no remainder.
This means that n is a factor of 105

On factorizing, 105 = 3*5*7
Of the options, Only 7 is a factor of 105
Option D

Abkhazian · Answer

105 / n = k (with k an integer)
(7)(5)(3) / n = k

n must have a 7 in his prime factorization to divide 105 without remainder.

answer D

yosita18 · Answer

stonecold · Answer

A cool property => A number is divisible by factors as well as factors of its factors.
e.g => 27 is divisible by 9 
here 27 is also divisible by all the factors of 9 => 1,2,9

in the question => 105/n = integer
the number which will be a factor of n must also divide 105
hence the number we choose must also divide 105
only option that divides 105 is D => 7
Hence D .

Manonamission · Answer

N/105 = Some K + 0

N = Some K x 105

N must contain factors of 105

i.e. 5 x 7 x 3

option D

AkshdeepS · Answer

First step : Find prime factors of 105

3 * 5 * 7

Now, 7 must be a factor of n

(D)

nigina93 · Answer

105=3*5*7, from answer choices we see that 7 is option D, which is the correct answer

CrackverbalGMAT · Answer

Solution: 
 
Its a question that tests on your fundamentals.

The factors of 105 are 5*7*3 and any of 5,7 or 3 on dividing 105 will perfectly divide it with no remainder.

Only option d carries 7 and no other option is a factor of 105. (option d)
 
  Devmitra Sen
GMAT SME

BrushMyQuant · Answer

105 divides into n with no remainder

=> n is divisible by 105
=> n is a multiple of 105
So, any factor of 105 will also be a factor of n
Only factor of 105 in the answer choice is 7 as 105 = 7 *15

So,  Answer will be D 
Hope it helps!

Watch the following video to learn the Basics of Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

bumpbot · Answer

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If 105 divides into n with no remainder, which of the following must

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GMAT Problem Solving (PS) Questions

If 105 divides into n with no remainder, which of the following must

Prep Toolkit

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