GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Oct 2018, 19:57

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# The expression 1014 - 120 is divisible by all of the following integer

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49968
The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

### Show Tags

25 Jul 2018, 01:44
00:00

Difficulty:

5% (low)

Question Stats:

85% (00:49) correct 15% (00:47) wrong based on 123 sessions

### HideShow timer Statistics

The expression 10^14 - 120 is divisible by all of the following integers EXCEPT

(A) 2

(B) 3

(C) 4

(D) 8

(E) 10

_________________
Senior RC Moderator
Status: Perfecting myself for GMAT
Joined: 22 May 2017
Posts: 761
Concentration: Nonprofit
Schools: Haas '21
GPA: 4
WE: Engineering (Computer Software)
The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

### Show Tags

Updated on: 25 Jul 2018, 02:04
3
If X is a multiple of Z and Y is a multiple of Z then X-Y is a multiple of Z

$$10^{14}$$ is a multiple 2,4,8 and 10

=> $$10^{14}$$ is a multiple of all option choices except option B

120 is a multiple of all option choices 2,3,4,8 and 10

=> 120 is a multiple of all option choices

So $$10^{14} - 120$$ is multiple of 2,4,8 and 10 except 3

Hence option B
_________________

If you like my post press kudos +1

New - RC Butler - 2 RC's everyday

Tag me in RC questions if you need help. Please provide your analysis of the question in the post along with the tag.

Originally posted by workout on 25 Jul 2018, 01:53.
Last edited by workout on 25 Jul 2018, 02:04, edited 1 time in total.
Director
Joined: 31 Oct 2013
Posts: 651
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

### Show Tags

25 Jul 2018, 02:02
1
Bunuel wrote:
The expression 10^14 - 120 is divisible by all of the following integers EXCEPT

(A) 2

(B) 3

(C) 4

(D) 8

(E) 10

$$10^{14}$$ must end with 14 zeros. Now we can reduce the power and deduct 120 from the result.

$$10^3 =1000$$

1000 - 120 = 880

880 is divisible by all except 3.

$$10^4 = 10000$$

10000 -120 = 9880

9880 is divisible by all except 3.

This is true for $$10^{14}$$ also.

Intern
Joined: 30 Mar 2017
Posts: 1
The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

### Show Tags

25 Jul 2018, 05:36
first find last three digits of the big number =1000-120=880

(A) 2 [divisible by 2 because the number has 0 in unit digit
(B) 3[not divisible by 3]
(C) 4 [divisible by 4 because last two digit of the number 80 is divisible by 4]
(D) 8 [divisible by 8 because last three digit of the number 880 is divisible by 8]
(E) 10 [divisible because last digit has 0]

so B is the right answer
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

### Show Tags

26 Jul 2018, 16:28
Bunuel wrote:
The expression 10^14 - 120 is divisible by all of the following integers EXCEPT

(A) 2

(B) 3

(C) 4

(D) 8

(E) 10

Since 120 is divisible by 3 but 10^14 is not, their difference is not divisible by 3.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Joined: 16 Jul 2018
Posts: 1
Re: The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

### Show Tags

28 Aug 2018, 21:17
I found prime factors of 10 and 120 here

then prime factors were 10 = 2,5 and 120 = 2^3, 3, 5

Then I chose B because 3 was not commonly present in both numbers.

Is this a lucky coincident?
Senior Manager
Joined: 07 Oct 2017
Posts: 267
Re: The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

### Show Tags

28 Aug 2018, 22:56
2
awchoi1213 wrote:
I found prime factors of 10 and 120 here

then prime factors were 10 = 2,5 and 120 = 2^3, 3, 5

Then I chose B because 3 was not commonly present in both numbers.

Is this a lucky coincident?
Yes, it was a lucky co-incidence.

3 properties--->

1) if both integers a and b are multiple of some integer k (k>1), their sum and difference will be divisible by k

2) if only one integer out of a and b is multiple of integer k (k>1), their sum and difference will not be a multiple of k

3) if none of integer a and b are multiple of integer k (k>1), their sum and difference may be or may not be divisible by k

Eg: a=5, b=4
K= 3

Hope this helps

Thank you = Kudos
_________________

Thank you =Kudos
The best thing in life lies on the other side of the pain.

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

### Show Tags

03 Sep 2018, 19:06
Bunuel wrote:
The expression 10^14 - 120 is divisible by all of the following integers EXCEPT

(A) 2

(B) 3

(C) 4

(D) 8

(E) 10

We see that 120 is divisible by 3, but 10^14 is not. Thus, the difference 10^14 - 120 is not divisible by 3, either.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: The expression 1014 - 120 is divisible by all of the following integer &nbs [#permalink] 03 Sep 2018, 19:06
Display posts from previous: Sort by