Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 16 Jul 2019, 11:47

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If x is the product of integers a, b, c, and d, is x divisible by 128?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56244
If x is the product of integers a, b, c, and d, is x divisible by 128?  [#permalink]

Show Tags

New post 29 Jan 2015, 08:24
1
4
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

63% (01:38) correct 37% (01:51) wrong based on 176 sessions

HideShow timer Statistics


Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7764
Re: If x is the product of integers a, b, c, and d, is x divisible by 128?  [#permalink]

Show Tags

New post 29 Jan 2015, 11:15
ans B...
statement 1 not sufficient
2) statement 2 tells us they are consecutive even nos so two will be multiple of atleast 2, one of atleast 4or2^2 and one will be multiple of atleast 8 or2^3.. all four combined will be multiple of 2^6*3=128*3 so sufficient
_________________
Intern
Intern
avatar
Joined: 24 Jan 2014
Posts: 35
Location: France
Concentration: General Management, International Business
GMAT 1: 700 Q47 V39
GPA: 3
WE: General Management (Advertising and PR)
GMAT ToolKit User
Re: If x is the product of integers a, b, c, and d, is x divisible by 128?  [#permalink]

Show Tags

New post 01 Feb 2015, 11:20
2
Hello Bunuel, I gave it a try:

the question is actually is abcd/128 an integer?

(1) insufficient if a is 24 then 24bcd/128 should be, by simplifying we find 3bcd/16 which can give both integer and non-integer results:

ex: if b = 3 ,c= 7, d = 2 => (3x3x7x2)/16 = non integer
b = 2, c =2, d =4 => 3x2x2x4 = integer, div by 16

(2) is sufficient as the product of any 4 consecutive even integers will be divisible by 128 (2^7 = 2x2x2x2x2x2x2)

2, 4, 6, 8 (contains the factors that together are divisible by 128)
4, 6, 8, 10 (contains the factors that together are divisible by 128)

etc,

SO B CORRECT ANSWER

Bunuel wrote:
If x is the product of integers a, b, c, and d, is x divisible by 128?

(1) a = 24

(2) a, b, c, and d are consecutive even integers

Kudos for a correct solution.

_________________
THANKS = KUDOS. Kudos if my post helped you! :)

Napoleon Hill — 'Whatever the mind can conceive and believe, it can achieve.'
Manager
Manager
User avatar
Joined: 27 Jun 2014
Posts: 68
Location: New Zealand
Concentration: Strategy, General Management
GMAT 1: 710 Q43 V45
GRE 1: Q161 V163

GRE 2: Q159 V166
GPA: 3.6
WE: Editorial and Writing (Computer Software)
Re: If x is the product of integers a, b, c, and d, is x divisible by 128?  [#permalink]

Show Tags

New post 01 Feb 2015, 15:07
1
Bunuel wrote:
If x is the product of integers a, b, c, and d, is x divisible by 128?

(1) a = 24

(2) a, b, c, and d are consecutive even integers

Kudos for a correct solution.



Statement 1: A= 2^3*8. Therefore, we need another four 2s from the other three integers. Not sufficient.
Statement 2: A, B, C, D are consecutive even integers. Lowest possible option will be 2, 4, 6, and 8 (or their negative counterparts), which has 2^7 in it, or even 0, 2, 4, 6 (0 is even) in which case X is 0 and 0/128=0, so answer to the question is yes. Sufficient.

B.
_________________
"Hardwork is the easiest way to success." - Aviram

One more shot at the GMAT...aiming for a more balanced score.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56244
Re: If x is the product of integers a, b, c, and d, is x divisible by 128?  [#permalink]

Show Tags

New post 02 Feb 2015, 05:20
Bunuel wrote:
If x is the product of integers a, b, c, and d, is x divisible by 128?

(1) a = 24

(2) a, b, c, and d are consecutive even integers

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

B. While 128 may seem an arbitrary number, look a bit closer and recognize that it's a power of 2. 27=128. If you didn't see this right away, there are clues in the answer choices; 24 from statement 1 is 3x8, and 8 is 23, and in statement 2 you're given several even numbers, so your mind might see those as clues that 2 is an important number here.

Statement 1 is insufficient alone, as without any knowledge of the other three numbers you can only account for the three 2s contained within 24.

Statement 2, however is sufficient, and you might find that by looking at patterns in numbers. Consider a string of consecutive even numbers:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24....

if you're thinking in terms of "2 to a big exponent" like 128 is, you should be conscious of where you get more than one factor of 2. If you list those numbers out in terms of factors of 2, you have:

2, (2 * 2), (2 * 3), (2 * 2 * 2), (2 * 5), (2 * 2 * 3), (2 * 7), (2 * 2 * 2 * 2), (2 * 9), (2 * 2 * 5), (2 * 11), (2 * 2 * 2 * 3)

And you should see that within any stretch of four of those, you get two that contain one 2, but one that contains at least two 2s (the multiples of 4) AND one that contains at least three 2s (the multiples of 8). So at a minimum, any string of four even numbers will give you at least seven factors of 2, meaning that just knowing you have four consecutive even numbers will be sufficient.

And a note - since 0 is divisible by 128 (and every other integer other than 0), even crossing 0 with your consecutive integers will still work, as if one of those evens is 0 the product will still be divisible by 128.
_________________
Manager
Manager
avatar
Joined: 23 Sep 2016
Posts: 92
If x is the product of integers a, b, c, and d, is x divisible by 128?  [#permalink]

Show Tags

New post 01 Nov 2016, 09:26
If x is the product of integers a, b, c, and d, is x divisible by 128?

(1) a = 24
(2) a, b, c, and d are consecutive even integers
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56244
Re: If x is the product of integers a, b, c, and d, is x divisible by 128?  [#permalink]

Show Tags

New post 01 Nov 2016, 09:30
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2609
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User
Re: If x is the product of integers a, b, c, and d, is x divisible by 128?  [#permalink]

Show Tags

New post 15 Jan 2017, 01:37
Great Question.
Here is what i did in this one =>

We are told that a,b,c,d are all integers.
We need to see if x=a*b*c*d is divisible by 128 or not.

Statement 1->
Lets use test cases.
Case 1=>
a=24
b=1
c=1
d=1
x=24 => Clearly it is not divisible by 128.
Case 2=>
a=24
b=1
c=1
d=128
x=24*128 => divisible by 128.
Hence not sufficient.

Statement 2->
Consecutive evens =>
a=2n
b=2n+2
c=2n+4
d=2n+6


Taking the Product => x=2n(2n+2)(2n+4)(2n+6)=> 8*n(n+1)(n+2)(n+3)

Property -> Product of n consecutive integers is always divisible by n!

Hence x=8*24k For some integer k=> 128k'
Hence x must be divisible by 128.

Hence sufficient.

Hence B.

_________________
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 11658
Re: If x is the product of integers a, b, c, and d, is x divisible by 128?  [#permalink]

Show Tags

New post 07 Apr 2019, 12:28
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: If x is the product of integers a, b, c, and d, is x divisible by 128?   [#permalink] 07 Apr 2019, 12:28
Display posts from previous: Sort by

If x is the product of integers a, b, c, and d, is x divisible by 128?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne