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

 It is currently 21 Oct 2019, 23:06 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Is the product of a, b and c divisible by 3?

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

Hide Tags

Math Expert V
Joined: 02 Aug 2009
Posts: 8007
Is the product of a, b and c divisible by 3?  [#permalink]

Show Tags 00:00

Difficulty:   95% (hard)

Question Stats: 39% (02:09) correct 61% (01:49) wrong based on 148 sessions

HideShow timer Statistics

Is the product of a, b and c divisible by 3?

(1) a + b + c is divisible by 3.
(2) a - b = b - c

_________________
Intern  B
Joined: 08 Nov 2017
Posts: 12
Re: Is the product of a, b and c divisible by 3?  [#permalink]

Show Tags

1
I feel it's either one. Option 2 is AP. eg: 5,6,7. Or 11,13,15. If you take any 3 numbers in AP one of them should be a multiple of 3.

Option 1: divisible by 3. Take any set of examples. Even this satisfies

Hence each statement alone

Please correct me if wrong

Sent from my Moto G (5S) Plus using GMAT Club Forum mobile app
Manager  B
Joined: 07 Sep 2013
Posts: 61
Re: Is the product of a, b and c divisible by 3?  [#permalink]

Show Tags

VijayRocky wrote:
I feel it's either one. Option 2 is AP. eg: 5,6,7. Or 11,13,15. If you take any 3 numbers in AP one of them should be a multiple of 3.

Option 1: divisible by 3. Take any set of examples. Even this satisfies

Hence each statement alone

Please correct me if wrong

Sent from my Moto G (5S) Plus using GMAT Club Forum mobile app

Can't a,b,c be same ?
In that case, 1+1+1 is divisible by 3 but not its product and 3+3+3 is divisible by 3 and its product too.

Sent from my Redmi Note 4 using GMAT Club Forum mobile app
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82
Is the product of a, b and c divisible by 3?  [#permalink]

Show Tags

chetan2u wrote:
Is the product of a, b and c divisible by 3?

(1) a + b + c is divisible by 3.
(2) a - b = b - c

Hi chetan2u

I think for clarity, the question must mention that a, b, c are integers and/or different, otherwise it becomes very easy to eliminate both the options.

Statement 1: if we assume a=b=c=2, then a+b+c=6, divisible by 3 but a*b*c=8 not divisible by 3, but if a=b=c=3, then abc will be divisible by 3

again if a=1.1 b=2 and c=2.9, then a+b+c=6, divisible by 3 but a*b*c clearly not divisible by 3

and if a=2, b=5 & c=8, then a+b+c=15, divisible by 3 but a*b*c=80, not divisible by 3

Hence Insufficient

statement 2:implies that a, b & c is an AP series, so if a=2, b=5 & c=8, then abc=80 not divisible by 3

but if a=2, b=4 & c=6, then abc=48, divisible by 3. Insufficient

Combining 1 & 2, again if we have a=b=c=3 or a=2, b=4 & c=6, then abc is divisible by 3

but if a=2, b=5 & c=8, then abc is not divisible by 3.

Insufficient

Option E
Current Student S
Joined: 22 Apr 2017
Posts: 106
Location: India
GMAT 1: 620 Q46 V30 GMAT 2: 620 Q47 V29 GMAT 3: 630 Q49 V26 GMAT 4: 690 Q48 V35 GPA: 3.7
Is the product of a, b and c divisible by 3?  [#permalink]

Show Tags

niks18 wrote:
chetan2u wrote:
Is the product of a, b and c divisible by 3?

(1) a + b + c is divisible by 3.
(2) a - b = b - c

Hi chetan2u

I think for clarity, the question must mention that a, b, c are integers and/or different

Statement 1: if we assume a=b=c=2, then a+b+c=6, divisible by 3 but a*b*c=8 not divisible by 3, but if a=b=c=3, then abc will be divisible by 3

again if a=1.1 b=2 and c=2.9, then a+b+c=6, divisible by 3 but a*b*c clearly not divisible by 3

and if a=2, b=5 & c=8, then a+b+c=15, divisible by 3 but a*b*c=80, not divisible by 3

Hence Insufficient

statement 2:implies that a, b & c is an AP series, so if a=2, b=5 & c=8, then abc=80 not divisible by 3

but if a=2, b=4 & c=6, then abc=48, divisible by 3. Insufficient

Combining 1 & 2, again if we have a=b=c=3 or a=2, b=4 & c=6, then abc is divisible by 3

but if a=2, b=5 & c=8, then abc is not divisible by 3.

Insufficient

Option E

I agree with niks18. 2) a+c=2b is valid for three consecutive numbers 1,2,3.....3,4,5 as well as APs such as 4,7,10... 5,8,11 etc.
Intern  B
Joined: 08 Nov 2017
Posts: 12
Re: Is the product of a, b and c divisible by 3?  [#permalink]

Show Tags

alokgupta1009 wrote:
VijayRocky wrote:
I feel it's either one. Option 2 is AP. eg: 5,6,7. Or 11,13,15. If you take any 3 numbers in AP one of them should be a multiple of 3.

Option 1: divisible by 3. Take any set of examples. Even this satisfies

Hence each statement alone

Please correct me if wrong

Sent from my Moto G (5S) Plus using GMAT Club Forum mobile app

Can't a,b,c be same ?
In that case, 1+1+1 is divisible by 3 but not its product and 3+3+3 is divisible by 3 and its product too.

Sent from my Redmi Note 4 using GMAT Club Forum mobile app

As some others have mentioned here, I guess the question also has a point that a,b and c are distinct numbers

Sent from my Moto G (5S) Plus using GMAT Club Forum mobile app
Math Expert V
Joined: 02 Aug 2009
Posts: 8007
Re: Is the product of a, b and c divisible by 3?  [#permalink]

Show Tags

niks18 wrote:
chetan2u wrote:
Is the product of a, b and c divisible by 3?

(1) a + b + c is divisible by 3.
(2) a - b = b - c

Hi chetan2u

I think for clarity, the question must mention that a, b, c are integers and/or different, otherwise it becomes very easy to eliminate both the options.

Statement 1: if we assume a=b=c=2, then a+b+c=6, divisible by 3 but a*b*c=8 not divisible by 3, but if a=b=c=3, then abc will be divisible by 3

again if a=1.1 b=2 and c=2.9, then a+b+c=6, divisible by 3 but a*b*c clearly not divisible by 3

and if a=2, b=5 & c=8, then a+b+c=15, divisible by 3 but a*b*c=80, not divisible by 3

Hence Insufficient

statement 2:implies that a, b & c is an AP series, so if a=2, b=5 & c=8, then abc=80 not divisible by 3

but if a=2, b=4 & c=6, then abc=48, divisible by 3. Insufficient

Combining 1 & 2, again if we have a=b=c=3 or a=2, b=4 & c=6, then abc is divisible by 3

but if a=2, b=5 & c=8, then abc is not divisible by 3.

Insufficient

Option E

Hi..
The Question is 600-700 level, so it doesn't have too deep a secret involved in it.
Very many will go wrong by not differentiating between integers and non integers and few answers on top do point towards that and ofcourse the OA is accordingly written.
_________________
Manager  B
Joined: 02 Jul 2017
Posts: 67
Re: Is the product of a, b and c divisible by 3?  [#permalink]

Show Tags

I am considering a , b and c as integers .
is product of abc divisible by 3 ..for this to happen among a,b and c at least one should be 3 or should have a factor 3 .

Now check

statement 1 : a+b+c is divisible by 3 ... a=1 b=1 c=1 a+b+c =3 is divisible by 3 but abc=1 not divisible by 3

or a=4 b =16 c=10 abc not divisible by 3

so statement 1 is insufficient .

Statement 2 : 2b =a+c
i.e terms are in AP ..lets consider terms are a-d , a and a+d ...Sum is 3a which is always divisible by 3 i.e statement 1 always hold correct for sum of 3 terms which are in AP.
now check if a(a-d)(a+d) are divisible by 3 or not
i.e a=10 d=3 abc=10* 7*13 ...means insufficient ..

we already proved statement 2 auto validates statement 1 so both statements together also are not sufficient ..

Hence , answer is E .

Please respond if you feel otherwise
Director  P
Joined: 31 Jul 2017
Posts: 512
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33 GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: Is the product of a, b and c divisible by 3?  [#permalink]

Show Tags

chetan2u wrote:
Is the product of a, b and c divisible by 3?

(1) a + b + c is divisible by 3.
(2) a - b = b - c

Hi @Chetan2u,

I think both the options will be insufficient when a,b,c is a non-integer.

Sent from my Lenovo P1a42 using GMAT Club Forum mobile app
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!
Intern  Joined: 08 Jul 2017
Posts: 1
Is the product of a, b and c divisible by 3?  [#permalink]

Show Tags

chetan2u wrote:
Is the product of a, b and c divisible by 3?

(1) a + b + c is divisible by 3.
(2) a - b = b - c

I took it this way:

ST1: a + b + c is a multiple of 3, this has many options a=b=c=2, then a+b+c is 6, which is div by 3 but a*b*c is 8 not div by 3. If a=b=c=3, a+b+c is 9 and a*b*c is div by 3.

INSUFFICIENT

ST2: It's kind of giving us the same info that the first statement.

a - b = b - c
a + c = 2b
(We sum b to each side)
a + b + c = 3b (this is telling us already what ST1 said, that the sum of a,b,c is a multiple of 3)

INSUFFICIENT

And since ST1 and ST2 give us the same info, taking them together won't add new info.

HENCE E.
Intern  Joined: 11 Nov 2017
Posts: 1
Re: Is the product of a, b and c divisible by 3?  [#permalink]

Show Tags

chetan2u wrote:
niks18 wrote:
chetan2u wrote:
Is the product of a, b and c divisible by 3?

(1) a + b + c is divisible by 3.
(2) a - b = b - c

Hi chetan2u

I think for clarity, the question must mention that a, b, c are integers and/or different, otherwise it becomes very easy to eliminate both the options.

Statement 1: if we assume a=b=c=2, then a+b+c=6, divisible by 3 but a*b*c=8 not divisible by 3, but if a=b=c=3, then abc will be divisible by 3

again if a=1.1 b=2 and c=2.9, then a+b+c=6, divisible by 3 but a*b*c clearly not divisible by 3

and if a=2, b=5 & c=8, then a+b+c=15, divisible by 3 but a*b*c=80, not divisible by 3

Hence Insufficient

statement 2:implies that a, b & c is an AP series, so if a=2, b=5 & c=8, then abc=80 not divisible by 3

but if a=2, b=4 & c=6, then abc=48, divisible by 3. Insufficient

Combining 1 & 2, again if we have a=b=c=3 or a=2, b=4 & c=6, then abc is divisible by 3

but if a=2, b=5 & c=8, then abc is not divisible by 3.

Insufficient

Option E

Hi..
The Question is 600-700 level, so it doesn't have too deep a secret involved in it.
Very many will go wrong by not differentiating between integers and non integers and few answers on top do point towards that and ofcourse the OA is accordingly written.

What is correct answer..?

Sent from my Lenovo A6000 using GMAT Club Forum mobile app
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1428
Location: India
Re: Is the product of a, b and c divisible by 3?  [#permalink]

Show Tags

Hi..
The Question is 600-700 level, so it doesn't have too deep a secret involved in it.
Very many will go wrong by not differentiating between integers and non integers and few answers on top do point towards that and ofcourse the OA is accordingly written.[/quote]
What is correct answer..?

Sent from my Lenovo A6000 using GMAT Club Forum mobile app[/quote]

Hi

Correct answer is E only, as mentioned. Since its not specified that a, b, c are integers - they can be non-integers also, in which case both statements together become insufficient to find the answer.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8025
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Is the product of a, b and c divisible by 3?  [#permalink]

Show Tags

chetan2u wrote:
Is the product of a, b and c divisible by 3?

(1) a + b + c is divisible by 3.
(2) a - b = b - c

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables and 0 equations, E is most likely to be the answer. So, we should consider 1) & 2) first.

Conditions 1) & 2):
$$a - b = b - c$$
$$⇔ a + c = 2b$$
$$a + b + c = ( a + c ) + b = 2b + b = 3b$$

Case 1: $$a = b = c = 1$$
$$abc = 1$$ is not divisible by 3.

Case 2: $$a = b = c = 3$$
$$abc = 27$$ is divisible by 3.

Both conditions together are not sufficient.

Therefore, the answer is E.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
_________________ Re: Is the product of a, b and c divisible by 3?   [#permalink] 20 Jan 2018, 22:19
Display posts from previous: Sort by

Is the product of a, b and c divisible by 3?

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

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