BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Is the positive integer P a multiple of 11 [A] P = M+N

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 1622
Joined: Thu Mar 01, 2018 7:22 am
Followed by:2 members

Is the positive integer P a multiple of 11 [A] P = M+N

by Gmat_mission » Fri May 25, 2018 12:40 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Is the positive integer P a multiple of 11

(1) P = M+N where M and N are integers
(2) M is divisible by 11 and N is not divisible by 11

[spoiler]OA=C[/spoiler].

How can I conclude something here using both statements? Could someone help me? Thanks in advance. <i class="em em-frowning"></i>
Top
Source: — Data Sufficiency |
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pm
Thanked: 6 times
Followed by:5 members

by Vincen » Mon May 28, 2018 3:10 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Hello Gmat_mission.

Let's take a look at your question.
(1) P = M+N where M and N are integers
This statement does tell us anything about P. We can have the following cases:

1. M=13, N=9, then P=M+N=22 and then P is divisible by 11.
2. M=13, N=2, then P=M+N=15 and then P is NOT divisible by 11.

Hence, NOT SUFFICIENT.
(2) M is divisible by 11 and N is not divisible by 11
This statement only talks about M and N. Not about P. Hence, NOT SUFFICIENT. .
Using both statements together
We have that P=M+N, where M and N are integer and M is divisible by 11 and N, is not.

Now, we have that $$\frac{M}{11}=\frac{M+N}{11}=\frac{M}{11}+\frac{N}{11}=integer\ +\ not\ integer\ =\ not\ integer.\ $$ This implies that M is not divisible by 11.

Hence this statement is SUFFICIENT. .

The correct answer is the option C.

I hope it helps.
Top
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Tue May 29, 2018 4:57 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Gmat_mission wrote:Is the positive integer P a multiple of 11

(1) P = M+N where M and N are integers
(2) M is divisible by 11 and N is not divisible by 11

We need to determine if P is a multiple of 11.

Statement One Alone:

P = M+N where M and N are integers.

Since we have no information regarding the values of M or N, statement one alone is not sufficient to answer the question.

Statement Two Alone:

M is divisible by 11 and N is not divisible by 11.

Since we have no information about P, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Since P = M + N, and since M is a multiple of 11, but N is not, there is no possible way for P to be a multiple of 11. So the answer to the question is no.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pm
Followed by:5 members

by deloitte247 » Tue May 29, 2018 5:28 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Statement 1 = P=M+N where M and N are integers
11=6+5------>Yes
20=9+11----->Yes
Hence statement 1 is not sufficient

Statement 2= M is indivisible by 11 and N is not divisible by 11
There is no specific relationship between M, N and P so statement 2 is not sufficient

statement 1 and 2 together
P is the sum of two integers in which is divisible by 11 ( a multiple of 11) while other is not;
Hence statement 1 and 2 together is sufficient.
answer = Option C because neither statements are sufficient alone.
Top
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pm
Followed by:5 members

by deloitte247 » Tue May 29, 2018 5:31 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Statement 1 = P=M+N where M and N are integers
11=6+5------>Yes
20=9+11----->Yes
Hence statement 1 is not sufficient

Statement 2= M is indivisible by 11 and N is not divisible by 11
There is no specific relationship between M, N and P so statement 2 is not sufficient

statement 1 and 2 together
P is the sum of two integers in which is divisible by 11 ( a multiple of 11) while other is not;
Hence statement 1 and 2 together is sufficient.
answer = Option C because neither statements are sufficient alone.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Tue May 29, 2018 5:57 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Gmat_mission wrote:Is the positive integer P a multiple of 11

(1) P = M+N where M and N are integers
(2) M is divisible by 11 and N is not divisible by 11
Target question: Is P a multiple of 11

Statement 1: P = M+N where M and N are integers
Definitely NOT SUFFICIENT

Statement 2: M is divisible by 11 and N is not divisible by 11
Since there's no information about P, there's no way to answer the target question
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that P = M+N where M and N are integers
Statement 2 tells us that M is divisible by 11 and N is not divisible by 11

Here are some nice divisibility rules:
1. If integers A and B are each divisible by integer k, then (A + B) is divisible by k
2. If integers A and B are each divisible by integer k, then (A - B) is divisible by k
3. If integer A is divisible by integer k, BUT integer B is NOT divisible by integer k, then (A + B) is NOT divisible by k
4. If integer A is divisible by integer k, BUT integer B is NOT divisible by integer k, then (A - B) is NOT divisible by k

So, when we apply Rule #3, we can conclude that M+N is NOT divisible by 11
Since P = M+N, we can conclude that P is NOT divisible by 11
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1