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

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

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

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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>

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Source: Beat The GMAT — Data Sufficiency | Fri May 25, 2018 12:40 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Mon May 28, 2018 3:10 am

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.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

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

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]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

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

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.

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

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

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

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

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