When the members of group A are divided into subgroups of 13 people

Question

When the members of group A are divided into subgroups of 13 people, m subgroups are formed, and no one is left over. When the members of group B are divided into subgroups of 11 people, n subgroups are formed, with 8 people left over. What is the total number of members in group B?

(1) m = n
(2) The total numbers of members in groups A and B are the same.

Source: Math Revolution
 
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dhart · Answer

m subgroups of 13 , 13m ; n subgroups of 11 , 11n + 8 with leftover

stmt 1 ) m=n ; 
 for m=n=4 ; 13 * 4 = 52 and 11 *4 +8 =52
group ba has 52 members sufficient

stmt 2 ) total no. of members are same

13m = 11n+8, 
m=4,n = 4 , .m =15 , n =17 , can't say how many group has 
insufficeint

option A

MintLog · Answer

Option C is the correct answer

Let's define the groups.

Group A has (13m) members (since they're divided into groups of 13 with no remainder).
Group B has (11n + 8) members (since they're divided into groups of 11 with 8 left over).

We need to find Group B = (11n + 8).

### Statement (1): (m = n)

Then

Group A = (13m)
Group B = (11m + 8)

But we don't know the value of (m).

Examples:

If (m=2), Group B = (22+8=30)
If (m=5), Group B = (55+8=63)

Different values are possible.

Statement (1) is NOT sufficient.

### Statement (2): The total numbers of members in groups A and B are the same.

So,

Statement (2) is NOT sufficient.

### Both statements together

From (1), (m=n).

Substitute into

m=4

Hence,
n=4

Group B:

Unique value.

Both statements together are sufficient.

Edskore · Answer

Load this one up as a remainder/Diophantine setup dressed as DS, and the classic trap is picking C before actually checking if the statements are insufficient alone.

1. Group A divided into subgroups of 13, none left over, so total in A = 13m.
2. Group B divided into subgroups of 11, with 8 left over, so total in B = 11n + 8. That's what the question wants.
3. Statement 1: m = n. That just says A and B have the same number of subgroups, not what that number is. m could be 1, 4, 100, whatever, B changes every time. Insufficient.
4. Statement 2: 13m = 11n + 8. One equation, two unknowns. Try m=4, n=4: 52=52, works. Try m=15, n=17: 195=195, also works. Two different values for B. Insufficient alone.
5. Combine both: m=n and 13m=11n+8 becomes 13m=11m+8, so m=4, n=4, B=11(4)+8=52. One clean number.

Answer is C.

I got burned by almost this exact structure on a practice test, saw two equations and figured "sufficient, has to be C" without testing whether statement 2 alone pins down a unique value. It doesn't, a single linear equation in two integer unknowns almost always has multiple solutions unless something else bounds it.

Takeaway: whenever a DS statement gives you one equation with two unknowns, go hunt for a second solution before calling it insufficient, don't just trust your gut.

When the members of group A are divided into subgroups of 13 people

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GMAT Data Sufficiency (DS) Questions

When the members of group A are divided into subgroups of 13 people

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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745 with Only Self-Prep and GMAT Club

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Perfect 805 Score Debrief by Julia

My Rewards