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20 Jul 2026, 19:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
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Question Stats:
62% (02:11) correct
38%
(02:12)
wrong
based on 156
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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
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
(1) m = n
(2) The total numbers of members in groups A and B are the same.
Source: Math Revolution
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
21 Jul 2026, 00:40
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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
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
21 Jul 2026, 01:31
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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,
[13m = 11n + 8]
[13m - 11n = 8]
Statement (2) is NOT sufficient.
### Both statements together
From (1), (m=n).
Substitute into
[13m = 11m + 8]
[2m = 8]
m=4
Hence,
n=4
Group B:
[11(4)+8 = 52]
Unique value.
Both statements together are sufficient.
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,
[13m = 11n + 8]
[13m - 11n = 8]
Statement (2) is NOT sufficient.
### Both statements together
From (1), (m=n).
Substitute into
[13m = 11m + 8]
[2m = 8]
m=4
Hence,
n=4
Group B:
[11(4)+8 = 52]
Unique value.
Both statements together are sufficient.
