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When the members of group A are divided into groups of 13 people, m su

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When the members of group A are divided into groups of 13 people, m su  [#permalink]

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New post 08 Jul 2018, 23:56
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

53% (02:15) correct 47% (01:58) wrong based on 57 sessions

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[GMAT math practice question]

When the members of group A are divided into groups of 13 people, m subgroups are formed. When the members of group B are divided into groups of 11 people, n subgroups are formed, and 8 people are left over. What is the number of members of group B?

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

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Re: When the members of group A are divided into groups of 13 people, m su  [#permalink]

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New post 09 Jul 2018, 01:46
MathRevolution wrote:
[GMAT math practice question]

When the members of group A are divided into groups of 13 people, m subgroups are formed. When the members of group B are divided into groups of 11 people, n subgroups are formed, and 8 people are left over. What is the number of members of group B?

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


Given that #A=13m & #B=11n+8

Question stem: #B=?

st1:-
m=n
But we don't have any info on the values of m or n.
So, insufficient.
st2:-
#A=#B
But we don't have info on m or n.
So, insufficient.

combining we have, 13m=11n+8 (from st2)
since m=n (from st1)
So, we can definitely determine value of m & n ;subsequently value of #B.

So, sufficient.

Ans. (C)
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Re: When the members of group A are divided into groups of 13 people, m su  [#permalink]

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New post 09 Jul 2018, 01:47
1
MathRevolution wrote:
[GMAT math practice question]

When the members of group A are divided into groups of 13 people, m subgroups are formed. When the members of group B are divided into groups of 11 people, n subgroups are formed, and 8 people are left over. What is the number of members of group B?

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


Let the members be A and B
So A=13m and B=11n+8. What is B?

1) m=n
So B=11m+8
Nothing much.too many variables left
Insufficient

2) A=B
13m=11n+8
Again value of n not known
Insufficient

Combined
13m=11n+8 and m=n
So 13n=11n+8........2n=8........n=4
B=11*4+8=52
Sufficient

C
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Re: When the members of group A are divided into groups of 13 people, m su  [#permalink]

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New post 11 Jul 2018, 00:08
=>

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 2 variables (m and n) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
The conditions give the equations \(m = n\) and \(13m = 11n + 8\).
Plugging the first equation into the second yields \(2n = 8\) or \(n = 4.\)
Thus, group B has \(11*4 + 8 = 52\) members.
Both conditions together are sufficient.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
The equation \(m = n\) is not sufficient for determining the value of \(n\).
Thus, condition 1) alone is not sufficient.

Condition 2)
\(13m = 11n + 8\) does not give enough information to find the value of \(n\).
Thus, condition 2) is not sufficient.

Therefore, the answer is C.

Answer: C

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Re: When the members of group A are divided into groups of 13 people, m su  [#permalink]

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New post 20 Jul 2018, 22:46
Using option B only we can deduce that n should be 4,If we put the numbers in the equation it is clear that m and n both should have value 4. why we are using the combining both the statements?
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Re: When the members of group A are divided into groups of 13 people, m su  [#permalink]

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New post 20 Jul 2018, 23:18
1
sghoshgt wrote:
Using option B only we can deduce that n should be 4,If we put the numbers in the equation it is clear that m and n both should have value 4. why we are using the combining both the statements?


Hi sghoshgt,
You stopped your working at m=4, n=4 and concluded the answer option.
There may be some pairs of (m,n) such as (15,17), (37,43) etc. for which 13m=11n+8 is validated. In this way, numerous pairs exist; so we have more than one value of n, hence st2 alone is insufficient. We must combine st1 & st2 for further checking of sufficiency.

Hope it's clear.
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Re: When the members of group A are divided into groups of 13 people, m su &nbs [#permalink] 20 Jul 2018, 23:18
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When the members of group A are divided into groups of 13 people, m su

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