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# The table above shows the number of students in a certain high school

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Ans is B

Option A will only give us number of boys who are not studying biology and number of girls who are studying biology which will insufficient to find total number of students in class.

Option B gives us the relationship between Total number of girls and total number of students who are not study biology.

If we consider Number of students not studying as X then,

Number of girls would be 2x

Total number of students should match by calculating it either way therefore ,

we can write 26 + x = 18 + 2x

Solving the equation we get x = 8

Hence total students would be 26 + 8 = 18 +2*8 = 34.
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Re: The table above shows the number of students in a certain high school [#permalink]
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Bunuel wrote:

The table above shows the number of students in a certain high school class who are boys and the number of students in the class who are studying biology. What is the total number of students in the class?

(1) Of the boys in the class, 15 are studying biology.
(2) The number of girls in the class is twice the number of students in the class who are NOT studying biology.

Kudos for a correct solution.

Attachment:
2015-10-26_2106.png

Well this is a very good question.

Statement 1 : gives the number of boys, No talk about the number of girls.
Insufficient.

Statement 2:The number of girls in the class is twice the number of students in the class who are NOT studying biology.

Let the number of students in the class who are NOT studying biology =x
therefore the number of girls in the class=2x

Now total number of students in the class= the number of students in the class who are NOT studying biology+the number of students in the class who are studying biology =x+26 --(i)

Also total number of students in the class=the number of girls in the class+the number of boys in the class=2x+18---(ii)
(i)=(ii)
x+26=2x+18

Sufficient
Ans - B
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Re: The table above shows the number of students in a certain high school [#permalink]
Bunuel wrote:

The table above shows the number of students in a certain high school class who are boys and the number of students in the class who are studying biology. What is the total number of students in the class?

(1) Of the boys in the class, 15 are studying biology.
(2) The number of girls in the class is twice the number of students in the class who are NOT studying biology.

Kudos for a correct solution.

(1) Insufficient. Still cannot arrive at any information regarding the girls.

(2) Sufficient:
Students who dont study Biology = x
Number of girls = 2x

From the table,

Bio + No Bio = 26 + x = Total no of students

Likewise,

Boys + Girls = 18 + 2x = Total no of students

Solving for x, we get x = 8

Therefore, total (from either of the two) = 26 + 8 = 34

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Re: The table above shows the number of students in a certain high school [#permalink]
Bunuel wrote:

The table above shows the number of students in a certain high school class who are boys and the number of students in the class who are studying biology. What is the total number of students in the class?

(1) Of the boys in the class, 15 are studying biology.
(2) The number of girls in the class is twice the number of students in the class who are NOT studying biology.

Kudos for a correct solution.

Attachment:
2015-10-26_2106.png

A does not give an answer since total # of girls not studying biology is unknown.

B is sufficient.
let total students be y. and those who don't study biology be x, making total girls as 2x.
=> 26 + x = y
and 18 + 2x = y
=> x = 8 and y = 34.
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Re: The table above shows the number of students in a certain high school [#permalink]
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

The table above shows the number of students in a certain high school class who are boys and the number of students in the class who are studying biology. What is the total number of students in the class?

(1) Of the boys in the class, 15 are studying biology.
(2) The number of girls in the class is twice the number of students in the class who are NOT studying biology.

When you modify the original condition and the question, it is frequently given in the Gmat Math test, which is “2 by 2” question like the table below.
Attachment:

GCDS Bunuel The table above shows the number of students (20160106).jpg [ 40.42 KiB | Viewed 30536 times ]

In the table, there are 4 variables(a,b,c,d) and 2 equations(a+c=26, a+b=18), which should match with the number of equations. So you need 2 more equations, which is likely to make C the answer.
When 1) & 2), a=15 and c=11, b=3 is derived from c+d=2(b+d). Also, d=5 is derived from 11+d=2(3+d)=6+2d, which is unique and sufficient. Therefore, the answer is C. However, since this is integer question which is one of the key questions, apply the mistake type 4(A).
For 1), even if you know that a=15, you don’t know d, which is not sufficient. For 2), c+d=2b+2d and (a+c)-(a+b)=b+d, which is 26-18=b+d=8 is derived from c-b=b+d. So, the answer from a+b+c+d=a+c+b+d=26+8=34 is unique and sufficient. Therefore, the answer is not C but B. You need to get this type of questions correct to reach the score range 50-51.

 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: The table above shows the number of students in a certain high school [#permalink]
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Bunuel wrote:

The table above shows the number of students in a certain high school class who are boys and the number of students in the class who are studying biology. What is the total number of students in the class?

(1) Of the boys in the class, 15 are studying biology.
(2) The number of girls in the class is twice the number of students in the class who are NOT studying biology.

Kudos for a correct solution.

Attachment:
2015-10-26_2106.png

ASIDE: Since the diagram closely resembles a Double Matrix Method diagram, I'll treat it as such.

Target question: What is the total number of students in the class?

Statement 1: Of the boys in the class, 15 are studying biology.
Add this information to our diagram to get:

Since the top row must add to 18, we know that the top-right box must have 3 students.
Also, since the left-hand column must add to 26, we know that the bottom-left box must have 11 students.
Add this information to the diagram to get:

At this point, we still don't have a value for the bottom-right box, which means that are many possible scenarios. Here are two possible scenarios:

In the left-side diagram, there is a total of 49 students
In the right-side diagram, there is a total of 129 students

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The number of girls in the class is twice the number of students in the class who are NOT studying biology.
We can add this information to our diagram as follows:

KEY CONCEPT #1: the sum of the rows must equal the sum of the columns.
So, we can write: 18 + 2x = 26 + x
Solve to get: x = 8

KEY CONCEPT #2: the total number of students = the sum of the two rows
So, the total number of students = 26 + 8 = 34
The answer to the target question is there are 34 students in the class
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
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Re: The table above shows the number of students in a certain high school [#permalink]
The table above shows the number of students in a certain high school class who are boys and the number of students in the class who are studying biology. What is the total number of students in the class?

(1) Of the boys in the class, 15 are studying biology.
(2) The number of girls in the class is twice the number of students in the class who are NOT studying biology.

Statement 1 - 15 bio boys. so 3 non-bio boys. and 9 bio girls. we dont know total girls because we dont know no. of girls not in bio. NOT sufficient
statement II -

Let number of girls be G.

so. G=2*not bio

based on matrix.

18+2*not bio=total - (a)
and
bio+not bio=total
26+not bio=total - (b)

from (a) and (b) we can solve for total.

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Re: The table above shows the number of students in a certain high school [#permalink]
Bunuel wrote:

The table above shows the number of students in a certain high school class who are boys and the number of students in the class who are studying biology. What is the total number of students in the class?

(1) Of the boys in the class, 15 are studying biology.
(2) The number of girls in the class is twice the number of students in the class who are NOT studying biology.

Kudos for a correct solution.

Attachment:
2015-10-26_2106.png

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