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# If a certain charity collected a total of 360 books, videos

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Re: If a certain charity collected a total of 360 books, videos [#permalink]
we get two equations using two statemnets .so we will be able to get value of v and g right?
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Re: If a certain charity collected a total of 360 books, videos [#permalink]
rohitgoel15
If a certain charity collected a total of 360 books, videos, and board games, how many videos did the charity collect?

(1) The number of books that the charity collected was 40 percent of the total number of books, videos, and board games that the charity collected.

(2) The number of books that charity collected was 66 32 percent of the total number of videos and board games that charity collected.

skamal7
we get two equations using two statemnets .so we will be able to get value of v and g right?

Statement 1 tells us of the 360 books, videos, and board games, 144 were books. (360 b v g * .4 books = 140 books) That leaves 216 videos and board games. Insufficient.

Statement 2 states of that the number of books is 66.32% of the total number of videos and board games, in this case 216 * .6623 = just under 144, but for our purposes 144 books. Insufficient.

1 + 2: 360 = 144 books + 216 videos and board games. We don't have enough information to tell us how many of the 216 remaining items are videos or board games.
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Re: If a certain charity collected a total of 360 books, videos [#permalink]

three equations have been formed-

1. from question stem. B+V+G =360
2. from statement 1. B= 144 NOT SUFF ALONE
3. from statement 2. B= .66( V+G) NOT SUFF ALONE

Now, i just saw 3 equations , and 3 variables. and proceeded that with 3 equations 3 variables can be found and , therefore , chose 'C' as the answer.
Why did it go wrong?

pl help with the explanation.....
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Re: If a certain charity collected a total of 360 books, videos [#permalink]
thanks a lot.....
indeed it is imp to check the three eqns whether they are distinct before deciding on outcome....
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Re: If a certain charity collected a total of 360 books, videos [#permalink]
Bunuel
semwal

three equations have been formed-

1. from question stem. B+V+G =360
2. from statement 1. B= 144 NOT SUFF ALONE
3. from statement 2. B= .66( V+G) NOT SUFF ALONE

Now, i just saw 3 equations , and 3 variables. and proceeded that with 3 equations 3 variables can be found and , therefore , chose 'C' as the answer.
Why did it go wrong?

pl help with the explanation.....

The point is that we don't have 3 distinct equations: the third equation is the same as the second one.

If a certain charity collected a total of 360 books, videos, and board games, how many videos did the charity collect?

Given: B + V + G = 360.

(1) The number of books that the charity collected was 40 percent of the total number of books, videos, and board games that the charity collected --> B = 2/5*360 --> B = 144. Not sufficient.

(2) The number of books that charity collected was 66 2/3 percent of the total number of videos and board games that charity collected --> B = 2/3*(V + G) --> B = 2/3*(360 - B) --> B = 144. Not sufficient.

(1)+(2) We only know that B = 144 and B + V + G = 360 (V + G = 216) --> we cannot solve for V. Not sufficient.

Hope it's clear.

Bunuel How can we avoid falling in such a trap? Since it's a DS Q, one would not usually solve the value for B in stmt 2, and hence would not realize that equations in stmt 1 and stmt 2 are same. We would think that C is the answer since we have 3 equations and 3 unknowns, without realizing that we don't have 3 unique equations. Any suggestions or tricks to avoid this error? Thanks!
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Re: If a certain charity collected a total of 360 books, videos [#permalink]
dabaobao
Bunuel
semwal

three equations have been formed-

1. from question stem. B+V+G =360
2. from statement 1. B= 144 NOT SUFF ALONE
3. from statement 2. B= .66( V+G) NOT SUFF ALONE

Now, i just saw 3 equations , and 3 variables. and proceeded that with 3 equations 3 variables can be found and , therefore , chose 'C' as the answer.
Why did it go wrong?

pl help with the explanation.....

The point is that we don't have 3 distinct equations: the third equation is the same as the second one.

If a certain charity collected a total of 360 books, videos, and board games, how many videos did the charity collect?

Given: B + V + G = 360.

(1) The number of books that the charity collected was 40 percent of the total number of books, videos, and board games that the charity collected --> B = 2/5*360 --> B = 144. Not sufficient.

(2) The number of books that charity collected was 66 2/3 percent of the total number of videos and board games that charity collected --> B = 2/3*(V + G) --> B = 2/3*(360 - B) --> B = 144. Not sufficient.

(1)+(2) We only know that B = 144 and B + V + G = 360 (V + G = 216) --> we cannot solve for V. Not sufficient.

Hope it's clear.

Bunuel How can we avoid falling in such a trap? Since it's a DS Q, one would not usually solve the value for B in stmt 2, and hence would not realize that equations in stmt 1 and stmt 2 are same. We would think that C is the answer since we have 3 equations and 3 unknowns, without realizing that we don't have 3 unique equations. Any suggestions or tricks to avoid this error? Thanks!

VeritasKarishma Bunuel I noticed the same concept/trap being tested in another Q: https://gmatclub.com/forum/if-company-m ... ml?kudos=1

Any suggested short cuts without having to actually solve the value of required variable? I guess making sure to reduce N equations to only 2 distinct equations and 2 unknowns, one being the required unknown, would be enough?

Thanks!

ENGRTOMBA2018
jbburf
This looks straight forward at first. From the question, two equations are introduced and four variables are introduced.

Then (1) and (2) each introduce what appears to be an additional equation so we have four equations and four variables.

At this point I selected answer C without solving assuming that our variable could be solved by rules of solvability with 4 equations. The problem is that the equation that (2) introduces is in fact identical to the information you already have. In essence it is not a new equation and thus you are still left with 4 variables and only 3 equations.

Does anyone have a more succinct way to explain this or identify this pattern in future problems?

The rule is that you need to have n "distinct" equations to solve to "n" variables. This is especially true for DS questions. Do not mark C or E in DS questions without actually loooking at the equations you get either from the question stem and the statements. This is the "pattern" you are talking about.

You get the same equations of $$C_m + P_m = 50$$ from the question stem+2 statements combined.

Thus, be very careful in DS questions when you are given 'n' variables and 'n' equations. These equations must be distinct to give any unique value.

Hope this helps.
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Re: If a certain charity collected a total of 360 books, videos [#permalink]
1
Kudos
You need to ensure not only 2 distinct equations with 2 unknowns but also that the two equations do have a unique solution (they are not parallel lines). Then you don't need to actually solve them.

Multiple equations with multiple variables can be confusing so reducing to two equations will be helpful.
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If a certain charity collected a total of 360 books, videos [#permalink]
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Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 3 variables and 1 Equation: Let the original condition in a DS question contain 3 variables and 1 Equation. Now, 3 variables and 1 Equation would generally require 2 more equations to give us the value of the variables.

We know that each condition would usually give us an equation, and since we need 2 more equations to match the number of variables and equations in the original condition, the equal number of equations and variables should logically lead to answer C.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

Let us give variable to each entity: Books(B) ; Videos(V) and Board Games(C).

We have to find the value of 'V'

=> Given that 'B + V + C = 360'.

Second and the third step of Variable Approach: From the original condition, we have 3 variables (B, V and C) and 1 Equation( B + V + C = 360). To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.

Let’s take a look at both condition together.

Condition(1) tells us that the number of books that the charity collected was 40 percent of the total number of books, videos, and board games that the charity collected.

Condition(2) tells us that the number of books that charity collected was 66 2/3 percent of the total number of videos and board games that charity collected.

=> B = $$\frac{40}{100}$$ * 360 = 144

=> 144 = $$\frac{200 }{ 300}$$ * (V+G)

=> V + G = 144 * $$\frac{3 }{ 2}$$ = 216

But we cannot solve for the unique value of 'V'

Since the answer is not unique, both the conditions combined are not sufficient by CMT 2.

Both conditions (1) and (2) combined are not sufficient.

So, E is the correct answer.

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Re: If a certain charity collected a total of 360 books, videos [#permalink]

Can you please highlight how does 66 2/3 translate into B = 2/3*(V + G) --> B = 2/3*(360 - B) --> B = 144.
I simply understood it as 66 2/3 = (198+2)/3 = 200/3 and so I got B = 200/3 * (360-B) = Some weird fraction.

BR,
Ankita
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Re: If a certain charity collected a total of 360 books, videos [#permalink]
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Ankyta333

Can you please highlight how does 66 2/3 translate into B = 2/3*(V + G) --> B = 2/3*(360 - B) --> B = 144.
I simply understood it as 66 2/3 = (198+2)/3 = 200/3 and so I got B = 200/3 * (360-B) = Some weird fraction.

BR,
Ankita

"The number of books that charity collected was 66 2/3 percent of the total number of videos and board games that charity collected."

Note 66 2/3 percent = 66.67% = 2/3

The formatting is not perfect above and that is what confused you perhaps.

$$66\frac{2}{3}$$% = 66.67%

$$\frac{66.67}{100} = \frac{2}{3}$$

So number of books is 2/3rd of number of videos and games

$$B = \frac{2}{3} (V + G)$$
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Re: If a certain charity collected a total of 360 books, videos [#permalink]
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Re: If a certain charity collected a total of 360 books, videos [#permalink]
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