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Manager  Joined: 07 Nov 2009
Posts: 222
If a certain charity collected a total of 360 books, videos  [#permalink]

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6 00:00

Difficulty:   35% (medium)

Question Stats: 70% (01:46) correct 30% (01:47) wrong based on 249 sessions

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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 2/3 percent of the total number of videos and board games that charity collected.
Math Expert V
Joined: 02 Sep 2009
Posts: 58453
Re: If a certain charity collected a total of 360 books, videos  [#permalink]

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5
1
semwal wrote:
could some instructor please explain:-

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.
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Manager  B
Joined: 13 Mar 2012
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Re: If a certain charity collected a total of 360 books, videos  [#permalink]

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rohitgoel15 wrote:
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 32percent of the total number of videos and board games that charity collected.

360 = b+v+g

1) we have b
but no info for g

INSUFFICIENT

2) b= 0.6 (v+g) (ASSUMING THE BOLD PART TO SOME KNOWN VALUE AS ITS NOT CLEAR)
g is unknown

INSUFFICIENT

1) +2)

No info for g

INSUFFICIENT

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

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we get two equations using two statemnets .so we will be able to get value of v and g right?
Manager  Joined: 22 Apr 2013
Posts: 79
Re: If a certain charity collected a total of 360 books, videos  [#permalink]

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rohitgoel15 wrote:
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 wrote:
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]

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could some instructor please explain:-

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.....
Senior Manager  B
Joined: 04 May 2013
Posts: 268
Location: India
Concentration: Operations, Human Resources
Schools: XLRI GM"18
GPA: 4
WE: Human Resources (Human Resources)
Re: If a certain charity collected a total of 360 books, videos  [#permalink]

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thanks a lot.....
indeed it is imp to check the three eqns whether they are distinct before deciding on outcome....
Director  D
Joined: 24 Oct 2016
Posts: 533
GMAT 1: 670 Q46 V36 GMAT 2: 690 Q47 V38 Re: If a certain charity collected a total of 360 books, videos  [#permalink]

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Bunuel wrote:
semwal wrote:
could some instructor please explain:-

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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Director  D
Joined: 24 Oct 2016
Posts: 533
GMAT 1: 670 Q46 V36 GMAT 2: 690 Q47 V38 Re: If a certain charity collected a total of 360 books, videos  [#permalink]

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dabaobao wrote:
Bunuel wrote:
semwal wrote:
could some instructor please explain:-

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 wrote:
jbburf wrote:
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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Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: If a certain charity collected a total of 360 books, videos  [#permalink]

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1
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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