A movie buff owns movies on DVD and on Blu-ray in a ratio of

Question

A movie buff owns movies on DVD and on Blue ray in a ratio of 7:2. If she buys 6 more Blue ray movies, that ratio would change to 11:4. If she owns movies on no other medium, what was the original number of movies in her library before the extra purchase.

A 22
B 28
C 77
D 99
E 105

P.S : Please help to find algebraic solution to question (how to set up equations)

A. 22 
B. 28 
C. 77 
D. 99 
E. 105

KarishmaB · Accepted Answer

Where possible, use a single variable. It's faster and chances of error are reduced.
Since initial ratio is 7:2, I would say that he has '7a' DVDs and '2a' BluRay Disks where 'a' is any positive integer. After he buys 6 more BluRay disks, the ratio changes to 11:4
So, 7a/(2a + 6) = 11/4
28a = 22a + 66
a = 11

So initially, he had 7a + 2a = 9a = 9*11 = 99 movies

agdimple333 · Answer

\frac{D}{B} =  \frac{7}{2}

\frac{B}{T} =  \frac{2}{9}   --- 1

B1 = B + 6
T1 = T+6

\frac{D1}{B1}  =  \frac{11}{4}

\frac{B1}{T1}  =  \frac{4}{15}

\frac{(B+6)}{(T+6)} =  \frac{4}{15}   --- 2

solving 1 and 2
B = 22
==> T = 99.. Answer

Sudhanshuacharya · Answer

Given

D/B = 7/2 ; D = DVD and B= Blue ray

D = 7B/2

after addition 6 B.
we have D/(B+6) = 11/4
or 7B/  = 11/4

B = 22 so D becomes 77 Total 99.

danielle2708 · Answer

Hey everyone,

thanks alot for your answers. I knew this was actually not a hard question, I guess sometimes you just get stuck and it's great to get some external input.

Best,
Daniela

gladvijay · Answer

7x / (2x + 16) = 11/4, solve for x => x = 11

total disks before was 9x = 99

PareshGmat · Answer

Oh GOD!!! I was doing this problem with 11:14 & not getting the answer. Can someone please rectify it as 11:4

PareshGmat · Answer

One easy method:

The earlier ratio is 7:2
So total components are 9; Luckily there is only one nos in the options which is divisible by 9, so answer = D

Zatmah · Answer

Well , just hint first that a DVD has to be whole number and since the ratio is 7:2 it means that DVD fraction is 7/9 therefore the answer has to be a multiple of 9 and in this case only D fits the bill

sismail · Answer

Thats how I did it too. I always feel like I am cheating if I do things like that though.

Gmatdecoder · Answer

A movie buff owns movies on DVD and on Blue ray in a ratio of 7:2. If she buys 6 more Blue ray movies, that ratio would change to 11:4. If she owns movies on no other medium, what was the original number of movies in her library before the extra purchase.

A 22
B 28
C 77
D 99
E 105

P.S : Please help to find algebraic solution to question (how to set up equations)

A 22
B 28
C 77
D 99
E 105

P.S : Please help to find algebraic solution to question (how to set up equations)

jayanth7290 · Answer

if u can just keep an eye on the options 99 is the only multiple of 9 in options given .. SO you can mark it wid in seconds. Now coming to the process m(D) = 7x and b(D) = 2x now from the next line the new eqn becomes 7x/ (2x + 6) = 11/4 Solving it 28x = 22x + 66 x =11 which means m (d) = 77 and b(d) = 22 SO total initially is m(d) + b(d) = 99 :-D

Gmatdecoder · Answer

Yeah sure... Thanks..

Posted from my mobile device

EMPOWERgmatRichC · Answer

Hi gmatdecoder,

jayanth7290 is correct - since the original ratio is 7:2, the total number of original items MUST be a multiple of 9 (since a multiple of 7 added to the same multiple of 2 will sum to a multiple of 9). In this question, there's only one answer that fits that pattern. The Official GMAT will likely NOT make it that easy for you - usually 2 or 3 of the answers will be a multiple of the ratio that you're dealing with, so you will have to do ratio "math" or TEST THE ANSWERS to get to the solution.

GMAT assassins aren't born, they're made,
Rich

Konstantin1983 · Answer

Hi Gmatdecoder!
Here is algebraic solution
Let D be the number of DVD and B number of Blue-rays. We have that (D/B)=(7/2) (1) . After she buys 6 new Blue-ray disks the new ratio is (D/(B+6))=(11/4) (2). Hence we can write from equation (1) that 2*D=7*B. And from equation (2) we have that 4*D=11*B+66 ==> multiply equation (1) by 2 and plug this into equation (2) ==> we have 14*B=11*B+66 ==> 3*B=66 and B=22. Hence D=(154/2)=77 and B+D=22+77=99. Hope it is clear

PareshGmat · Answer

Answer = D 99

DVD ................ Blue Ray

7x ........................ 2x (Initial quantity; Say "x" is the variable. Total = 9x)

7x ......................... 2x+6 (Adding 6 blue ray, ratio changes to 11:4)

Setting up the equation

\frac{7x}{2x+6} = \frac{11}{4}

\frac{7x}{x+3} = \frac{11}{2}

x = 11; 9x = 99

pacifist85 · Answer

I also used the approach with which you give an initial variable value for the original number of DVD (D) and BlueRays (B):

Let's say that the original number of D is D, and the original number of B is B.
D/B=7/2

When 6 mores B are bought the new ratio becomes D/B= D/B+6 = 11/4.  
When you are here, you see that you need to get rid of one of the unknowns, either D or B.

So,going back to the initial ratio: D/B=7/2 --> 7B=SD--> D=7B/2. Now, you can replace this value for D in the second relationship  .

D/B+6 = 11/4
(7B/2)/B+6 = 11/4
11(B+6)=4(7B/2)
11B + 66 = 28B/2
11B + 66 = 14B
66 = 3B
B=66/3
B= 22.

Now, from the initial ratio: 
D/B=7/2
7/2=D/22
2D=154
D=154/2
D=77.

Finally, adding D + B = 77 + 22 = 99.

ScottTargetTestPrep · Answer

We can let the original number of DVD and Blu-ray she owns be 7x and 2x, respectively. Thus we can create the equation:

7x/(2x + 6) = 11/4

4(7x) = 11(2x + 6)

28x = 22x + 66

6x = 66

x = 11

She originally had 7x + 2x = 9x movies; therefore, she owned 9(11) = 99movies.

Answer: D

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