2D tables

[maihuna]

In a class of 30 students, 17 students study Chinese, and r students study Japanese. Every student studies either Chinese, Japanese, or both. How many students study both Chinese and Japanese?

(1) r = 14
(2) Thirteen students take only Japanese.


Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT SUFFICIENT

[logitech]

(1) r = 14

30 = 17+r - BOTH

SUF

(2) Thirteen students take only Japanese.

17 CH
13 J-only

Insuf

A

[moadhia]

I agree with explanation above... A it is

[Stuart@KaplanGMAT]

In a class of 30 students, 17 students study Chinese, and r students study Japanese. Every student studies either Chinese, Japanese, or both. How many students study both Chinese and Japanese?

(1) r = 14
(2) Thirteen students take only Japanese.

It can be very helpful to know the overlapping sets formula:

True # of objects = (total # in group 1) + (total # in group 2) + (# in neither group) - (# in both groups)

or, simplifed:

True # = group 1 + group 2 + neither - both

From the original, we know that:

30 = 17 + r - both

(Since everyone studies at least one language, "neither" = 0.)

(1) gives us the value for r, so we can certainly solve for both: sufficient.

(2) tells us how many people study ONLY Japanese, which isn't one of the variables in our equation, so offers no help in solving: insufficient.

[coffee5251]

It can be very helpful to know the overlapping sets formula:

True # of objects = (total # in group 1) + (total # in group 2) + (# in neither group) - (# in both groups)

or, simplifed:

True # = group 1 + group 2 + neither - both

From the original, we know that:

30 = 17 + r - both

(Since everyone studies at least one language, "neither" = 0.)

(1) gives us the value for r, so we can certainly solve for both: sufficient.

(2) tells us how many people study ONLY Japanese, which isn't one of the variables in our equation, so offers no help in solving: insufficient.

Can this also be solved using a double set matrix? I tried to set it up as "Chinese --not Chinese -- Total" for the columns going across and "Japanese -- not Japanese -- Total" for the rows going down on the left. But then I got stuck because it says everyone studies one or the other both so I didn't know what I should/could fill in for the "not chinese" and "not japanese" boxes. ?? Maybe my approach is completely wrong on this. Help...

[cramya]

Can this also be solved using a double set matrix? I tried to set it up as "Chinese --not Chinese -- Total" for the columns going across and "Japanese -- not Japanese -- Total" for the rows going down on the left. But then I got stuck because it says everyone studies one or the other both so I didn't know what I should/could fill in for the "not chinese" and "not japanese" boxes. ?? Maybe my approach is completely wrong on this. Help...

Hi Coffee,

Ur approach is correct. Double matrix approach can help in a problems related to sets with confusing terminology. Its easy to drwaw a table and visualaize the info guven. Knowing the formula will also come in handy. You would always want to have different methods to solve problems as we dont know which one will come to our rescue on test day. Just a friendly suggestion!


Coming to the actual problem:

On the intersection of Not Chinese and Not Japanese u would put a 0.

Try it and u can solve with a double matrix using stmt I. U will get a 1 as the answer (same as using the formula Stuart mentioned above)
This may have been the missing link with this method.

Hope this helps and hit us back with any question if u do hv.

Regards,
Cramya

[Bidisha800]

x people study both.

17 people study Chinese
Therefore, 17-x studies ONLY Chinese

r people study Japanese
r-x study Japanese.

(17-x)+x+(r-x) =30
17 + (r-x) =30
(r-x) =13

From (A) x=1 SUFF

From (B) we get r-x =13
which we already know. So (B) doesn't provide any new info.