A student has decided to take GMAT and TOEFL examinations

Question

A student has decided to take GMAT and TOEFL examinations, for which he has allocated a certain number of days for preparation. On any given day, he does not prepare for both GMAT and TOEFL. How many days did he allocate for the preparation?

(1) He did not prepare for GMAT on 10 days and for TOEFL on 12 days.
(2) He prepared for either GMAT or TOEFL on 14 days.

From, raceacademy's training material.

Bunuel · Accepted Answer

A student has decided to take GMAT and TOEFL examinations, for which he has allocated a certain number of days for preparation. On any given day, he does not prepare for both GMAT and TOEFL. How many days did he allocate for the preparation?

It's more Overlapping Sets problem than Statistics, I guess.

We have:  {Total} = {GMAT } + {TOEFL} - {Both} + {Neither} . Since we are told that "on any given day, he does not prepare for both GMAT and TOEFL", then  {Both} = 0 , so  {Total} = {GMAT } + {TOEFL} + {Neither} . We need to find  {Total}

(1) He did not prepare for GMAT on 10 days and for TOEFL on 12 days -->  {Total} - {GMAT } = 10  and  {Total} - {TOEFL} =12 . Not sufficient.
(2) He prepared for either GMAT or TOEFL on 14 days -->  {GMAT } + {TOEFL} = 14 . Not sufficient.

(1)+(2) We have three linear equations ( {Total} - {GMAT } = 10 ,  {Total} - {TOEFL} =12  and  {GMAT } + {TOEFL} = 14 ) with three unknowns ( {Total}, {GMAT }, and {TOEFL} ), so we can solve for all of them. Sufficient.

Answer: C.

Just to illustrate. Solving gives:
 {Total} = 18  - he allocate total of 18 days for the preparation;
 {GMAT } = 8  - he prepared for the GMAT on 8 days;
  {TOEFL} = 6  - he prepared for the TOEFL on 6 days;
  {Neither} = 4  - he prepared for neither of them on 4 days.

Hope it's clear.

For more check  ADVANCED OVERLAPPING SETS PROBLEMS

cyberjadugar · Answer

Hi, Using Venn diagram approach, (my favorite

) let, a = Days on which student prepares for GMAT, b = Days on which student prepares for Toefl, c = Days on which student prepares neither for GMAT nor for TOEFL, Using (1), He did not prepare for GMAT on 10 days and for TOEFL on 12 days a+c=12 b+c=10, two equation, 3 variables. can't solve.Insufficient. Using (2) He prepared for either GMAT or TOEFL on 14 days a+b=14. Insufficient. Combining both (1) & (2), a+c=12 b+c=10 a+b=14, addition all three, 2(a+b+c)=36 a+b+c=18, Sufficient. Thus, Answer is (C) Regards,

damham17 · Answer

1)
NS since we don't know how many days the student did not study at all.
We do know that Total-GMAT= 10 and Total-TOEFL= 12.

2)
NS but we do know there were 14 days spent studying.

Together:
Let Z= Total Days
G= GMAT
T= TOEFL

Z-G = 10
Z-T = 12
T+G = 14
(Sum these up in a system of equations)
2Z= 36 and simplifying to Z = 18.

Arthur1000 · Answer

Is this a badly worded question? - it tells me that how many days of preparation has the student taken, but if he has studied for neither GMAT or TOEFL then this idle day is not a day of preparation and doesnt count.

Therefor the answer is D, both can give us the answer

Therefor the answer is D, both can give us the answer

Sachin9 · Answer

I thought the same too.. 
Could somebody please confirm?

Vaico · Answer

I agree... the wording of this question sucks, it's not clear if the days he did not spend studying should be taken into consideration

Sachin9 · Answer

what makes me worried is that this question appears in the gmatclub math book.

aishwarye · Answer

Can this question come in GMAT ? I doubt because i've never seen such SETs qshn ever. Whats the source pl ?

Sachin9 · Answer

congrats on your first post.

This question will never come in GMAT.. Guaranteed. 
IMHO One that's floating around in internet,never :D

aishwarye · Answer

Thank you for the warm welcome Sachin ! I have baan a part of gmatclub since long.. Now trying to get active.. i think getting active on gmatclub will keep me focussed and help learn more !

Sachin9 · Answer

yupp . . all the best!!

xmizer · Answer

Where are the answer choices?

I can only see that the correct answer is C but I don't see any of the answer choices.

Bunuel · Answer

This is a data sufficiency question.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

The correct answer to this question is C:  BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked .

Hope it helps.

PiyushK · Answer

What is the difference between following two statements:
(2) He prepared for either GMAT or TOEFL on 14 days. // I considered it 14 days GMAT or 14 days TOEFL, not G + T =14.
OR
(2) He prepared for GMAT and TOEFL on 14 days. // this can be interpreted as G + T =14.

himanshujovi · Answer

I am having the same confusion. Bunuel can you please explain how to interpret this ?

Sentence was -  "He prepared for either GMAT or TOEFL on 14 days"

Why can't this be interpreted as G/T = 14 i.e. 14 days could be  either  for G  or  for T

Bunuel · Answer

"He prepared for either GMAT or TOEFL on 14 days" means that out of 14 days some were for GMAT and the rest for TOEFL. It does not mean that either all 14 were for GMAT or all 14 were for TOEFL.

gunna · Answer

I solved it classicly with a 4x4 Matrix since the task has only 2 Sets

sagnik242 · Answer

Dear Bunuel:

Can you please illustrate solving the linear eqns with steps? Thank you.

I know once we get one value we can plug in to others but I am confused how we got the values, starting with 18.

Thanks

Bunuel · Answer

We have:
(i) {Total} - {GMAT } = 10; 
(ii) {Total} - {TOEFL} =12; 
(iii) {GMAT } + {TOEFL} = 14.

Add (ii) and (iii): {Total} - {TOEFL} + {GMAT } + {TOEFL} = 12 + 14 --> {Total} + {GMAT } = 26.

Now, add (i) to that: {Total} + {GMAT } + {Total} - {GMAT } = 26 + 10 --> 2*{Total} = 36 --> {Total} = 18.

Hope it's clear.

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