The table lists the women enrolled as a percent of the total enrollmen

Question

The table lists the women enrolled as a percent of the total enrollment for each of the 3 universities—University X, University Y, and University Z—in Province A for the fall term of several consecutive years. For the fall term of each of these years, the table also lists the women enrolled at the 3 universities combined as a percent of the total combined enrollment at the 3 universities.

Women Enrolled, as a Percent of Total Enrollment

Fall  
  University X  
  University Y  
  University Z  
  Province A  
 
  2000 
 52.8 
 44.2 
 58.5 
 50.6 
 
  2001 
 53.1 
 44.1 
 58.9 
 50.7 
 
  2002 
 53.6 
 44 
 55.8 
 50.8 
 
  2003 
 53.3 
 43.6 
 58.6 
 50.5 
 
  2004 
 53 
 43.9 
 58.1 
 50.5 
 
  2005 
 52.5 
 43.7 
 58.3 
 50.2 
 
  2006 
 52.2 
 43.8 
 58.1 
 50.1 
 
  2007 
 52 
 43.2 
 57.8 
 49.7 
 
  2008 
 51.4 
 43.8 
 58.3 
 49.7

For each of the following statements, select  T  if the statement is true based on the information provided; otherwise, select  F .

AndrewN · Accepted Answer

It is important in IR table reading questions to make sure you know exactly what information you are given, as well as what, exactly, the question is asking. The following is my take on each part of this question, which asks us to make an assessment  based on the information provided .

This is a trap designed for the test-taker who looks down the University Y column and notices that the numbers are lower than those on either side for any given year. The problem is, the table provides information on the  percent  of women within the total enrollment at a school, not the  number  of women enrolled. With a little knowledge of weighted averages, we can tell, without actually crunching the numbers, that the number of women at University Y in Fall 2000 must have been  greater  than the number of women at at least one of the two other schools, since the Province A average, 50.6,  must  be brought down by a number below, well, 50.6, and the percentage of women at both universities X and Z is above that number. Alternatively, you could set the number of  students  at all three universities equal to each other and derive the number of female students, just to see how the percentages would work out. For instance, say that each university enrolled 1000 students.

University X: 0.528 * 1000 = 528 female students

University Y: 0.442 * 1000 = 442 female students

University Z: 0.585 * 1000 = 585 female students

Total: 3000 students, 1555 female students

Deduction: Since 1555 is greater than 50.6 percent of 3000—50 percent is 1500, and even 1 percent more (of 3000) is 30, so 51 percent is 1530—there must be more female students at University Y than the 1000 we have accounted for.

Conclusion: The statement  cannot  be true based on the information provided, so it is  FALSE .

Again, this is a trap designed for a rookie test-taker who does not consider the difference between a percent and an actual number of something. We cannot make any such year-to-year comparison without a number attached to the total student enrollment (or some part therein, such as the  number  of female or male students at a given university) for both years in discussion.

Conclusion: The statement  cannot  be true based on the information provided, so it is  FALSE .

Unlike in the previous two statements, the keywords in this one match up with those of the table. That is, we  can  make a percent-to-percent comparison from one year to another. Any of the following yearly intervals would suffice:

University X—2002-2003, 2003-2004, 2004-2005, 2005-2006, 2006-2007, 2007-2008 (the  percent  decreased each year from 2002 to 2008)

University Y—2000-2001, 2001-2002, 2002-2003, 2004-2005, 2006-2007

University Z—2001-2002, 2003-2004, 2005-2006, 2006-2007

Notice that the statement does  not  specify that the decrease must have occurred within the same time period, even if that happens once (2006-2007). In any case, this is probably a statement that we could justify with nothing more than a glance.

Conclusion: The statement  must  be true based on the information provided, so it is  TRUE .

I hope that helps. Good luck with your studies.

- Andrew

KarishmaB · Answer

It is important to understand what exactly the table gives you. It gives women enrolled as a percent of the total enrollment for each of the 3 universities. So if University X had 1000 students enrolled in 2000, 528 were women. If in the same year, university Y had 2000 students enrolled, then 884 of them were women. 
This is all the info we get from the table. No info about the actual number of students enrolled and women enrolled.

Of the 3 universities, University Y had the smallest total fall enrollment in each of the years 2000 through 2008.

We have no idea about total fall enrollement of any university in any year. Answer F

In 2008, fewer women were enrolled in college in Province A than in 2000.

Since we don't know anything about number of enrollments (only percentage of women in them), so answer here is also F.

Each of the 3 universities experienced at least one decline from one fall to the next in the number of women enrolled as a percent of the total enrollment.

We are looking at decline in "the number of women enrolled as a percent of the total enrollment." This information we have.
For university X, the percentage declined from 53.6 to 53.3 from 2002 to 2003. 
For university Y, the percentage declined from 44.2 to 44.1 from 2000 to 2001.
For university Z, the percentage declined from 58.9 to 55.8 from 2001 to 2002. 
Answer T

mpobisetty · Answer

Thanks  KarishmaB .  AndrewN's  response above indicates something about "weighted average".

So, is there any knowledge of "weighted average" required in this question?

KarishmaB · Answer

The column of Province A is the weighted average of the other three columns (where weights are the number of people enrolled in each univ in that year.) 
We do not need to use the concept of weighted averages to solve this question but another question based on this table could involve the concept.
Weighted averages is a useful tool for your IR type DI questions.

AndrewN  's analysis is perfectly good, as usual. We need to ensure that the column of  Province A is possible even when the enrollments in University Y are more than others. You can assume that university X has a minute number of people (so that its weight is negligible) and the other 2 balance out to get Province A figures and hence you can ignore weighted averages here. 
But in a question with say 2 universities, you will be able to find out which univ has more enrollments and which has less each year based on column of Province A (which will give weighted average of those 2 univs only).

mpobisetty · Answer

Can you explan this a bit more  KarishmaB . For instance, the total enrollment may have changed from 2002 to 2003. So, how can we concluded something about the "number of women" based on the percentage?

chetan2u · Answer

We are looking at percent of women and not number of women.

Each of the 3 universities experienced at least one decline from one fall to the next  in the number of women enrolled as a  percent  of the total enrollment.

KarishmaB · Answer

What data does the table give us? "Women Enrolled, as a Percent of Total Enrollment " in 2001, in University X, of the total enrollment, 52.8% were women. Now read the question once again: Each of the 3 universities experienced at least one decline from one fall to the next in the number of women enrolled as a percent of the total enrollment . They are looking for decline in this same quantity. So all you have to see is whether the entries reduce from one year to the next at some time for each univ. Check out this video on Table Analysis: https://youtu.be/41uPmg6ipos

Confusion · Answer

In 2008, fewer women were enrolled in college in Province A than in 2000.

I understood this - typing so that anyone else does not faces similar issue.

📘 Example:
Imagine:
 
 In 2000, total enrollment = 10,000 → 50.6% women →  5,060 women  
 In 2008, total enrollment = 12,000 → 49.7% women →  5,964 women   
Even though the  percentage went down , the  actual number of women increased !

So, it will be False.

Globethrotter · Answer

AndrewN  I think I understood your explanation. But, what I don't understand is if we cannot say something is true does it make the statement false automatically? If it also cannot be asserted as false always, the answer should be "can't say" instead of false, right?

cheshire · Answer

Most of the time this type of question will use "can be concluded" or "cannot be concluded" as the answer choices. Here, they use true and false. Both usually end up confusing people one way or the other but as a general rule for these questions: if there is sufficient data and the statement is true then it's "true;" if there is not enough data or there is enough data to prove the statement false it's "false."

NITISHMISHRA · Answer

Hi Brunel,

Can you please explain this solution, as i have a doubt that since Number of enrollments not mentioned and can increase or decrease in subsequent years.

So won't it be like.......answer would vary on our assumption of the Actual Numbers of enrollment.

Pls explain the concept of this question.

Thanks

Bunuel · Answer

I won’t go into solving the question step by step, since a couple of very good solutions are already given above. Instead, let me explain what the question is really testing and how to interpret the statements.

We are given a table that shows only  percentages . Then the question says:  for each statement, select T if the statement is true based on the information provided, otherwise select F . The key point is that we can select T only if we can verify with certainty that the statement is absolutely true. If we cannot verify it as true, we must select F. But notice that selecting F does not always mean the statement must be false, it can also mean that we simply don’t have enough information to confirm it.

Now, looking at the statements:

First statement : This one can actually be shown false. Just look at the year 2000. The province-wide percentage is lower than the percentages for both University X and University Z. That would be impossible if University Y had the smallest total enrollment, because in that case, the province average would have been pulled upward, not downward. So this statement is false. 
  Second statement : This one says that in 2008, fewer women were enrolled in Province A than in 2000. The  percentage  in 2008 is indeed lower than in 2000. But that does not guarantee that the absolute number of women was smaller, since the total enrollment could have changed. For example, if in 2008 the total enrollment was 10,000, the number of women would be 4,970. If in 2000 the total enrollment was only 1,000, the number of women would be 506. So it is possible that more women were enrolled in 2008 despite the smaller percentage. Therefore, we cannot confirm the statement as true. But note that this is not the same as proving the statement is false, it’s just that we cannot with 100% certainty say that it’s true. So we select F, meaning false in this case.

Third statement : This one is straightforward. Each university experienced at least one year-to-year decline in women’s  percentage , and that is visible directly in the table. Since it is about percentages (not absolute numbers), we can verify it directly. So this statement is true.

Final results:  F, F, T.

MANASH94 · Answer

I really liked how Andrew and the other experts explained this...
However I solved this is :

If we read carefully the statements: 
 Statement 1:  Of the 3 universities, University Y had the smallest total fall enrollment in each of the years 2000 through 2008. 
 Trap to be considered : The statement  asks about Total Enrolment  and not only Women's enrolment and  table mentions only Women percentages .
=> Since only percentages are mentioned per Fall, we cannot actually conclude on the actual numbers.  Hence False.

Statement 2:  In 2008, fewer women were enrolled in college in Province A than in 2000.
 Trap to be considered : The statement  asks about no. of women enrolled not the percentage. 
=> Since only percentages are mentioned per Fall, we cannot actually conclude on the actual numbers.  Hence False. 
 
  Statement 3:  Each of the 3 universities experienced at least one decline from one fall to the next in the number of women enrolled as a percent of the total enrollment. 
=> Just by checking the table's percentages in increasing order per University we can find that every university has at-least one decline and 1 increase. Hence it is  TRUE.

The table lists the women enrolled as a percent of the total enrollmen

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

Fall	University X	University Y	University Z	Province A
2000	52.8	44.2	58.5	50.6
2001	53.1	44.1	58.9	50.7
2002	53.6	44	55.8	50.8
2003	53.3	43.6	58.6	50.5
2004	53	43.9	58.1	50.5
2005	52.5	43.7	58.3	50.2
2006	52.2	43.8	58.1	50.1
2007	52	43.2	57.8	49.7
2008	51.4	43.8	58.3	49.7

GMAT Graphs and Tables (G&T) Questions

The table lists the women enrolled as a percent of the total enrollmen

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia