The graph shows data for physicians who, in 2000 and 2008, were survey

Question

https://gmatclub.com/forum/download/file.php?id=81592 The graph shows data for physicians who, in 2000 and 2008, were surveyed about the average number of times per month they used each of 3 methods (telephone, email, and video conferencing) to communicate with their patients. The bars represent the percentage of the respondents who reported using the indicated method the indicated number of times per month. Select from each drop-down menu the option that completes the statement so that it most accurately reflects the information provided. It must be the case that the median number of times per month respondents reported having communicated with patients by GRAPH_1_PLACEHOLDER in the 2008 survey was less than that in the 2000 survey. It must be the case that the percentage of respondents who reported having communicated with patients by both GRAPH_2_PLACEHOLDER was as great or greater in the 2008 survey as it was in the 2000 survey. GMAT-Club-Forum-xbpkwaue.png 700210

KarishmaB · Accepted Answer

The tricky part of this question is the data given to us. Once we understand it, the questions are fairly simple. Say 10 physicians were surveyed. 2000 survey would look something like this Question: How many times in a month did you communicate with patients using telephone? Response of the 10 physicians: 0, 0, 1, 1, 2 , 4, 4, 5, 7, 9 20% people said 0, 20% said 1, 30% said more than 1 but less than or equal to 4 and 30% said more than 4. Same was repeated for email, video and then again in 2008 too. It must be the case that the median number of times per month respondents reported having communicated with patients by _____ in the 2008 survey was less than that in the 2000 survey. For which of telephone/email/video was the median for 2008 less than the median for 2000? The median for telephone in 2000 is 2 or 3 or 4. Black region is where 50% is. The median for telephone in 2008 is 1. The 50% corresponds to the yellow region. Hence the median is lower for telephone (ANSWER) . For both email and video, median is the same in both years i.e. 0. It must be the case that the percentage of respondents who reported having communicated with patients by both ______ was as great or greater in the 2008 survey as it was in the 2000 survey. So we are looking for the overlap of two sets. We need this overlap to be higher or same in 2008 than in 2000. In 2008, 80% physicians communicated via telephone with their patients. (all regions except white) In 2008, 40% physicians communicated via email with their patients. (all regions except white) Hence there must be an overlap of at least 20% here. 20% physicians must have communicated via both. Think Sets. In 2000, 83% physicians communicated via telephone with their patients. (all regions except white) In 2008, 18% physicians communicated via email with their patients. (all regions except white) Is it even possible that 20% communicated via both? No. At the most only 18% could have communicated via both. Hence answer is telephone and email. ANSWER Maxsparrow Was it hard to arrive at this? Not at all. Notice the graph. The "communication regions" (yellow, black and blue in which the physician communicated at least once with the patients) for email are much higher in 2008 and the overlap is necessitated with telephone only because its communication region is very high. So you can straight away jump to "telephone and email" and evaluate that to know if it is the answer. Check out the discussion on another graph here: https://youtu.be/ilMxPjHNeic GMAT-Club-Forum-plaj4ib6.png

chetan2u · Answer

Solution for statement 2 added:

The statement is
It must be the case that the percentage of respondents who reported having communicated with patients by both A and B was as great or greater in the 2008 survey as it was in the 2000 survey.

We can see that we know the % individually but not combined. So, we have to find a pair whose combined % in 2008 would always be greater than that in 2000. For this, you will have to compare worst case scenario of 2008 with best scenario of 2000.
 Worst scenario:  Minimum overlap between A and B
 Best scenario:  Maximum overlap between A and B

Let us take telephone and email
 Best scenario:  Maximum overlap between the two in 2000. So, take all connected through email were connected through telephone, that is complete overlap. Answer:  entire 19% of email. 
 Worst scenario:  Minimum overlap between the two in 2008. tele - 80% and email - 40%. So, take all connected through email fill up % not connected through tele, so 100-80 or 20% is filled up. But remaining 40-20 or 20% have to overlap with tele. Answer:  20% of email.

Thus, worst in 2008 is better than best in 2000. Hence, 'Telephone and email' is the answer 
 https://www.youtube.com/watch?v=V1mujIqhfX8

chetan2u · Answer

The statement is
It must be the case that the percentage of respondents who reported having communicated with patients by both A and B was as great or greater in the 2008 survey as it was in the 2000 survey.

We can see that we know the % individually but not combined. So, we have to find a pair whose combined % in 2008 would always be greater than that in 2000. For this, you will have to compare worst case scenario of 2008 with best scenario of 2000.
 Worst scenario:  Minimum overlap between A and B
 Best scenario:  Maximum overlap between A and B

Let us take telephone and email
 Best scenario:  Maximum overlap between the two in 2000. So, take all connected through email were connected through telephone, that is complete overlap. Answer:  entire 19% of email. 
 Worst scenario:  Minimum overlap between the two in 2008. tele - 80% and email - 40%. So, take all connected through email fill up % not connected through tele, so 100-80 or 20% is filled up. But remaining 40-20 or 20% have to overlap with tele. Answer:  20% of email.

Thus, worst in 2008 is better than best in 2000. Hence, 'Telephone and email' is the answer

EMPOWERgmatVerbal · Answer

With everything on the GMAT, including DI, the key is to focus to consume the information with fanatical energy, care, and enthusiasm. Get into it. That way you can confidently select the correct options, much faster than other test-takers. Dropdown 1 For the first drop-down, we need to determine which communication method had a lower median number of uses per month in 2008 compared to 2000. Instead of getting bogged down in calculations, let's look for the biggest shifts in the usage distributions. Telephone: Big shift towards higher usage in 2008. Median went up. Video conferencing: Spread out more evenly in 2008. Median went up. Email: Pretty similar in both years. Median didn't change much. So, Telephone is the only method where the median clearly decreased, so that's our answer for drop-down one. Dropdown 2 Now, for the second drop-down, we're looking for the pair of methods where the percentage of respondents using both was definitely at least as high in 2008 as in 2000. The key is to look at the "n = 0" percentages for each method and subtract them from 100% to find out the proportion of respondents who used each method. Telephone + Email: 2000 - Telephone: ~10% didn't use, so ~90% used. Email: ~0% didn't use, so ~100% used. 2008 - Telephone: ~5% didn't use, so ~95% used. Email: ~0% didn't use, so ~100% used. In both years, the vast majority were using both methods (at least ~90% in 2000 and ~95% in 2008). So the percentage using both was definitely at least as high in 2008 as in 2000. Slam dunk! We don't even need to check the other pairs since we only need one definitive answer. Telephone and emai l for the win here. Done. So, our final answers are: Telephone Telephone and email By zeroing in on the most critical info and looking for definitive answers, we can cruise through this question efficiently and confidently. That's the power of empowered, tactical thinking on GMAT Focus! GMAT-Club-Forum-yanawyo9.png

PavanV1 · Answer

I'm looking for much simpler explanation for 2nd question please, really trick to solve it under 2 mints.

EMPOWERgmatVerbal · Answer

Let me boil it down. For the second drop-down, we're looking for the pair of methods where the percentage of respondents using both was definitely at least as high in 2008 as in 2000. The key is to look at the "n = 0" percentages for each method and subtract them from 100% to find out the proportion of respondents who used each method.
Telephone + Email: 2000 - Telephone: ~10% didn't use, so ~90% used. Email: ~0% didn't use, so ~100% used. 2008 - Telephone: ~5% didn't use, so ~95% used. Email: ~0% didn't use, so ~100% used.
In both years, the vast majority were using both methods (at least ~90% in 2000 and ~95% in 2008). So the percentage using both was definitely at least as high in 2008 as in 2000. Slam dunk!
We don't even need to check the other pairs since we only need one definitive answer.
Telephone and email, done.

Iwillget770 · Answer

Hi EMPOWERgmatVerbal

I am not able to understand your explanation. Sorry for asking you to clarify again.

Quote:

The "n = 0" percentages are our secret weapon here. If they're really low for a pair in both years, almost everyone must have been using both methods.

Telephone + Email: 2000 - ~10% and ~0% 2008 - ~5% and ~0% Percentages are super low, so nearly 100% were using both. Definite yes!

For 2000
If we see n= 0
Telephone is ~15% and email is ~80%
or
If we see n>0
in 2000 almost 85% respondents used telephone and almost 20 % respondents used email.

Similary for 2008.
If we see n =0
Telephone is ~20% and email is ~60% i
If we see n>0
in 2008 almost 80% respondents used telephone and almost 40 % respondents used email.

My interpretation of data is not matching with yours.

Please guide.

Regards

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Attachment:

GMAT-Club-Forum-ohzgjryj.png [ 36.52 KiB | Viewed 4774 times ]

EMPOWERgmatVerbal · Answer

No probelm, let's take a closer look: For 2000: n = 0: Telephone is ~10% (not ~15%), Email is ~0% (not ~80%) n > 0: ~90% used Telephone, ~100% used Email For 2008: n = 0: Telephone is ~5% (not ~20%), Email is ~0% (not ~60%) n > 0: ~95% used Telephone, ~100% used Email Focus on the "n = 0" percentages and subtract from 100% to get the usage percentages. The data shows that in both years, nearly all respondents used both Telephone and Email , so the percentage was at least as high in 2008 as in 2000. GMAT-Club-Forum-fvho8qu4.png

mickkronik · Answer

My solution: Telephone, Email and Video Conferencing

Telephone: 
As you see in the pic I put the times per month for every communication type in an ascending order so the median will fall into the 50%.

Email and Video Conferencing: 
Adding the highlighted percentages for 2000 and 2008 for each communication type that n>=1 show that:

2000
E-mail: 10+5+5= 20
Video Conf: 5

2008
E-mail: 20+10+10= 40
Video Conf: 5+5=10

Hence, Email and Video Conferencing is the correct answer.

manasp35 · Answer

Drop down 2 solution : say X, Y are two methods (X & Y ) = physicians communicated with both X and Y methods. We need to find (X & Y) in 2008 greater or equal to (X & Y) 2000 imply min of ((X & Y) in 2008) greater or equal to max of ((X & Y) 2000) ? ------ eq (1) if X & Y is Email & video min of ((X & Y) in 2008) = 0 (it's possible that no one who used email also used video) max of ((X & Y) 2000) = 4% (it's possible that all the ones using video also used email) doesn't satisfy eq (1) if X & Y is Telephone& video min of ((X & Y) in 2008) = 0 (it's possible that no one who used telephone also used video) max of ((X & Y) 2000) = 4% (it's possible that all the ones using video also used telephone) doesn't satisfy eq (1) if X & Y is Email & Telephone min of ((X & Y) in 2008) = 20% (atleast 20% should use both) max of ((X & Y) 2000) = 19% (it's possible that all the ones using email also used telephone) does satisfy eq (1) Ans: Email & Telephone GMAT-Club-Forum-hgj7hy2e.png

manasp35 · Answer

Drop down 2 solution : say X, Y are two methods (X & Y ) = physicians communicated with both X and Y methods. We need to find (X & Y) in 2008 greater or equal to (X & Y) 2000 imply min of ((X & Y) in 2008) greater or equal to max of ((X & Y) 2000) ? ------ eq (1) if X & Y is Email & video min of ((X & Y) in 2008) = 0 (it's possible that no one who used email also used video) max of ((X & Y) 2000) = 4% (it's possible that all the ones using video also used email) doesn't satisfy eq (1) if X & Y is Telephone& video min of ((X & Y) in 2008) = 0 (it's possible that no one who used telephone also used video) max of ((X & Y) 2000) = 4% (it's possible that all the ones using video also used telephone) doesn't satisfy eq (1) if X & Y is Email & Telephone min of ((X & Y) in 2008) = 20% (atleast 20% should use both) max of ((X & Y) 2000) = 19% (it's possible that all the ones using email also used telephone) does satisfy eq (1) Ans: Email & Telephone GMAT-Club-Forum-p1wpsbh7.png

akshay.sachdeva · Answer

chetan2u  Could u please help with explanation of question 2, its tricky to understand

Anonymous · Answer

manasp35 avigutman GMATCoachBen KarishmaB Bunuel could you explain why we want min for the 2008 and max for the 2000 when we want the duet of methods to be more than or equal to the corresponding in 2000 (X,Y of 2008) ≥ (X,Y of 2000)? In general, the whole method please, it seems helpful but I'm missing some point.. Thank you all in advance ! GMAT-Club-Forum-x4fapoa8.png

manasp35 · Answer

Q: It must be the case that the percentage of respondents who reported having communicated with patients by both (X,Y) was as great or greater in the 2008 survey as it was in the 2000 survey.

So it must be the case (X,Y of 2008) ≥ (X,Y of 2000)
Let (X,Y of 2008) = K
(X,Y of 2000) = M

So it must be the case K ≥ M, but we don't know the exact values of K and M

However,
If we can show that the least value of K is still higher than the maximum value of M, the above statement ( K ≥ M ) becomes true for any value of K and M.

thats why I was trying to prove with min and max. Hope this helps.
Please do ask if it doesn't make sense.

Anonymous · Answer

manasp35 I appreciate your help! It does make sense now many kudos!! Could you also explain the whole method, since I thought that we were looking in each pair which color bar has the smallest and greatest % but again I'm missing something...

https://gmatclub.com/forum/download/file.php?id=81980 For instance, in email & video in 2008 the minimum seems to be the blue one which is almost 0% and in 2000 the maximum the yellow one approximately 10%. GMAT-Club-Forum-5t8dpu31.png

manasp35 · Answer

Making a set venn diagram would help. In telephone and email 2008 we are given 80% use telephone, 40% use email Lets find minimum number of people using both telephone and email is it possible that email users use email only and telephone users use telephone only. No, because we have only 100%. 80 + 40 becomes 120. We need adjustment. 20 extra. Meaning there are 20 people who use both. 60 use telephone only, 20 use email only, 20 use both . Now we get 100. It could also have been 50 telephone only, 10 email only, 30 use both, 10 neither. But we need find minimum for both, so min is 20. In email and video 2008 we are given 40% use email, 10% use video But we need to find the minima of people who use both email and video. is it possible that email users use email only and video users use video only. Yes it is possible. Both users are different. Hence minimium number of people using both is 0. GMAT-Club-Forum-7pu9c0xq.png

Anonymous · Answer

Just bear in mind that your explanations are very helpful !!

So, accordingly for  TV & video in 2008  since 80% use TV, 10% video and they add up to less than 100% the  minimum  of people using both is  0% , whereas  in   2000  with TV approximately 80% and video 5% the  maximum is 15%  since it is possible that the category "none of these two" to be zero ? (so it's 100% - 80% - 5% = 15%)

manasp35 · Answer

2000  with Telephone approximately 80% and video 5%
80 people using telephone, 5 people using video
maximum of 5 people can use both. Because it is limited by video users. 
For maximum will be 5%

KarishmaB · Answer

You haven't misunderstood anything. 1% is the minimum overlap in 2000 and 18% is the maximum possible overlap (notice the highlighted part) In 2008, minimum possible overlap is 20% and hence the overlap of 2008 will always be higher. GMAT-Club-Forum-9k3uo2ph.png

The graph shows data for physicians who, in 2000 and 2008, were survey

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The graph shows data for physicians who, in 2000 and 2008, were survey

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