For each of four symptoms, the graph shows the percentage chances that

Question

https://s3.amazonaws.com/wmx-api-production/courses/50731/images/GID2558.gif

For each of four symptoms, the graph shows the percentage chances that someone will have that symptom on each day of the 2 weeks after first developing a cold. The lines for certain symptoms do not continue past a certain day because the chance that someone will have those symptoms beyond that day is less than 1%.

Select the options from the drop-down menus that create the statement that is most strongly supported by the information provided.

It can be determined from the graph that the probability is greater than 0.98 that someone with a cold will have  GRAPH_1_PLACEHOLDER  of the four symptoms on day  GRAPH_2_PLACEHOLDER .

ID: 700216

manasp35 · Accepted Answer

Total probability = P(no symp) + P (exactly 1) + P (exactly 2) + P(exactly 3) + P (exactly 4)

We need to find probability that is greater than 0.98 , meaning almost 1. This implies that almost covers all the cases.

Acc. to options, we have Day 2 , Day 6 , Day 10

For Day 2 and Day 6, 
Total probability = P(no symp) + P (exactly 1) + P (exactly 2) + P(exactly 3) + P (exactly 4)

Options given: one or fewer, one or more, two or fewer, exactly two

None of the options cover all the cases.

For Day 10,
Total probability = P(no symp) + P (exactly 1) + P (exactly 2)

In this case, two or fewer cover all the cases.

answer: two or fewer, Day 10

KarishmaB · Answer

We need higher than 98% probability of something. That is as good as certainty, including certainty.

What am I almost certain about? Am I certain that on Day 2, a person will have at least 1 symptom? No. On Day 2, there is 62% probability of nasal drainage, 49% of sore throat, 38% of cough and 16% of fever. What if all other probabilities lie within the circle of nasal drainage? That is the same 62% people see other symptoms also? Then the probability of a person showing at least one symptom will be 62% only.

But what I am certain about is that at Day 10, a person can show at most 2 symptoms. For the other 2 symptoms, the probability is less than 1%. Even if I assume it to be almost 1% and different set of people show the third and fourth symptoms, still there is a more than 98% probability that a person shows 2 or fewer symptoms on Day 10.

ANSWER: two or fewer symptoms on Day 10

ashutosh_73 · Answer

KarishmaB   chetan2u   Bunuel

For Day-2:
Nasal drainage = 60%
Sore throat = almost 50%
Cough = 38%
Fever = 15 %

If i have to calculate ''one or fewer'' for Day-2, how do i do it? Is the below process correct?

One of fewer =  
 Only TWO:  ((0.6 x .50) + (0.60 x 38) +(0.60 x 0.15) + (0.50 x 0.38) + (0.50 x 0.15) +(0.38 x 0.15))
 Only THREE:  Likewise taken 3 at a time
 Only Four:  (0.60 x 0.50 x 0.38 x 0.15)

Moreover, how would you attempt this question?

manasp35 · Answer

Only TWO equation is not correct. 
(( 0.6 x .50 ) + (0.60 x 38) +(0.60 x 0.15) + (0.50 x 0.38) + (0.50 x 0.15) +(0.38 x 0.15))
While writing 0.6. x .50,
If I am right, you are considering cases when there is ONLY nasal & sore throat. Instead of 0.6 x 0.5 , it should be 0.6 x .5 x .62 x .85 
 ONLY nasal & sore throat = (have nasal) x (have sore throat) x (DON'T HAVE cough) X (DON'T HAVE fever)

Meanwhile I will not approach this question this way as it would be too much calculation. I have given solution above with id "manasp35". Let me know if you have any doubts.

ruis · Answer

Official answer: 
On Day 9, the lines for fever and sore throat stop. This means that, for each of these symptoms, there is less than a 1% chance that someone with a cold will have the symptom beyond Day 9. Therefore, on Day 10, the chance, p, that someone with a cold will have at least one of these symptoms is less than 2%, and they will have at most two (that is, two or fewer of the remaining symptoms). Also, from p < 0.02, it follows that 1 − p > 0.98. Thus, the probability is greater than 0.98 that someone with a cold will have two or fewer of the four symptoms on Day 10.

Freddy12 · Answer

KarishmaB  can you explain why "Only Two symptoms" is incorrect for Day 10?

KarishmaB · Answer

On Day 10, there is about 20% chance of nasal drainage and about 30% chance of cough. So a person would have at most 2 symptoms. He can have 1 or 0 symptoms too. Hence 'Exactly two' is not correct. After all, there is only 20% chance of nasal drainage and only 30% chance of having cough on day10.

zoezhuyan · Answer

dear  KarishmaB , @ chetan2u

I am afraid I did get what the graph says.

say on day 10, the chance of getting sore throat is 21%, that of getting cough is 29% 
 IMO , the chance of getting either sore throat or cough or both is most 29%

ANSWER: two or fewer symptoms on Day 10,  which confused me a lot

would you experts explain further ?

have a nice day

KarishmaB · Answer

On Day 10

chance of getting -

nasal drainage is 21%
cough is 29%
sore throat is about 0% (less than 1)
fever is about 0% (less than 1)

What is the probability of getting 3 or more of the given symptoms? Since chance of both sore throat and fever is about 0, chance of getting 3 or all 4 symptoms is about 0. 
This means that chance of getting 2 or 1 or 0 symptoms is almost 100% i.e. more than 98%. So almost certainly one would have either 0 or 1 or at most 2 symptoms. The chance of a third symptom is almost 0 so having 3 or more symptoms will be very rare.

Hence the answer is chance of "2 or fewer" is more than 98%.

SmileAndSolve · Answer

Required: Probability for someone WITH cold >= 0.98
element = Number of symptoms.
Hence, Probability ("Num of symptoms" being two or less) on day 10 = almost 100%.
 Don't get confused by extra data. It is NOT probability of cold BUT probability of number of symptoms.

UDEMYtutorJackson · Answer

This would be true only if we know that the symptoms occuring are independent events which is not given in the question.

So we may not be able to calculate ONLY TWO , ONLY THREE, ONLY FOUR for this question with the information provided. We can try to find the maximum probability of exactly 2 events occuring but for that this question will become a Linear Programming Problem ( which is not required / out of scope I would say )

BEST WAY TO SOLVE - If we think about the probabilities as venn diagrams , then we can side step thinking about wheather the events are dependent or independent. We just need to think about minimising overlaps and maximising overlaps , and in this way we can get ranges for any probability and eliminate wrong options / indetify the correct option.

agrasan · Answer

Thanks  KarishmaB

Is it  "Two or Fewer"  because   sore throat   can be a part of   cough  ?

cheshire · Answer

It's because after day 10 those are the only two symptoms remaining on the graph. The fact that they usually correspond with each other is outside the scope of the question.

egmat · Answer

I can see why this graph interpretation question might be tricky - you need to connect the probability concept with what the graph is actually showing you. Let me walk you through this step-by-step.

Understanding What We're Looking For

The question asks us to find when the probability is greater than 0.98 (or 98%) that someone with a cold will have a certain number of symptoms. Let's think about what this means: we need to be  almost certain  about how many symptoms a person has.

Key Insight from the Graph

Notice how the problem tells us something crucial: "lines for certain symptoms do not continue past a certain day because the chance that someone will have those symptoms beyond that day is  less than 1% ." This is your golden clue!

When a line disappears from the graph, it means that symptom has become extremely rare (less than 1% chance).

Step-by-Step Solution

Step 1:  Let's track what happens to each symptom by looking at the graph:
- Fever (squares): disappears around day 6-7
- Sore throat (hollow squares): disappears around day 8-9
- Nasal drainage (circles): continues through day 14
- Cough (dots): continues through day 14

Step 2:  Now, check day 10 specifically:
- Nasal drainage: still present (around 22%)
- Cough: still present (around 29%)
- Sore throat: gone (below 1%)
- Fever: gone (below 1%)

Step 3:  Here's the key reasoning:
On day 10, since sore throat and fever have probabilities less than 1%, the chance someone has either of these is practically zero. That means the  maximum  number of symptoms someone can realistically have is 2 (just nasal drainage and/or cough).

The probability of having more than 2 symptoms is less than 2% (since that would require having a symptom with less than 1% chance). Therefore, the probability of having  "two or fewer"  symptoms is greater than 98% (or 0.98).

Answer:  Two or fewer symptoms on day 10

Notice how we didn't need "exactly two" because someone might have just one symptom or even zero symptoms. And "one or fewer" would be too restrictive since having two symptoms is still quite possible.

---

You can check out the  step-by-step solution on Neuron by e-GMAT  to master the systematic approach for interpreting probability graphs and learn the framework that applies to all similar data interpretation questions. You can also explore other GMAT official questions with detailed solutions on Neuron for structured practice  here .

MarkGMATMentor · Answer

Data Insights problems like this, where  the two sub-questions are closely linked and you must use the answer choices to solve , are potentially confusing and can suck up a lot of time.  They can be solved efficiently by matching the data to the question and picking the easier blank before trying the choices.

Match the Data: 
The question asks about a probability higher than 98% -- a very high probability. How does this match with the data? Nothing in the graph is even over 70%.

But remember, a greater than 98% probability of something happening is the same as a less than 2% probability of something NOT happening. And that is very close to both sore throat and fever after day 9, since we’re told that after the lines stop the chance is less than 1%. You have a match.

Pick the Easier Blank: 
With that data match in mind, take a look at the answer choices. What you DON’T want to do is start trying random combinations of choices – with 4 possibilities for the first blank and 3 possibilities for the second blank, you’d have 12 possible combinations to try.

Instead, pick the easier blank to start with. Here, the second blank is easier. Not only does it have fewer answer choices, but it also will allow you to analyze each scenario (day 2, day 6, and day 10) one at a time if needed.

Try the Choices: 
You’ve already deduced that the data matches the question most closely after day 9, so day 10 is the logical one to try first. On day 10, two of the symptoms (sore throat and fever) have virtually disappeared from the graph, while two others (nasal drainage and cough) have a reasonable chance of showing as symptoms.

But they are both in the 20 – 30% range, so they don’t  have to be  symptoms either. Someone on day 10 could have no symptoms, one symptom, or two symptoms, but they’re highly unlikely to have three or more symptoms. Thus, “two or fewer” is correct for the second blank. You don't even need to try the other choices.

By solving smartly, this potentially overwhelming problem becomes very manageable. On all Data Insights problems (other than Data Sufficiency),  first match the data to the question. And on a two-blank DI problem where you must use the answer choices together to solve, start with the easier blank, using any deductions you've made to narrow down your choices.

Note that this pattern can be found in both Graphics Interpretation and Two Part Analysis questions.

MrMaxMan · Answer

"Greater than .98" is almost 100% sure.
At a glance, without any math we can be sure that the probability at day 10 of having 2 or fewer is very high since 2 of our symptoms dropped off to 0%.
If you're in a rush you can be fairly sure this is right.
If you want to do the math you can but, trying to calculate over 98% for the next likely spot which would be having 2 or more on day 2 is possible but less likely than the day 10 option.

For each of four symptoms, the graph shows the percentage chances that

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

My Rewards

GMAT Graphs and Tables (G&T) Questions

For each of four symptoms, the graph shows the percentage chances that

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

My Rewards