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

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aoyanf

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13 Jun 2025, 23:30

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I think the key issue of this quesiton is that it does not specify each sympton is independent, which some of the comments missed here.
Therefore, we cannot calculate the probability of, for example, someone who have all the four symptons.

The guy who created this question did not indent to make us calculate, but he should want us to use information of "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%".

Then we can reach the answer without any multiple calculations.

agrasan

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Thanks KarishmaB

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

KarishmaB

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

cheshire

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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.

agrasan

Thanks KarishmaB

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

egmat

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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.

UditA1

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28 Dec 2025, 10:19

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Work from wrong to right (Elimination Strategy) instead of directly finding the right answer. Check all possibilities.

rameezhasalife

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The Late-Night Diner Analogy
Imagine you walk into a diner late at night. There are only four items on the menu: Burgers, Fries, Shakes, and Pie. (These represent our 4 symptoms).

Because it is so late, the kitchen is almost out of food:

Burgers and Fries are completely sold out. There is a 0% chance you can order them. (This is Fever and Sore throat on Day 10).

Shakes and Pie are still available. (This is Nasal drainage and Cough).

Now, imagine we watch a new customer walk through the door. We ask ourselves: "How many items is this customer going to eat?"

We know for an absolute fact that they cannot eat 3 or 4 items, because two of the items are sold out. The maximum number of items they can possibly eat is 2.

But does the fact that there are exactly two items available on the menu guarantee that the customer will order Exactly two items?

No. The customer has a few options:

They might be really hungry and order both the Shake and the Pie (2 items).

They might just want a Shake (1 item).

They might look at the menu, decide they don't want either, and leave (0 items).

Because we don't know exactly how hungry the customer is—we only know what is available on the menu—the only thing we can say with 100% certainty is that they will order Two or fewer items.

Back to the Graph
The exact same logic applies to the cold symptoms on Day 10:

Fever and Sore throat are "sold out." (Less than a 1% chance).

Nasal drainage and Cough are "still available." (Roughly 20% and 30% chances, respectively).

Just because Nasal drainage and Cough are the only two possible symptoms left doesn't mean a patient will get hit with both of them. A patient on Day 10 might have both, they might just have a lingering cough, or they might be completely symptom-free!

Therefore, the number of symptoms they have must be Two or fewer.

MarkGMATMentor

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15 Jun 2026, 20:51

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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.

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24 Jun 2026, 03:27

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Graph Probability Question — Consolidated Learning

Step 1: Read the Question Correctly

Quote:

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

750-Scorer Translation
Replace:

Quote:

Probability > 0.98
with
More than 98% of people
So the stem becomes:
Find a day and symptom count such that more than 98% of people satisfy the statement.

Step 2: Understand "One or Fewer Symptoms"
The four symptoms are:

Nasal drainage
Sore throat
Cough
Fever

One or fewer symptoms means
✅ 0 symptoms
OR
✅ Exactly 1 symptom
Not:
❌ 2 symptoms
❌ 3 symptoms
❌ 4 symptoms
Step 3: Use Complements
A 750 scorer rewrites:

Quote:

Probability(One or fewer symptoms) > 98%
as
Probability(2 or more symptoms) < 2%
because
1 - 0.98 = 0.02
This is often much easier to test.

Step 4: Biggest Trap
Can I add the symptom probabilities?
Suppose Day 14 shows:

Cough = 18%
Nasal drainage = 11%
Many students do:
18% + 11% = 29%
and conclude:
P(0 or 1 symptom) = 71%

Wrong
Why?
The graph only gives:
P(Cough)
P(Nasal)
It does NOT give:
P(Cough ∩ Nasal)
Some people may have both symptoms.
Some may have only one.
Some may have neither.
We don't know.
Step 5: What Information Does the Graph Give?
Only:
P(Fever)
P(Cough)
P(Sore Throat)
P(Nasal Drainage)
It does NOT give:

Exactly 1 symptom
Exactly 2 symptoms
At least 2 symptoms
All 4 symptoms
directly.

Step 6: How 750 Scorers Solve These
They ask:

Quote:

What must happen for the statement to be FALSE?

Example
Suppose option says:

Quote:

Three or fewer symptoms on Day 8

False case
To NOT have three or fewer symptoms,
a person must have:

Quote:

All 4 symptoms

Check graph
Day 8:

Fever < 1%
To have all 4 symptoms,
fever must occur.
Therefore
P(4 symptoms) < 1%
Thus
P(3 or fewer symptoms) > 99%
Since
99% > 98%
the statement is guaranteed.

Step 7: Pattern Recognition
Whenever you see

Quote:

Probability > 98%
Think:
Failure probability < 2%

Whenever you see

Quote:

Three or fewer symptoms
Think:
Failure = all 4 symptoms

Whenever you see

Quote:

Two or fewer symptoms
Think:
Failure = 3 or 4 symptoms

Whenever you see

Quote:

One or fewer symptoms
Think:
Failure = 2, 3, or 4 symptoms

Step 8: Speed Rule
Bad approach
Trying to calculate exact probabilities.
Good approach
Ask:

Quote:

What event makes the statement false?
Then see if that false event has probability under 2%.

Final GMAT Takeaway
Concept
Individual probabilities ≠ joint probabilities.
Never assume independence.
Pattern
For graph probability questions:

Translate 98% into complement (2%).
Identify the failure event.
Use the graph to place an upper bound on that failure event.
If failure < 2%, statement must be true.

750-Scorer Mindset
Don't ask:

Quote:

"What is the exact probability?"
Ask:
"Can I prove the opposite event happens less than 2% of the time?"
That single shift is what makes these difficult graph questions manageable.

UditA1

Work from wrong to right (Elimination Strategy) instead of directly finding the right answer. Check all possibilities.

MrMaxMan

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"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.

parkhydel

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 of the four symptoms on day .

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