Each of 1,455 runners registered to run in an upcoming marathon answer

Question

Each of 1,455 runners registered to run in an upcoming marathon answered "Yes" or "No" to two questions on the registration form: (1) Do you run at least 25 miles per week? and (2) Do you experience joint pain? Of those who answered "Yes" to the first question, 785 answered "Yes" to the second question, and 380 answered "No" to the second question. Of those who answered "No" to the first question, x runners answered "Yes" to the second question, and y runners answered "No" to the second question, where x > y.

Select for x and for y values that are jointly consistent with the given information. Make only two selections, one in each column.

Select for  x  and for  y  values that are jointly consistent with the given information. Make only two selections, one in each column.

Redmaster2 · Answer

Total runners = 1,455

"Yes" to Q1 (25+ miles/week):
 785 said "Yes" to Q2 (joint pain)
 380 said "No" to Q2
→ So total who said "Yes" to Q1 = 785 + 380 = 1,165

Remaining runners = 1,455 − 1,165 = 290
 → These are runners who said "No" to Q1.
 Of these,
 x said "Yes" to Q2
 y said "No" to Q2
 and we’re told: x + y = 290, with x > y

From the answer choices:

x = 290 and y = 0 → valid (x > y, and total = 290)

All other pairs either don’t sum to 290 or violate x > y

Final Answer:
x = 290
y = 0

Bunuel · Answer

The same question with different options: https://gmatclub.com/forum/each-of-1-45 ... 02151.html

lawyeroffduty · Answer

can someone please explain the language of the question, i'm finding it very difficult to understand it and i have spent 5mins into it and still not gotten my answer correct. i'm confused in the language too much.

Bunuel · Answer

• There are 1455 runners total.
• Everyone answers two Yes or No questions.

The problem already tells you  exactly  how many said Yes to question 1:
785 + 380 = 1165. (That’s because we are told that “of those who answered ‘Yes’ to the first question, 785 answered ‘Yes’ to the second question, and 380 answered ‘No’ to the second question,” which exhausts everyone who answered Yes to the first question.)

So the remaining runners who said No to question 1 must be:
1455 - 1165 = 290.

Those 290 runners are split into two parts:
x said Yes to question 2
y said No to question 2

So  x + y = 290 , and the only extra rule is  x > y .

That’s it. Nothing else is going on.

egmat · Answer

Think of this as a  2x2 table . Every runner answers TWO yes/no questions:
- Q1: Do you run  ≥25 miles/week ?
- Q2: Do you have  joint pain ?

What the question tells us:

For runners who said YES to Q1 (run ≥25 miles/week): 
-  785  also said YES to joint pain
-  380  said NO to joint pain
- Total in this group:  785 + 380 = 1,165  runners

For runners who said NO to Q1 (run <25 miles/week): 
-  x  said YES to joint pain
-  y  said NO to joint pain
- We need to find x and y

Step 1: Find how many runners are in the "No to Q1" group 
Total runners =  1,455 
Runners who said Yes to Q1 =  1,165 
Runners who said No to Q1 =  1,455 - 1,165 = 290

Therefore:  x + y =  290

Step 2: Apply the constraint x > y 
We need two values from { 0, 145, 215, 290, 455 } that:
- Add up to  290 
- Have x  greater than  y

Testing:  290 + 0 = 290  ✓ and  290 > 0  ✓

Answer: x = 290, y = 0

When you see "Of those who answered Yes/No to  ..." - it's creating  groups within groups . Draw a quick 2x2 table and fill in what you know. The rest becomes simple arithmetic!

Hope this clears up the confusion!

yudude88 · Answer

Seems my GMAT question bank has a glitch

I saw in this thread the linked question with slightly different answers where 215 is the correct answer for x, wondering with the new app update if this resulted in some bugs

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KarishmaB · Answer

We are given information on those who answered Yes to 1st question --> 785 answered Yes to 2nd and 380 answered No to 2nd. Since the only answers are Yes and No, it means total 785 + 380 =1,165 people answered Yes to the 1st question. This means 1455 - 1165 =290 people answered No to the 1st question. Now all we need is two values for x and y that add up to 290 from the options. x must be greater than y as given. Note that x and y can take many many values (x, y) --> (290, 0) OR (289, 1) OR (288, 2) etc. But only one of these sets is available to us in the options. We have the pair (290, 0) available to us. None of the other options add up to 290. Answer: x = 290, y = 0 Here are some discussions on other official TPA questions: https://youtu.be/-9i-MmJE8Jg https://youtu.be/sOzRtWGu3G0 https://youtu.be/K-weMRndUEA https://youtu.be/WassWEtmcGo https://youtu.be/CuEUshOOlK0 https://youtu.be/bRrlJBzcM3w

Each of 1,455 runners registered to run in an upcoming marathon answer

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GMAT Two-part Analysis (TPA) Questions

Each of 1,455 runners registered to run in an upcoming marathon answer

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