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.

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Official Answer

x: 215 y: 75

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munir151991 · Answer

I got stuck on this one too so I'll reply:

The key thing is here to read carefully: Of those who answered "Yes" to the first question, 785 answered "Yes" to the second question, and 380 answered "No" to the second question.

Basically this is saying 785 + 380 = 1170 is what people said "Yes" to the first question. Given we know the "Yes" now and 1,455 of total participants, we can figure out the number of "No" for the 1st question which is 290.

Now it's asking us what happened to the 290 so we know that x + y must equals 290 and x>y so we are just looking for two values that add up to 290. Hope that helps

Apt0810 · Answer

785 - Yes to first question, Yes to second question
380- Yes to first question, No to second question

Total yes to first question = 785+380= 1165

1455-1165 = 290

290 = x(No to first, yes to second)+y(No to first, no to second)

x>y so x = 215,y= 75

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toxtimmy · Answer

==

Should be 1165 and not 1170

IshanSaini · Answer

Total people = 1455.
There are 2 questions in consideration :
1. run >25m/week ?
2. joint pain experienced ?

Possible options 2 - Yes or No.
Of those who answered "Yes" to the first question, 785 answered "Yes" to the second question, and 380 answered "No" to the second question.

Question	Yes	No
run >25m/week ?	1165
joint pain experienced ?	785	380

From the above statement we can say that 785 + 380 answered yes to the first question = 1165.
From this we can also infer that 1455 - 1165 = the number of people who answered NO to the first question = 290

II. 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

Question	Yes	No
run >25m/week ?	1165	290
joint pain experienced ?	785+x	380+y

from here we can say that 785+ x + 380+ y = 1165 +x + y = 1455 or simply x + y = 290.
Or x = 290 - y.
We also know that x>y

Simply put the values from the options to check.
i.e put y = 75 we get x = 215.
Which satisfies the conditions.

x	y	Values
	*	75
		145
*		215
		290
		455

Apologies for the formatting of the tables, believe me i tried but unfortunately was unable to reduce the gap.

SMQazi · Answer

I solved it using 2x2 matrix

where
MY - people who said yes to running 25 miles
MN - People who said no to running 25 miles
JY - People who said yes to joint pain
JN - people who said no to joint pain

given x>y, then it's just a matter of plugging values for X and Y that equal 280. Hence, x=215, y=75.

az168 · Answer

Bunuel   Sajjad1994 
This is an OG Question and should be tagged as one.

Bunuel · Answer

Added the tag. Thank you.

Bunuel · Answer

The same question with different options: https://gmatclub.com/forum/each-of-1-45 ... 46071.html

bhavsan · Answer

how did we determine, x>y? Thanks!

Bunuel · Answer

Check the highlighted part:

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 .

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

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