Challenge question 03/21/05

[jigar24]

03/21/05
Question
Some of the people in Town X are left-handed, some are tall, some are both, and some are neither. In Town Y, three times as many people are left-handed as are left-handed in Town X, three times as many people are tall as are tall in Town X, three times as many people are both as are both in Town X, but no one is neither. If the total number of people in Town X is four times greater than the total number of people in Town Y, which of the following could be the number of people in Town X who are neither left-handed nor tall?

(A) 23
(B) 39
(C) 72
(D) 143
(E) 199





OA - D

I think the question is slightly flawed:

"Town X is four times greater than the total number of people in Town Y, which of the following could be the number of people in Town X who are neither left-handed nor tall?"

The above sentence technically means that

Total town X = 5(total of town B)

However, if we use this equation we do not get the right answer.

According to the solution,
Total town X = 4(total of town B)

I think it's either wrong english by question makers or wrong interpretation by solution maker. If we go by the solution maker's equation, the question should be
"The total number of ppl in town X is four times the total number of ppl in town Y.."


Please correct me if I am wrong.

Jigar

[uzzy724]

Personally I think the question is fine. the answer should be D.

X,Y denotes the towns, "T" tall, "L" lefty , "TL" tall and Lefty, and "tl" neither tall nor lefty.

soo we get from the question
YL=3XL
YT=3XT
YTL=3XLT
Ytl = 0
and 4Ytotal = Xtotal

then form simultaneous equ's:

YL + YT - YLT + 0 = Ytotal
and XL + XT - XTL +Xtl = Xtotal

using substitution and subtracting one from the other I got to
(11/3)Ytotal = Xtl

since the only answer choice divisible by 11 is 143....thats the answer!! I think!!!

Hope this helps

[Ben Ku]

03/21/05
Question
Some of the people in Town X are left-handed, some are tall, some are both, and some are neither. In Town Y, three times as many people are left-handed as are left-handed in Town X, three times as many people are tall as are tall in Town X, three times as many people are both as are both in Town X, but no one is neither. If the total number of people in Town X is four times greater than the total number of people in Town Y, which of the following could be the number of people in Town X who are neither left-handed nor tall?

(A) 23
(B) 39
(C) 72
(D) 143
(E) 199





OA - D

I think the question is slightly flawed:

"Town X is four times greater than the total number of people in Town Y, which of the following could be the number of people in Town X who are neither left-handed nor tall?"

The above sentence technically means that

Total town X = 5(total of town B)

However, if we use this equation we do not get the right answer.

According to the solution,
Total town X = 4(total of town B)

I think it's either wrong english by question makers or wrong interpretation by solution maker. If we go by the solution maker's equation, the question should be
"The total number of ppl in town X is four times the total number of ppl in town Y.."


Please correct me if I am wrong.

Jigar

Jigar,

I think you're technically correct about the English in this problem. "four times greater than" means you are increasing an amount by four times. So technically it's x + 4x or 5x, as you pointed out.

However, the intent of the problem is to state the total number of people in town X is "four times as many as" in town Y. I will submit this problem for review to see if it can be more clearly worded.