How about ambidextrous?

Logic Level 1

A class consists of 100 boys and 100 girls. A survey was conducted on everyone to determine whether there are more left-handed students or more right-handed students. Each student was either asked "Are you left-handed" or "Are you right-handned", and the results were tabulated as:

Boys : 24 out of 30 are left-handed, and 49 out of 70 are right-handed.

Girls : 28 out of 70 are left-handed, and 6 out of 30 are right-handed.

By tabulating the data, we have:

Gender Left-handed Right-handed
Boy 24 30 = 80 % \frac{24}{30} = \mathbf{80\%} 49 70 = 70 % \frac{49}{70} = 70\%
Girl 28 70 = 40 % \frac{28}{70} = \mathbf{40\%} 6 30 = 20 % \frac{6}{30} = 20\%

Is it true that there are more left-handed students than right-handed students in this class?

Note: Assume that no student is included in more than one statistical representation.

Image Credit: Wikimedia Erik Wannee .
True False Insufficient Information

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Pi Han Goh by Pi Han Goh , 30, Malaysia

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6 solutions

Matthias Matthias
Sep 26, 2015

This is Math. Left Handed people equal number of left handed boys plus number of left handed girls, this is found by taking:

Number of Lboys=24+(70-49)=45

Number of Lgirls= 28+(30-6)=52

Total number of Left handed=97

This compared to the number of Right Handed

Number of RBoy= 49+(30-24)=55

Number of Rgirls=6+(70-28)=48

Total number of right handed=103

103>97

4 Helpful 1 Interesting 1 Brilliant 0 Confused
Rich Haskell
Sep 20, 2015

Because of the wording of the question, the correct answer was indeed false. Insufficient information would have also technically been correct, but I think the intention here was for us to identify if there simply were other possibilities. To see further beyond those other possibilities, more information is indeed needed, but for this problem we didn't need the other information.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

well since no student is accounted for more than twice,cant we just ignore d denominators in percentage notation and add up the numerators which would indicate that right handed ones are more.....?

Sanjana Sebastian - 5 years, 8 months ago

Oh I didn't realize that there's ambiguities. How should I rephrase my question? I'm new in posting questions like these. Thanks.

Pi Han Goh - 5 years, 8 months ago
Sunil Setia
Dec 18, 2015

Just use difference

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Dan Heller
Sep 27, 2015

Even though the proportion of left handers is higher than right handers for both boys and for girls, the overall number is higher for right handers overall. I think this is an example of Simpsons paradox.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Victor Locoman
Sep 23, 2015

97LH vs 103RH

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Sidrah Amin
Sep 18, 2015

Left-Handed 24+28 / 100

Right-Handed 49+6 /100

Naturally, Right-Handed students are in a greater percentage

0 Helpful 0 Interesting 0 Brilliant 0 Confused

You have not specified the number of students in the class, or that the sample is representative, or complete. Thus, not enough information.

Roger Williams - 5 years, 8 months ago

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I also thought this question has inadequate information. There are no explanations about "which 30" and "which 70", how these students are classified, or is it possible that a cluster of 30 has nothing to do (does not intersect) with the cluster of 70 of each group.

Henny Lim - 5 years, 8 months ago

I think it should be: Left-Handed 24+28/200 Right-Handed 49+6/200 Because there are 200 students in the class.

Lovely Rose Mendoza - 5 years, 8 months ago

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