Portada del sitio > Recursos GMAT > GMAT QUANTITATIVE QUESTION > Data Sufficiency > Probability > If there are 15 children in a gym class and 2 children are to be randomly (...)

If there are 15 children in a gym class and 2 children are to be randomly chosen to perform a demonstration, how many of the children are left-handed?

Difficulty: Sub-600 Level, Probability, Data Sufficiency (DS)

Lunes 25 de julio de 2022, por hurtado claudio

If there are 15 children in a gym class and 2 children are to be randomly chosen to perform a demonstration, how many of the children are left-handed?
1) The probability of no left-handed children being chosen is 3/7
2) The number of left-handed children is less than the number of right handed children in the class


claudio hurtado maturana
mathematical reasoning consultant
TUTORIALS GMAT MATH, GRE MATH, SAT MATH
Private lessons GMAT QUANT GRE QUANT SAT QUANT
Classes group of 4 students GMAT QUANT GRE QUANT SAT QUANT
Distance learning courses GMAT QUANT GRE QUANT SAT QUANT
Coach GMAT QUANT
Coach GRE QUANT
Coach SAT QUANT

Website http://www.gmatchile.cl
Email clasesgmatchile@gmail.com
Skype: clasesgmatchile@gmail.com
Address Avenida Hernando de Aguirre 128 Of 904, Providencia, Santiago Chile.

EXPLANATION:
Statement 1: The probability of no left-handed children being chosen is 3/7
P(no left-handers among those selected) = P(both right-handers among those selected)
So, P(both right-handers among those selected) = 3/7
In other words, P(1st selection is right-handed AND 2nd selection is right-handed) = 3/7
So, P(1st selection is right-handed) x P(2nd selection is right-handed) = 3/7

Let R = # of right-handers in the group

We can write: R/15 x (R - 1)/14 = 3/7
Simplify to get: (R² - R)/210 = 3/7
Cross multiply to get: 7(R² - R) = 3(210)
Divide both sides by 7 to get: R² - R = 3(30)
Or....: R² - R = 90
Then: R² - R - 90 = 0
Factor: (R - 10)(R + 9) = 0
So, EITHER R = 10 OR R = -9
Since R cannot be negative, we know that R = 10 (i.e., there are 10 right-handers)

If 10 children are right-handed, then 5 children are left-handed
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The number of left-handed children is less than the number of right handed children in the class
There are several scenarios that satisfy statement 2. Here are two:
Case a: There are 4 left-handers and 11 right-handers. In this case, the answer to the target question is there are 4 left-handers
Case b: There are 5 left-handers and 10 right-handers. In this case, the answer to the target question is there are 5 left-handers
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

¿Un mensaje, un comentario?

Foro sólo para inscritos

Para participar en este foro, debe registrarte previamente. Gracias por indicar a continuación el identificador personal que se le ha suministrado. Si no está inscrito/a, debe inscribirse.

Conexióninscribirse¿contraseña olvidada?