In a certain daycare, are there more boys than girls?
(1) The number of girls is less than 3 times the number of boys.
(2) The number of boys is less than 3/4 the number of girls.
EXPLANATION FOR STATEMENT 1 PLEASE
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Let G = Girls
B=Boys
1) This can be written as G<3B. Using real numbers, let the number of boys equal 10. Hence, G<3(10)= G<30.
To satisfy G<30:
G could be 5 and B is 10, in which case G<B
G could also be 15 and B is 10, in which case G>B.
This statement is thus insufficient.
2)This can be written as B<(3/4)G. As B and G are positive integers (you cannot have a negative or a fraction amount of boys and girls), B<G.
Hope this helps!
B=Boys
1) This can be written as G<3B. Using real numbers, let the number of boys equal 10. Hence, G<3(10)= G<30.
To satisfy G<30:
G could be 5 and B is 10, in which case G<B
G could also be 15 and B is 10, in which case G>B.
This statement is thus insufficient.
2)This can be written as B<(3/4)G. As B and G are positive integers (you cannot have a negative or a fraction amount of boys and girls), B<G.
Hope this helps!
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I've found that some of these inequality problems often introduce a level of ambiguity making them insufficient. Anytime you can refute the established case, or establish a case that contradicts the earlier case, the answer is going to be insufficient.
b = Boys
g = Girls
b > g?
(1) g < 3b
b= 5
3b = 15
The number of girls can be 4 can be less than the number of 5 boys or the number of girls can 10 which is greater than 5 boys but still supports the statement that g < 3b or 10 < 15. Since there can be multiple cases to either support contradict the answer, (1) is insufficient.
(2) b < 3/4g or 4b < 3g. Since 4 times the number of boys is still less than 3 times the number of girls, this establishes that there are more girls than boys and the answer is sufficient, hence B.
b = Boys
g = Girls
b > g?
(1) g < 3b
b= 5
3b = 15
The number of girls can be 4 can be less than the number of 5 boys or the number of girls can 10 which is greater than 5 boys but still supports the statement that g < 3b or 10 < 15. Since there can be multiple cases to either support contradict the answer, (1) is insufficient.
(2) b < 3/4g or 4b < 3g. Since 4 times the number of boys is still less than 3 times the number of girls, this establishes that there are more girls than boys and the answer is sufficient, hence B.
heshamelaziry wrote:In a certain daycare, are there more boys than girls?
(1) The number of girls is less than 3 times the number of boys.
(2) The number of boys is less than 3/4 the number of girls.
EXPLANATION FOR STATEMENT 1 PLEASE
OAB
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From statement 1 :
G < 3(B)
Case 1 : B < G
B= 1, G = 2 -> 2 < 3(1) ..i,e 2 < 3
case 2 : B > G
B = 4, G =1 -> 1 < 3(4) ..i.e 1< 12 ..
hence, we are not able to determine from statement 1...
from statement 2, anyhow boys is less than 3/4 of girls .. it states the answer..
G < 3(B)
Case 1 : B < G
B= 1, G = 2 -> 2 < 3(1) ..i,e 2 < 3
case 2 : B > G
B = 4, G =1 -> 1 < 3(4) ..i.e 1< 12 ..
hence, we are not able to determine from statement 1...
from statement 2, anyhow boys is less than 3/4 of girls .. it states the answer..
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