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In a certain daycare, are there more boys than girls?

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In a certain daycare, are there more boys than girls? [#permalink] New post 07 May 2013, 12:49
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67% (01:45) correct 33% (01:19) wrong based on 43 sessions
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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 May 2013, 04:48, edited 1 time in total.
Renamed the topic and edited the question.
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Re: In a certain daycare are? [#permalink] New post 07 May 2013, 13:06
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In a certain daycare, are there more boys than girls?

(1) The number of girls is less than 3 times the number of boys.
G<3B
G=5 B=4, there are more girls
G=1 B=4, there are more boys.
Not sufficient

(2) The number of boys is less than 3/4 the number of girls.
B<\frac{3}{4}G

4B<3G

3B+1B<3G so \frac{1}{3}B<G-B. This means that the difference G-B is greater than 0, because the number of boys cannot be negative
(how could it be?). The \frac{1}{3}B part will be \geq{0} so G-B>0 => more Girls
Sufficient
B
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Re: In a certain daycare are? [#permalink] New post 07 May 2013, 14:06
Wow that is a great explanation thank you so so MUCH!
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Re: In a certain daycare are? [#permalink] New post 07 May 2013, 17:35
n a certain daycare, are there more boys than girls?

(1) The number of girls is less than 3 times the number of boys.

Insufficient for obvious reasons.


(2) The number of boys is less than 3/4 the number of girls.
If number of boys < 3/4 of the number of girls - > Girls > Boys . Sufficient
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Re: In a certain daycare are? [#permalink] New post 07 May 2013, 22:20
Expert's post
madzstar wrote:
:-D 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.


Let the no of Boys and Girls be b and g respectively.

From F.S 1, we know that g<3b = b>g/3. Take g = 3, b = 2 and b<g. However, for g=3 and b=4, b>g. Insufficient.

From F.S 2, we know that b<0.75g. Thus\frac{b}{g}<1, g>b. Sufficient.

B.
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Re: In a certain daycare are? [#permalink] New post 08 May 2013, 01:02
madzstar 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.


(1) The number of girls is less than 3 times the number of boys.
G < 3B (if G = 3, B = 2, more girls, G = 1, B = 2, more boys) - Insufficient

(2) The number of boys is less than 3/4 the number of girls.
B < (3/4) G
4B < 3G
As B,G cannot be negative,
4(2) < 3(3) - Girls are more
4(1) < 3(2) - Girls are more
- Sufficient

Answer: B
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Re: In a certain daycare are?   [#permalink] 08 May 2013, 01:02
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