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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]

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New post 07 May 2013, 12:49
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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.
(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]

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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]

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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]

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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]

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New post 07 May 2013, 22:20
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]

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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 there more boys than girls? [#permalink]

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Re: In a certain daycare, are there more boys than girls?   [#permalink] 04 Jan 2018, 23:22
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