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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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07 May 2013, 13:49
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35% (medium)

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68% (01:57) correct 32% (01:14) wrong based on 74 sessions

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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, 05:48, 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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07 May 2013, 14:06
1
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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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07 May 2013, 15:06
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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07 May 2013, 18:35
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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07 May 2013, 23:20
:-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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08 May 2013, 02:02
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

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Re: In a certain daycare are?   [#permalink] 08 May 2013, 02:02
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# In a certain daycare, are there more boys than girls?

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