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# M15-33

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:57
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55% (hard)

Question Stats:

61% (00:50) correct 39% (00:50) wrong based on 112 sessions

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If 4 small boxes and 5 big boxes weigh the same as 11 small boxes and 2 big boxes, how much does one small box weigh?

(1) One big box weighs 1 kg more than one small box.

(2) The ratio of the weight of one small box to the weight of one big box is $$\frac{3}{7}$$.
[Reveal] Spoiler: OA

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Joined: 02 Sep 2009
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15 Sep 2014, 23:57
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Official Solution:

If 4 small boxes and 5 big boxes weigh the same as 11 small boxes and 2 big boxes, how much does one small box weigh?

Given: $$4s+5b=11s+2b$$, so $$3b=7s$$. Question: $$s=?$$

(1) One big box weighs 1 kg more than one small box. Given: $$b=s+1$$. Substitute $$b$$: $$3(s+1)=7s$$, which gives $$s=\frac{3}{4}$$. Sufficient.

(2) The ratio of the weight of one small box to the weight of one big box is $$\frac{3}{7}$$. Given: $$\frac{s}{b}=\frac{3}{7}$$, or $$3b=7s$$, the same info as in the stem. Not sufficient.

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02 Dec 2014, 11:37
Bunuel wrote:
Official Solution:

Given: $$4s+5b=11s+2b$$, so $$3b=7s$$. Question: $$s=?$$

(1) One big box weighs 1 kg more than one small box. Given: $$b=s+1$$. Substitute $$b$$: $$3(s+1)=7s$$, which gives $$s=\frac{3}{4}$$. Sufficient.

(2) The ratio of the weight of one small box to the weight of one big box is $$\frac{3}{7}$$. Given: $$\frac{s}{b}=\frac{3}{7}$$, or $$3b=7s$$, the same info as in the stem. Not sufficient.

with s=3/4, is that telling us that the small box weighs 3/4 kg of that it is 3/4 the weight of the larger box?
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Joined: 02 Sep 2009
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03 Dec 2014, 03:12
bsmith37 wrote:
Bunuel wrote:
Official Solution:

Given: $$4s+5b=11s+2b$$, so $$3b=7s$$. Question: $$s=?$$

(1) One big box weighs 1 kg more than one small box. Given: $$b=s+1$$. Substitute $$b$$: $$3(s+1)=7s$$, which gives $$s=\frac{3}{4}$$. Sufficient.

(2) The ratio of the weight of one small box to the weight of one big box is $$\frac{3}{7}$$. Given: $$\frac{s}{b}=\frac{3}{7}$$, or $$3b=7s$$, the same info as in the stem. Not sufficient.

with s=3/4, is that telling us that the small box weighs 3/4 kg of that it is 3/4 the weight of the larger box?

$$s=\frac{3}{4}$$ means that the small box weighs 3/4 kg and the big box weighs $$3b=7*\frac{3}{4}$$ --> $$b = \frac{7}{4}$$ kg.
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10 Feb 2017, 06:45
Option A it is. As per the question, 4S+5B=11S+2B. From this , S/B=3/7. We need to find S.

Statement 1 : b=s+1. This is sufficient.
Statement 2 : S/B=3/7. No new info. Hence in-sufficient.

The answer must be option A.
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Re: M15-33   [#permalink] 10 Feb 2017, 06:45
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# M15-33

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