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# A conveyor belt moves bottles at a constant speed of 120 centimeters

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Re: A conveyor belt moves bottles at a constant speed of 120 centimeters [#permalink]
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Hi All,

We're told that a conveyor belt moves bottles at a constant speed of 120 centimeters per second (from a loading dock to an unloading dock). We're asked if the distance that the conveyor belt moves a bottle is less than 90 meters? (1 meter = 100 centimeters). This is a YES/NO question.

This prompt is clearly a 'rate' question, but it also is a 'unit conversion' question. You get to choose how you want to 'convert' the units - into either meters or centimeters and you can decide whether you want to use minutes or seconds. I'm going to convert the information into meters and seconds. To start, 120 centimeters = 1.2 meters

Here, I'm going to convert 1.2 minutes into seconds...
(1 2/10)(60) = 60 + 12 = 72 seconds

Thus, we know that the conveyor belt spent LESS than 72 seconds moving each bottle. Thus, the distance that each bottle was moved was LESS than ... (72 seconds)(1.2 meters/second) = 86.4 meters
By extension, the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

With this information, we can determine the distance that each bottled moved at the MINIMUM...
(1 1/10)(60) = 60 + 6 = 66 seconds
(66 seconds)(1.2 meters/second) = MORE than 79.2 meters .
IF... the distance was 80 meters, then the answer to the question is YES.
IF... the distance was 100 meters, then the answer to the question is NO.
Fact 2 is INSUFFICIENT

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Re: A conveyor belt moves bottles at a constant speed of 120 centimeters [#permalink]
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A conveyor belt moves bottles at a constant speed of 120 centimeters per second. If the conveyor belt moves a bottle from a loading dock to an unloading dock, is the distance that the conveyor belt moves the bottle less than 90 meters? (1 meter = 100 centimeters)

Sol. Given S = 120 cm or 1.20 m Is D < 90 m
we know that S * T = D
1) T < 1.2 * 60 i.e t < 72 sec
so D < 1.20*72 i.e D < 86.4
so less than 90 m sufficient

2) T> 1.1 min * 60 = 66
so D > 1.20 * 66 > 79.2
so Not sufficient

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Re: A conveyor belt moves bottles at a constant speed of 120 centimeters [#permalink]
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Speed of conveyor = 120 cm/second

Statement 1: The travel time is less than 1.2 minutes
1 minute = 60 seconds
1.2 minutes = 72 seconds

120 cms in 1 second
120 * 72 = 8640 cms in 72 seconds = 86.40 metres in 72 seconds. Lesser time than 1.2 minutes would mean lesser distance. Hence, Statement 1 is sufficient

Statement 2: More than 1.1 minute. While 1.1 and 1.2 minutes means less than 90 metres, 1.8 would mea more than 90 metres. Hence Insufficient.

Answer is A (Statement 1 is sufficient. Statement 2 is not)
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A conveyor belt moves bottles at a constant speed of 120 centimeters [#permalink]
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here is the OG Explanation
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A conveyor belt moves bottles at a constant speed of 120 centimeters [#permalink]
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A conveyor belt moves bottles at a constant speed of 120 centimeters per second. If the conveyor belt moves a bottle from a loading dock to an unloading dock, is the distance that the conveyor belt moves the bottle less than 90 meters? (1 meter = 100 centimeters)

First thing to watch out some values are in centimetre while some in meter so a uniformity is required hence convert 90 meters to centimetre which becomes 9000 cm . Now the question is asking is the distance<9000 meter?

Statement 1
the work is done in less than 1.2 minute so lets take maximum time as 1.2 minute=72 seconds and the speed is 120 cm/sec so total distance=72*120=8640 which is maximum distance so for any value less than 1.2 distance will be less than 8640 meters which means it is obviously less than 9000 cm, sufficient

Statement 2
the time is more than 1.1 minute but we donot know exactly how much, for instance: say its 1.2 minute then d<9000 cm but if its 10 min then d>9000cm hence insufficient

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Re: A conveyor belt moves bottles at a constant speed of 120 centimeters [#permalink]
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Bunuel wrote:
A conveyor belt moves bottles at a constant speed of 120 centimeters per second. If the conveyor belt moves a bottle from a loading dock to an unloading dock, is the distance that the conveyor belt moves the bottle less than 90 meters? (1 meter = 100 centimeters)

Given rate: 120 centimeters per second.
Since the statements are in terms of MINUTES, calculate the number of minutes required to move the bottle 90 meters:
$$\frac{90-meters}{1} * \frac{100-centimeters}{1-meter} * \frac{1-second}{120-centimeters} * \frac{1-minute}{60 -seconds} = \frac{90}{12*6} = \frac{15}{12} = \frac{5}{4} = 1.25$$ minutes

Implication of the yielded result:
For the bottle to be moved 90 meters, the time = 1.25 minutes.
Thus, for the bottle to be moved LESS THAN 90 METERS, the time must be LESS THAN 1.25 MINUTES.
Question stem, rephrased:
Is t < 1.25?

Statement 1:
Since t < 1.2, the answer to the rephrased question stem is YES.
SUFFICIENT.

Statement 2:
If t = 1.2, the answer to the rephrased question stem is YES.
If t = 1.3, the answer to the rephrased question stem is NO.
INSUFFICIENT.

.
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Re: A conveyor belt moves bottles at a constant speed of 120 centimeters [#permalink]
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Bunuel wrote:
A conveyor belt moves bottles at a constant speed of 120 centimeters per second. If the conveyor belt moves a bottle from a loading dock to an unloading dock, is the distance that the conveyor belt moves the bottle less than 90 meters? (1 meter = 100 centimeters)

Kudos for a correct solution.

Solution:

Question Stem Analysis:

We need to determine whether the distance the conveyor belt moves the bottle is less than 90 meters.

Statement One Alone:

Since it takes the conveyor belt less than 1.2 minutes to move the bottle from the loading dock to the unloading dock, the distance the conveyor belt moves the bottle is less than 120 x (1.2 x 60) = 120 x 72 = 8640 cm, or 86.4 meters. Since the distance is less than 86.4 meters, it’s less than 90 meters. Statement one alone is sufficient.

Statement Two Alone:

Since it takes the conveyor belt more than 1.1 minutes to move the bottle from the loading dock to the unloading dock, the distance the conveyor belt moves the bottle is more than 120 x (1.1 x 60) = 120 x 66 = 7920 cm or 79.2 meters. Since it’s more than 79.2 meters, it could be less than 90 meters (e.g., 80 meters) or more than 90 meters (e.g., 100 meters). Statement two alone is not sufficient.

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Re: A conveyor belt moves bottles at a constant speed of 120 centimeters [#permalink]
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Video solution from Quant Reasoning:
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Re: A conveyor belt moves bottles at a constant speed of 120 centimeters [#permalink]
rate -r= 120 cms/ s
is d<9000cms ?
lets say d=9000 then t=1.25 mins (r=d/t)
we can infer from the question that if d<9000 then t>1.25 mins
so basically Q asks is t >1.25 Y or N
st.1) t<1.2 mins ; definetly t is not > 1.25. so ans is No; d not < 9000cms . SUFFICIENT

st 2) t>1.1 mins ; t can be < 1.25 and also >1.25 . yes and no. INSUFFICIENT.

ans : A
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Re: A conveyor belt moves bottles at a constant speed of 120 centimeters [#permalink]
Given: S = 120 cm/sec = 1.2 m / sec
To find: Is D < 90 m

Statement 1:
T < 1.2 m < 72 sec.
Then D = 1.2 * 72 = 86.9 m , which is maximum possible value for D and is less than 9000 cm. Hence , sufficient.

Statement 2:
T > 1.1 m > 66 sec.
T = 66. D = 66 * 1.2 = 79.2 m
D > 79.20 m
Hence the value of D may be less than 90 m or may be greater than 90 m.
this statement is not sufficient.

A is correct
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A conveyor belt moves bottles at a constant speed of 120 centimeters [#permalink]
Bunuel wrote:
A conveyor belt moves bottles at a constant speed of 120 centimeters per second. If the conveyor belt moves a bottle from a loading dock to an unloading dock, is the distance that the conveyor belt moves the bottle less than 90 meters? (1 meter = 100 centimeters)

Kudos for a correct solution.

Given : Speed ; 120 Cm per sec.
Target question : is the distance that the conveyor belt moves the bottle less than 90 meters? (1 meter = 100 centimeters)

Statement 1(1) It takes the conveyor belt less than 1.2 minutes to move the bottle from the loading dock to the unloading dock
Lets convert the time from Min to seconds . 1.2 min = 1.2*60 = 72 seconds
So we have time = 72 sec . We have Speed = 120 Cms per sec therfore distance = speed* time = 72*120 = 8640 Cm per sec

Target question is the distance that the conveyor belt moves the bottle less than 90 meters? (1 meter = 100 centimeters)
So lets convert the Distance into Meters per sec by dividing
8640/100 = 86.4 Mper sec . Therefore we know the distance covered is less than 90 m yes Sufficient'

Given : Speed ; 120 Cm per sec.
Target question : is the distance that the conveyor belt moves the bottle less than 90 meters? (1 meter = 100 centimeters)

Here time taken is more than 1.1 minutes ....

We already checked for 1.2 minutes which is more than 1.1 min there the distance was 86.4 Mper sec which is less than 90

If time taken was 1.8 minutes would mea more than 90 metres. Hence Insufficient.

Time 1.8*60 = 108 sec Given : Speed ; 120 Cm per sec. = distance = 120*108 =12960 cm per sec
or 12960/100 = 129.6 which is more than 90. Cant ans with certainity therefore not sufficient

Ans A
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Re: A conveyor belt moves bottles at a constant speed of 120 centimeters [#permalink]
120 cm = 1.2m

1.2 minutes = 72 seconds
72 * 1.2 = 86.4
86.4 < 90 seconds. Sufficient

1.1 minutes = 66 seconds
66 * 1.2 = 79.2
Could be more than 90 seconds or less. Insufficient.

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Re: A conveyor belt moves bottles at a constant speed of 120 centimeters [#permalink]
Bunuel wrote:
A conveyor belt moves bottles at a constant speed of 120 centimeters per second. If the conveyor belt moves a bottle from a loading dock to an unloading dock, is the distance that the conveyor belt moves the bottle less than 90 meters? (1 meter = 100 centimeters)

Kudos for a correct solution.

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Re: A conveyor belt moves bottles at a constant speed of 120 centimeters [#permalink]
Bunuel Could you please tag some similar questions (if any)
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Re: A conveyor belt moves bottles at a constant speed of 120 centimeters [#permalink]
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Re: A conveyor belt moves bottles at a constant speed of 120 centimeters [#permalink]
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