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# When an object is dropped, the number of feet N that it falls is given

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When an object is dropped, the number of feet N that it falls is given  [#permalink]

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13 Nov 2018, 08:09
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56% (02:13) correct 44% (02:04) wrong based on 313 sessions

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When an object is dropped, the number of feet N that it falls is given by the formula $$N=\frac{1}{2} gt^2$$, where t is the time in seconds since it was dropped and g is 32.2, if it takes 5 seconds for the object to reach the ground, how many feet does it fall during the last 2 seconds?

(A) 64.4
(B) 96.6
(C) 161.0
(D) 257.6
(E) 402.5

Project PS Butler : Question #15

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Re: When an object is dropped, the number of feet N that it falls is given  [#permalink]

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13 Nov 2018, 08:27
1
HKD1710 wrote:
When an object is dropped, the number of feet N that it falls is given by the formula $$N=\frac{1}{2} gt^2$$, where t is the time in seconds since it was dropped and g is 32.2, if it takes 5 seconds for the object to reach the ground, how many feet does it fall during the last 2 seconds?

(A) 64.4
(B) 96.6
(C) 161.0
(D) 257.6
(E) 402.5

Project PS Butler : Question #15

Distance for the last TWO SECONDS $$N=\frac{1}{2} 32.2 *2^2$$= 64.4

IMO:A
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Re: When an object is dropped, the number of feet N that it falls is given  [#permalink]

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13 Nov 2018, 08:36
1
1
A different question, with a physics background.

I feel it should be mentioned explicitly that the formula is for an object dropped from rest but the word "dropped" kind of implies that.

So, the formula given is when the object is dropped from rest. So the distance it covers in the last two seconds will be distance covered from start till 5 secs minus
distance covered from start to 5-2 = 3 secs

This step is essential as the object already has a non zero velocity when it is 2 secs before it reaches the ground.

Let distance covered in last two sec be d.

$$d = 0.5gt^2 - 0.5gt'^2$$
$$d = 0.5g( t^2 - t'^2)$$ where t is 5 sec and t' is 3 sec
Hence,
$$d = 0.5*32.2*(25 - 9)$$
$$d = 16.1*16$$
$$d > 256$$ only slightly greater

Hence Option (D) is correct.

Best,

HKD1710 wrote:
When an object is dropped, the number of feet N that it falls is given by the formula $$N=\frac{1}{2} gt^2$$, where t is the time in seconds since it was dropped and g is 32.2, if it takes 5 seconds for the object to reach the ground, how many feet does it fall during the last 2 seconds?

(A) 64.4
(B) 96.6
(C) 161.0
(D) 257.6
(E) 402.5

Project PS Butler : Question #15

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When an object is dropped, the number of feet N that it falls is given  [#permalink]

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13 Nov 2018, 08:47
1
A different question, with a physics background.

I feel it should be mentioned explicitly that the formula is for an object dropped from rest but the word "dropped" kind of implies that.

So, the formula given is when the object is dropped from rest. So the distance it covers in the last two seconds will be distance covered from start till 5 secs minus
distance covered from start to 5-2 = 3 secs

This step is essential as the object already has a non zero velocity when it is 2 secs before it reaches the ground.

Let distance covered in last two sec be d.

$$d = 0.5gt^2 - 0.5gt'^2$$
$$d = 0.5g( t^2 - t'^2)$$ where t is 5 sec and t' is 3 sec
Hence,
$$d = 0.5*32.2*(25 - 9)$$
$$d = 16.1*16$$
$$d > 256$$ only slightly greater

Hence Option (D) is correct.

Best,

HKD1710 wrote:
When an object is dropped, the number of feet N that it falls is given by the formula $$N=\frac{1}{2} gt^2$$, where t is the time in seconds since it was dropped and g is 32.2, if it takes 5 seconds for the object to reach the ground, how many feet does it fall during the last 2 seconds?

(A) 64.4
(B) 96.6
(C) 161.0
(D) 257.6
(E) 402.5

Project PS Butler : Question #15

how abou this method

$$d = \frac{1}{2} * 32.2*5^2 = 805$$ feet distance for 5 seconds

805/5 = 161 distance for one second

$$161*2 = 322$$ closest to D
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Re: When an object is dropped, the number of feet N that it falls is given  [#permalink]

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13 Nov 2018, 08:51
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1
It doesn't work like that dave13.

When an object is dropped from rest it starts gaining speed and covers more and more distance with increasing time. So your assumption of equal distance covered in equal time intervals is wrong.

But this discussion is taking us far from GMAT PS so let's get back to using the formula given explicitly in the problem

Best,
dave13 wrote:

how abou this method

$$d = \frac{1}{2} * 32.2*5^2 = 805$$ feet distance for 5 seconds

805/5 = 161 distance for one second

$$161*2 = 322$$ closest to D

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Re: When an object is dropped, the number of feet N that it falls is given  [#permalink]

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15 Dec 2018, 11:39
A different question, with a physics background.

I feel it should be mentioned explicitly that the formula is for an object dropped from rest but the word "dropped" kind of implies that.

So, the formula given is when the object is dropped from rest. So the distance it covers in the last two seconds will be distance covered from start till 5 secs minus
distance covered from start to 5-2 = 3 secs

This step is essential as the object already has a non zero velocity when it is 2 secs before it reaches the ground.

Let distance covered in last two sec be d.

$$d = 0.5gt^2 - 0.5gt'^2$$
$$d = 0.5g( t^2 - t'^2)$$ where t is 5 sec and t' is 3 sec
Hence,
$$d = 0.5*32.2*(25 - 9)$$
$$d = 16.1*16$$
$$d > 256$$ only slightly greater

Hence Option (D) is correct.

Best,

HKD1710 wrote:
When an object is dropped, the number of feet N that it falls is given by the formula $$N=\frac{1}{2} gt^2$$, where t is the time in seconds since it was dropped and g is 32.2, if it takes 5 seconds for the object to reach the ground, how many feet does it fall during the last 2 seconds?

(A) 64.4
(B) 96.6
(C) 161.0
(D) 257.6
(E) 402.5

Project PS Butler : Question #15

I believe it requires Physics bg to solve such questions, Do we still receive such type of question in GMAT?
_________________
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Re: When an object is dropped, the number of feet N that it falls is given  [#permalink]

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15 Dec 2018, 23:37
1
Hi Gmatprep550,

The question does not "require" a physics background but knowing a bit of physics helps. This is very much similar to solving RC passages from particular fields. For ex. a science passage will favour someone who has a degree in science, even if any non-science test-taker can read it still get all questions correct. However, a good GMAT question will always have all the necessary info given in the question itself.

All the info needed to solve this questions is given in the question itself. Notice how the question specifically mentions "dropped" and also "last two seconds"... an attentive test-taker would realize that the formula given cannot be applied as it is with t = 2.

Hope this helps.

Best,

Gmatprep550 wrote:

I believe it requires Physics bg to solve such questions, Do we still receive such type of question in GMAT?

_________________
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When an object is dropped, the number of feet N that it falls is given  [#permalink]

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16 Dec 2018, 04:31
Hi Gmatprep550,

The question does not "require" a physics background but knowing a bit of physics helps. This is very much similar to solving RC passages from particular fields. For ex. a science passage will favour someone who has a degree in science, even if any non-science test-taker can read it still get all questions correct. However, a good GMAT question will always have all the necessary info given in the question itself.

All the info needed to solve this questions is given in the question itself. Notice how the question specifically mentions "dropped" and also "last two seconds"... an attentive test-taker would realize that the formula given cannot be applied as it is with t = 2.

Hope this helps.

Best,

Gmatprep550 wrote:

I believe it requires Physics bg to solve such questions, Do we still receive such type of question in GMAT?

Thanks for kind response Gladiator59, but from my past experience of GMAT question one would have simply used T =2 in formula or followed as stated by dave13 that it will travel distance of X in 5 min hence divide it by and multiply by 2 as they have not specified speed will increase or decrease at any point of time.

Please correct me if I am missing something.
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Re: When an object is dropped, the number of feet N that it falls is given  [#permalink]

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03 Feb 2019, 09:34
HKD1710 wrote:
When an object is dropped, the number of feet N that it falls is given by the formula $$N=\frac{1}{2} gt^2$$, where t is the time in seconds since it was dropped and g is 32.2, if it takes 5 seconds for the object to reach the ground, how many feet does it fall during the last 2 seconds?

(A) 64.4
(B) 96.6
(C) 161.0
(D) 257.6
(E) 402.5

Project PS Butler : Question #15

So N feet in last 2 seconds can be found

if we subtract N in last 5 seconds - N in last 3 seconds
N = 1/2 * 32.2 [ 16]

N = 257.6

D
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Re: When an object is dropped, the number of feet N that it falls is given  [#permalink]

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03 Feb 2019, 11:49

Gmatprep550 wrote:
Hi Gmatprep550,

The question does not "require" a physics background but knowing a bit of physics helps. This is very much similar to solving RC passages from particular fields. For ex. a science passage will favour someone who has a degree in science, even if any non-science test-taker can read it still get all questions correct. However, a good GMAT question will always have all the necessary info given in the question itself.

All the info needed to solve this questions is given in the question itself. Notice how the question specifically mentions "dropped" and also "last two seconds"... an attentive test-taker would realize that the formula given cannot be applied as it is with t = 2.

Hope this helps.

Best,

Gmatprep550 wrote:

I believe it requires Physics bg to solve such questions, Do we still receive such type of question in GMAT?

Thanks for kind response Gladiator59, but from my past experience of GMAT question one would have simply used T =2 in formula or followed as stated by dave13 that it will travel distance of X in 5 min hence divide it by and multiply by 2 as they have not specified speed will increase or decrease at any point of time.

Please correct me if I am missing something.

_________________
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Press +1 Kudos if my post helped you a little and help me to ulcock the tests Wish you all success

I'd appreciate learning about the grammatical errors in my posts

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When an object is dropped, the number of feet N that it falls is given  [#permalink]

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03 Feb 2019, 13:40
4
1
Gmatprep550 wrote:
Hi Gmatprep550,

The question does not "require" a physics background but knowing a bit of physics helps. This is very much similar to solving RC passages from particular fields. For ex. a science passage will favour someone who has a degree in science, even if any non-science test-taker can read it still get all questions correct. However, a good GMAT question will always have all the necessary info given in the question itself.

All the info needed to solve this questions is given in the question itself. Notice how the question specifically mentions "dropped" and also "last two seconds"... an attentive test-taker would realize that the formula given cannot be applied as it is with t = 2.

Hope this helps.

Best,
Gmatprep550 wrote:

I believe it requires Physics bg to solve such questions, Do we still receive such type of question in GMAT?

Thanks for kind response Gladiator59, but from my past experience of GMAT question one would have simply used T =2 in formula or followed as stated by dave13 that it will travel distance of X in 5 min hence divide it by and multiply by 2 as they have not specified speed will increase or decrease at any point of time.

Please correct me if I am missing something.
[/quote]
Gmatprep550 wrote:

Hi Gmatprep550 ,
I can understand where you are coming from.

My first thought was the same as yours:
But velocity increases rapidly!

In a way, because we do not import any outside knowledge,
these questions are similar to special symbol questions.

The formula may or may not be accurate . . .
and it is true only for the question at hand.

I shifted gears.
What are they testing? I asked myself.
What are we given? A total time and a partial time.
In what context?
We are given a formula for distance.

time . . . distance . . . and rate.

• In other words, we can start with something that we know
Use $$rt=D$$

If we focus only on $$rt=D$$ (ignore the formula for a moment), then we
can write something such as:

Distance total? t = 5 seconds: $$r * 5 = D_{total}$$
Distance partial? t = 2 seconds: $$r * 2 = D_{partial}$$

$$r$$ is constant. $$D$$ is fixed.
Rate is constant (inane, but the prompt does not say otherwise)
Aha! Time taken is proportional to distance traveled.
Factor the constant $$r$$ out.
$$\frac{D_{partial}}{D_{total}}=\frac{2secs}{5secs} = \frac{2}{5}$$

In 2 seconds, the object will travel $$\frac{2}{5}$$ of the distance that it traveled in 5 seconds.

• Formula
$$N=\frac{1}{2} gt^2$$,
N = number of feet = distance, D

Find $$D_{total}$$, i.e., the distance that the object travels in 5 seconds

Plug 5 into the "special" formula.
I'm changing N to D. It's easier for me.

TOTAL distance
$$D_{total}=\frac{1}{2} gt^2$$
$$D_{total}=\frac{1}{2} * 32.2 * 5^2$$
$$D_{total}= 402.5=$$ total D

Distance in 2 seconds?
-- The distance that the object travels in 2 seconds is $$\frac{2}{5}$$ of 402.5

$$D_{2secs} = \frac{2}{5} * 402.5$$
$$D_{2secs} = 161$$

Hope that helps. Ask again if it does not.

(For the record, physics and I were Not Friends ,
except for quantum mechanics, but I learned the latter in chemistry.)
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Re: When an object is dropped, the number of feet N that it falls is given  [#permalink]

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03 Feb 2019, 22:38
Hi generis,

What a beautiful explanation, I really liked it the way you have explained it.

Still have one question

How I will realize that I need to use different method like this. Just one point I can guess is out of 5 sec how much in 2 sec, Anything apart form it?
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Re: When an object is dropped, the number of feet N that it falls is given  [#permalink]

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04 Feb 2019, 05:31
1
Quote:

Thanks for kind response Gladiator59, but from my past experience of GMAT question one would have simply used T =2 in formula or followed as stated by dave13 that it will travel distance of X in 5 min hence divide it by and multiply by 2 as they have not specified speed will increase or decrease at any point of time.

Please correct me if I am missing something.

Note that it is an official question so definitely fair play. It is like a function question.
You are given the relation between Distance covered and time. All you can use is the given relation. Until and unless you know the relation is linear, you cannot assume that distance covered is same every second. You don't need to know physics for this. Otherwise, you didn't need the given relation. You already know that Distance = Speed*Time.
The relation is given to you because it is specifically defined.
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Re: When an object is dropped, the number of feet N that it falls is given  [#permalink]

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04 Feb 2019, 07:08

I already understood all that part but just wanted to know if I receive such kind of question in future what part from question will advice me to follow such procedure. for the same reason I asked generis

"How I will realize that I need to use different method like this. Just one point I can guess in this question is out of 5 sec how much in 2 sec, Anything apart form it? "

PS- I have added red part in it now as I missed that to specify in previous comments.
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Re: When an object is dropped, the number of feet N that it falls is given  [#permalink]

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04 Feb 2019, 22:45
Gmatprep550 wrote:

I already understood all that part but just wanted to know if I receive such kind of question in future what part from question will advice me to follow such procedure. for the same reason I asked generis

"How I will realize that I need to use different method like this. Just one point I can guess in this question is out of 5 sec how much in 2 sec, Anything apart form it? "

PS- I have added red part in it now as I missed that to specify in previous comments.

The hint is that they have given you the formula to calculate distance so that is what you must use in each case. Also, observe the formula. Distance depends on t^2 so it is not a linear relation. Hence dividing into 5 equal parts is incorrect.
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Re: When an object is dropped, the number of feet N that it falls is given  [#permalink]

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08 Jun 2019, 03:45
dave13 wrote:
A different question, with a physics background.

I feel it should be mentioned explicitly that the formula is for an object dropped from rest but the word "dropped" kind of implies that.

So, the formula given is when the object is dropped from rest. So the distance it covers in the last two seconds will be distance covered from start till 5 secs minus
distance covered from start to 5-2 = 3 secs

This step is essential as the object already has a non zero velocity when it is 2 secs before it reaches the ground.

Let distance covered in last two sec be d.

$$d = 0.5gt^2 - 0.5gt'^2$$
$$d = 0.5g( t^2 - t'^2)$$ where t is 5 sec and t' is 3 sec
Hence,
$$d = 0.5*32.2*(25 - 9)$$
$$d = 16.1*16$$
$$d > 256$$ only slightly greater

Hence Option (D) is correct.

Best,

HKD1710 wrote:
When an object is dropped, the number of feet N that it falls is given by the formula $$N=\frac{1}{2} gt^2$$, where t is the time in seconds since it was dropped and g is 32.2, if it takes 5 seconds for the object to reach the ground, how many feet does it fall during the last 2 seconds?

(A) 64.4
(B) 96.6
(C) 161.0
(D) 257.6
(E) 402.5

Project PS Butler : Question #15

how abou this method

$$d = \frac{1}{2} * 32.2*5^2 = 805$$ feet distance for 5 seconds

805/5 = 161 distance for one second

$$161*2 = 322$$ closest to D

you didn't divide it by 2, otherwise the execution was perfect to get the answer.
the actual value for 5 seconds will be 402.5, and not 805.
1/2*32.2 (25) = 402.5....(1)
subtract
1/2*32.2(9) = 144.9....(2)

(1)-(2) = 402.5-144.9 = 257.6 option D
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Re: When an object is dropped, the number of feet N that it falls is given  [#permalink]

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08 Jun 2019, 03:59
While looking at this question I have impression that it is a trap due to square in the formula and simply calculating N by plugging 2 seconds in the formula would lead to incorrect answer

In my opinion, the best approach is simply to calculate a difference between the total distance covered within 5 seconds (t1) and distance covered during first 3 seconds (t2)

To put it mathematically: [g(t1)^2][/2] - [g(t2)^2][/2] = [g[(t1)^2-(t2)^2][/2] = [g*(25-9)][/2][g*16][/2] = 8g=~257

HKD1710 wrote:
When an object is dropped, the number of feet N that it falls is given by the formula $$N=\frac{1}{2} gt^2$$, where t is the time in seconds since it was dropped and g is 32.2, if it takes 5 seconds for the object to reach the ground, how many feet does it fall during the last 2 seconds?

(A) 64.4
(B) 96.6
(C) 161.0
(D) 257.6
(E) 402.5

Project PS Butler : Question #15

Re: When an object is dropped, the number of feet N that it falls is given   [#permalink] 08 Jun 2019, 03:59
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